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Research ArticleSubway-Induced Vibration Measurement and Evaluation of theStructure on a Construction Site at Curved Section of Metro Line

Weixing Shi1 Ligang Bai1 and Jianping Han 2

1Research Institute of Structural Engineering and Disaster Reduction College of Civil Engineering Tongji UniversityShanghai 200092 China2Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu ProvinceLanzhou University of Technology Lanzhou 730050 China

Correspondence should be addressed to Jianping Han jphanlutcn

Received 12 July 2018 Revised 19 September 2018 Accepted 18 October 2018 Published 2 December 2018

Academic Editor Yuri S Karinski

Copyright copy 2018 Weixing Shi et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Metro property buildings developed rapidly in metropolitan cities over last several years in Chinae subway-induced vibrationwhich may influence the serviceability of the buildings and the comfortability of their occupants over or near the metro lines hasbeen paid more and more attention by professional and academic experts Based on the vibration measurement data ofa construction site over Shenzhen Metro line No 1 this paper utilizes the reasonable and completed data processing method tohandle and analyse the measured data rough the analysis of the data the subway-induced vibration propagation trend of freefield along the perpendicular direction to metro line was investigated It is demonstrated that the subway-induced vibrationpropagation along the perpendicular direction tometro line was damped out on free field as a whole But there may exist ldquoreboundphenomenonrdquo at local zones e responses on pile top and soil adjacent to pile in the vertical shaft along three directions wereinvestigated and their characteristics in time and frequency domains are compared Comparison indicates that the subway-induced vibration on pile top is stronger than soil site near the pile e measurement results on free field reveal that the mostobvious feature of this metro line with curved section is that the vibration along the perpendicular direction is stronger than theother directions But the measurement results in the vertical shaft show that the vertical vibration mainly transferring through thepile and pilersquos vibration in the vertical direction is dominant Finally the dynamic time-history analysis of the building modelunder the measured acceleration was conducted e analytical results show that the vibration response of two evaluationindicators increases with the decrease of damping ratio along all three directions e vertical vibration is more dominant thanother two directions at each floor of building e vibration levels decrease with the increase of story number along verticaldirection and firstly decrease and then increase with the increase of story number increasing along two lateral directions

1 Introduction

With the rapid development of urbanization and un-interrupted increase of population rational plan and ef-ficient utilization of urban land have become imperativee estate exploitation of metro depots and vicinity ad-jacent to metro station which is so-called development ofmetro property buildings gradually becomes the focus ofmajor property developers and would have a desirableprospect e metro property buildings over or near themetro line especially the buildings over the metro linepotentially have the problems for comfortability and

serviceability which were induced by subway e subway-induced vibration propagates to structures above thetunnel through rails and via track beds piles and soilcovered tunnels when metro vehicles pass e subway-induced vibration leads to the vibration and noise of thestructure which are undesirable environmental issues andcan cause occupantsrsquo discomfort and impair the com-mercial value of the residences when the vibration levelexceeded the certain limits For example according to fieldtest of vibration of metro depot of one city in China thevibration level of residential buildings rightly over themetro depot reached 85 dB when subway passes at the

HindawiShock and VibrationVolume 2018 Article ID 5763101 18 pageshttpsdoiorg10115520185763101

speed of 15sim20 km per hour where it caused the complaintfrom the occupants [1]

Environmental vibration induced by subway or other railtraffic is a type of vibration between the deterministic andrandom vibration e determinacy is that marshalling andmodel of train are almost unchanged and the sleeper spacingis also determinede randomness is that tread of wheel andtrack is distributed randomly and underground geotechnicalcondition is complex and the weight of the train is alsochanged It is difficult to accurately determine the impact ofthe environment vibration induced by metro meanwhile theanalysis should be combined with field measurement

Hassan [2] investigated the propagation of ground-borne vibration due to surface trains and subway It wasfound that the vibration propagates mainly through com-pression waves with particle motion in the direction ofpropagation shear waves with particle motion perpendic-ular to the direction of propagation and surface waves withthe elliptical particle motion in a vertical plane Yang andHung [3] reported that many factors cause the vibration ofthe tunnel structure when the subway passed through thetunnel including the load generation mechanism of thetrain-track system the geometry and location of the tunnelstructure and the irregularity of the soil layers e mag-nitude of the vibration from the soil into the building de-pends on the degree of coupling between the soil and thefoundation When the vibration propagates from the soil tothe foundation the energy of the interface is reflected due tothe mismatch or changing of impedances between twomedium which results in a decrease of the vibration level[4 5] When the base plate of building and soil is in fullcontact the coupling loss is determined to be 0 dB forfrequencies lower than the resonance frequency of the plateand the vibration of the base plate is similar to the soil [6]e coupling loss for lightweight buildings and buildingssupported directly on rock is 0 dB and for other base types itchanges among 2sim15 dB due to the diversity of the frequencydomain and base types [7] is explained the reason thatvibration levels inside some buildings are lower compared tomeasurements in open fields

Some field vibration measurements are carried out ondifferent zones For example Chen et al [8] shed new lighton the acceleration characteristics of vibration induced bytrain in the seasonally frozen region of Daqing in China andconveyed that the vertical component is prominent Weiet al [9] measured the subway-induced vibration fora tunnel and a 6-story masonry building over the tunnel inShanghai and reached the similar conclusion e subway-induced vibration in a building on the subway platform wasmeasured to find that vibration signal propagates mainlyalong the pile-column path to upper floors [10] e aboveresearch studies were all focused on subway-induced vi-bration at straight segment of metro line and the verticalcomponent is conspicuous For a curved section of themetroline subway-induced vibration of a free field or structuralbase potentially has different situations and the horizontalcomponent of subway-induced vibration is also necessary tobe noteworthy concerned On the metro-induced field vi-bration measurements several researchers investigated the

vibration transmission in themetro depot and the over-trackbuilding or nearby building [11ndash14] e research on vi-bration of over-track building related the curved section ofmetro line but the vibration is not obvious because the speedof metro is less than 10 km per hour

Also many numerical studies had been done on thesubway-induced vibration Zhou et al [15] made a numer-ical study on an over-track building and shown that vi-bration serviceability of the first floor cannot meet therequirement and some vibration reductionmeasures shouldbe taken e substructuring approach one of 3D FEMmethods was adopted to predict vibrations of the buildingdue to subway traffic e coupling of the building to theground is established by taking into account the soil-structure interaction (SSI) [16ndash18] Lopez-Mendoza et al[19] presented a scoping model that can predict ground-borne railway vibration levels within building typically re-quired to analyse a complex SSI problem and thus providea practical tool to rapidly analyse the vibration response ofnumerous buildings near railway lines Also a coupled finiteelement-boundary element methodology was employed toanalyse the interaction between a building and a railwaytunnel at the surface of a homogeneous half space re-spectively [20] Although these above numerical methods ormodels are relatively accurate the computational cost is toohigh e research studies on combination between nu-merical simulation and in situ measurement were carried onthe problem of subway-induced vibration [21ndash23]

is research mainly includes two parts In the first partfirstly the vibration measurements were carried out ona construction field over a curved segment of ShenzhenMetroline No 1 and measurement points were set on free field andin the vertical shaft Secondly the measured acceleration wasoperated by reasonable data processing technology includingremoval of background vibration which was emphasised andthen the dynamic time-history responses of accelerationvelocity and displacement at themeasurement points in threedirections were obtained Fourier transform technology (FFT)was used to gain the vibration characteristics of time-frequency domain of measurement points Finally fromthe perspectives of time and frequency domain the vibrationprorogation trend of free field in three directions was ana-lysed and the subway-induced vibration between pile top andsoil site near the pile is compared In the second part theanalysis was concentrated on the vibration analysis of thesubstructure Based on the structure model of the building tobe built over the vertical shaft and the measured accelerationsof the pile as the excitation to the base the influence ofdamping ratio on average vibration level of the evaluationpoints at each floor was studied e distribution of theaverage vibration level along the high-wise of the building wasalso reported

2 Field Vibration Measurement

Although there was already a lot of field measurements on thevibration induced by rail transit it is well known that thecomplexity of the soil itself the variability of the regional sitesand the randomness of the rail transit vibration will cause local

2 Shock and Vibration

dierences of subway-induced vibrations Carrying out eldvibration measurement is quite necessary in order to morereliably predict the vibration level of the proposed building

21 Arrangement of Measuring Points e vibration mea-surement was executed and the measuring points werearranged on the free eld and in vertical shaft of a constructionsite over the curved segment of Shenzhen Metro line No 1where a building complex will be built e vibration mea-surement includes two parts e rst part was executed ona free eld that its elevation is plusmn000m and the specicmeasuring point diagram is shown in Figure 1 Four mea-suring points were arranged along the radial direction ofmetro line which is perpendicular to forward direction ofmetro line e distances from the 4 measuring points (W1W2W3 andW4) to the right metro line (the upper line in theFigure 1) are 15m 27m 36m and 45m respectively esecond part was executed in vertical shaft where bearing test ofuplift pile was carried on e elevation of top of uplift pile isminus1200m and the specic measuring point diagram is alsoshown in Figure 1 and the eldmeasurement photo in verticalshaft is shown in Figure 2 Two measuring points (S1 and S2)were arranged on the vertical shafte S1 point was set on thetop of the uplift pile that the diameter is 1000mm and S2point was set on the original soil away from the S1 point 4mFor this curved section of metro line the curve radiuses of leftand right line are 415m and 400m respectively e depthfrom soil surface to tunnelrsquos top is about 17m and the soilparameters of dierent soil layers are shown in Table 1

When subway is been driving o on this curved section ofmetro line No1 the speed is under 40 km per hour For leftline the running direction of metro is from down to up and itis exactly the opposite for right line as shown as Figure 1 erunning metrorsquos type is the A-type which has ability to carry2500 people maximum has 6 compartments with 36-tonweight of each one and has 140m length e exible softsleeper was adopted as the wheel base to reduce the vibrationeect on running metro e diameter of tunnel is 6mthickness of tunnel segment is 30 cm and tunnel depth isabout 138sim1745m among this section of metro line

Each of the measuring points was mounted three ac-celeration sensors labelled with X Y and Z that are theidentiers of directions which are parallel to metro lineperpendicular to metro line and vertical to ground re-spectively e following chapters all obey this naming rule

22 Measuring Instrumentation e instrumentation usedthe SVSA data acquisition and signal processing system inthis measurement is system that was initially developedindependently by our research team in 2006 [24] has manyadvantages such as high sampling frequency long workingduration portable to carry etc It can not only acquire thehigh-precision vibration signal but also fully meet the testrequirements of rail transit environment vibration bypowerful data processing functions

Lance LC0132 T piezoelectric accelerometers (withsensitivity 4967Vg amplitude range plusmn01 g frequencyrange 005ndash500Hz resolution ratio 00000006 g weight

1200 g and using gravity to mount) are used All acceler-ometers were calibrated before the eld measurement edominant energy of targeted eld is generally below 100Hzand focused sensitive frequencies of vibration serviceabilityevaluation are in range 1sim80Hz Based on sampling theory(Nyquist theory) the sample frequency is set as 200Hzwhich can satisfy with the requirementse whole vibrationtest system mainly consisted of accelerometers and theSVSA data acquisition instrument is presented as Figure 3

3 Data Processing

e data or signal acquired by the vibration test systemneeds to be preprocessed to gain the probable time domaininformation of relative indexes such as acceleration velocityand displacement e frequency domain information of

W1

W2W3

W4Free field

S1S2

Vertical shaft

Right line

Left line

Figure 1 Measuring points of construction site

Figure 2 Photo of measuring points in vertical shaft

Shock and Vibration 3

relative indexes is obtained with an appropriate time-frequency analysis method after preprocessing the data[25 26] e classic Fourier transform (FFT) method wasadopted in this data processing

31DataPreprocessing Data preprocessing is the foundationof assessing environmental vibrations correctly e evalua-tion results will be inaccurate if the preprocessing steps are notappropriate or the impact of subjective human factors isintroduced According to the analysis needs of this researchthe preprocessing step is displayed as Figure 4 is wholepreprocessing step is developed in MATLAB software [27]e most commonly used signal processing methods such asdata interception low-pass filtering in the frequency domainsmoothing removal of the trend can be easily achieved withrelative Toolbox of MATLAB software But removing back-ground vibration as a key step has to be self-programmed toachieve it Each signal is intercepted to 40 seconds in thisresearch Section 32 and 33 will introduce the theory andexample of removing background vibration in detail

32 eory of Removing Background Vibration e Earthpulsates as a phenomenon of inherent environmentalvibration is called background vibration which is dom-inant in low frequency e vibration measured on fieldshows a tendency that components of low frequency isenhanced and high frequency is weakened as the distancebetween the measuring point and the vibration source(subway line) increases erefore removal of back-ground vibration from the vibration measured directly isnecessary In this section A signifies the subway-induced

vibration B signifies the background vibration and A + Bsignifies the overall vibration consisting of subway-induced vibration and background vibration e fol-lowing steps depict the process of removing the back-ground vibration

(i) Firstly for the acceleration time-history aA+B(t) andaB(t) acceleration frequency spectrum of AA+B(ω)AB(ω) is gained by Equation (1) respectively N isthe number of measured data ω is the frequency

A(ω) 1113944

Nminus1

t0a(t)eminusiωt2πN

(ω 0 1 2 Nminus 1)

(1)

(ii) Secondly AA+B(ω) and AB(ω) are substituted intoEquation (2) and the phase θω are eliminated to get|AA+B(ω)| and |AB(ω)| respectively

|A(ω)| A(ω)eminusiθω (ω 0 1 2 Nminus 1) (2)

(iii) irdly the difference between |AA+B(ω)| and|AB(ω)| is calculated to get absolute amplitude|AA(ω)| and then AA(ω) is gained through adoptingphase θω by

AA(ω) AA+B(ω)1113868111386811138681113868minus AB(ω)

11138681113868111386811138681113868111386811138681113868

1113868111386811138681113868 11138731113872 eiθω

(ω 0 1 2 Nminus 1)(3)

(iv) Lastly the discrete Fourier inverse transform isexecuted on AA(ω) by Equation (4) e real part isreserved and aA(t) of subway-induced vibration isgained finally

Table 1 Soil parameters of different soil layers

Soil layer no Soil type Water content () ickness (m) Depth (m) Density (kgm3) Shear wave velocity (ms)1 Filled Earth 406 120 120 1930 722 Mucky clay 536 340 460 1720 923 Clay 251 220 680 1940 844 Sandy clay 322 1030 1710 1950 115

Accelerometer

Signal line

PC

SVSA data acquisition instrument

Data line

Figure 3 SVSA vibration test system

4 Shock and Vibration

aA(t) 1N

1113944

Nminus1

t0AA(ω)a(t)e

iωt2πN

(ω 0 1 2 Nminus 1)

(4)

33 Example of Removing Background Vibration e cor-responding MATLAB computer program is compiledbased on the above theory Vertical vibration of measuringpoint W4 that is farthest from the metro line is taken as anexample and the acceleration time-history and Fourieramplitude spectrum of background vibration overall vi-bration and subway-induced vibration are presented asFigure 5

In Figure 5 the up row is time-history of vibration andthe down row is the Fourier amplitude spectrum forbackground overall and subway-induced vibration re-spectively e difference between overall and subway-induced vibration from time domain and frequency do-main is shown in Figures 5(b) and 5(c) us the evaluationresults may exit error if the background vibration cannot beremoved from overall vibrationis conclusion is especiallyimportant for the research focused on the low-frequencycomponent of vibrations or vibration where the measuringpoints are far from the source of vibration

4 Results of Field Vibration Measurement

Firstly the data of field vibration measurement were col-lected by the SVSA vibration test system shown in Figure 3en the field data were preprocessed though the illustrativesteps presented as Figure 4 e time domain information ofthree indexes such as acceleration velocity and displace-ment was gained e accelerations from field measurementare real but velocity and displacement were estimated basedon acceleration by frequency domain integral method Fi-nally the FFT was adopted to calculate the frequency do-main information based on the real acceleration data

More than one subway-induced vibration data werecollected when the field measurement was taken e sta-tistical results of peak value and root-mean-square (rms)value for all time-history signals of each measuring pointwere analysed

41 Propagation of Vibration on Free Field

411 Time Domain Analysis In order to illustrate the vi-bration on the free field the acceleration time-histories andcorresponding PSD of measuring point W1 in Z direction asthe typical example as Figure 6 and the time-histories ofmeasuring point W1 in three directions for metro 1 as thetypical example was shown as Figure 7 e results ofsubway-induced vibration of W1simW4 points on the freefield where the piles are not driven are shown as Figure 8and Table 2 e Figure 8 not only gives the statistical resultsof accelerations but also the statistical results of velocitiesand displacements estimated from the acceleration enumber of effective acceleration data in X Y and Z directionis limited because of the weather problem and disturbancefrom construction machinery etc which are 3 4 and 5 inthree directions respectively Statistical results of meanvalues standard deviations and variation coefficients ofpeak and Rms values of subway-induced vibrations in threedirections are presented in the Table 1 and only statisticalresults of acceleration were given due to length limitations

It can be found from Figure 6 that there are some dif-ferences on the amplitudes of vibrations measured whendifferent metros were passing off but the dominant fre-quencies have certain regularity is states the subway-induced vibration featured with randomness and regularityFigure 7 shows the general order of acceleration magnitudein three directions on the free field and the vibration of Ydirection is obviously dominant

Figure 8 shows propagation trend of average vibrationson free field in three directions e average accelerationvibrations in three directions as a whole are decaying as thedistance of measuring points away from the right line in-creases however there is ldquorebound phenomenonrdquo in localzone the average acceleration vibration of Y direction ismore significant than other two directionse reason is thatthe site lies at the curved segment over the metro line andthe average vibration perpendicular to metro line is pre-dominant which is caused by obvious lateral wheel-railinteraction is is very different from the vibration ofstraight segment of metro line where the vertical vibration ispredominant but the differences of vibrations in three di-rections are gradually disappeared as the distances ofmeasuring points away from the right line increase the

Data interception

Measured acceleration

data

Low-pass filtering in frequency

domain

Smoothing

Removal of trend

Removal of background

vibration

Plotting acceleration time history

Frequency-domain integral

1 time

Frequency-domain integral

2 times

Removal of trend

Removal of trend

Plotting displacement time history

Plotting velocity time

history

Figure 4 Preprocessing step of measured data

Shock and Vibration 5

average vibrations judged by the velocity and displacementestimated based on measured acceleration data also have thesimilar propagation trend and characteristics the maximumof peak velocities is quite small and no more than 200 micromsand the displacements are too small to measure with or-dinary displacement meter for which the maximum of peak

displacements is no more than 5 microm Whatever from theindexesrsquo peak value or Rms value the propagation trend andcharacteristics of vibration on the free eld are same exceptfrom the value of amplitude

Table 2 shows the detailed measured accelerations in-duced by subways and same results can be gained as the

Metro 1

0 20 40

Acc

eler

atio

n (c

ms

2 )

ndash2

ndash1

0

1

2Metro 2

0 20 40ndash2

ndash1

0

1

2Metro 3

Time (s)0 20 40

ndash2

ndash1

0

1

2Metro 4

0 20 40ndash2

ndash1

0

1

2Metro 5

0 20 40ndash2

ndash1

0

1

2

(a)

Metro 1

PSD

(cm

2 s3 )

1000

500

50 1000

0

2000

2500

1500

Metro 2

1000

500

50 1000

0

2000

2500

1500

Metro 3

1000

500

50 1000

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2000

2500

1500

Metro 4

1000

500

50 1000

0

2000

2500

1500

Metro 5

0

1000

500

50 1000

2000

2500

1500

Frequency (Hz)

(b)

Figure 6 e acceleration signals of measuring point W1 in Z direction (a) Time-history curves of acceleration (b) PSD curves ofacceleration

006

004

002

000

ndash002

ndash004

ndash0060 10 20 30 40

Time (s)

4

3

2

1

00 20 40 60 80 100

Frequency (Hz)

a B (t

) (cm

s2 )

A B (ω

) (cm

s)

times10ndash3

(a)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0002

00 20 40 60 80 100

Frequency (Hz)

0004a A

+B (

t) (c

ms

2 )A A

+B (

ω) (c

ms

)

(b)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0004

0002

00 20 40 60 80 100

Frequency (Hz)

a A (t

) (cm

s2 )

A A (ω

) (cm

s)

(c)

Figure 5 Signal comparison of background vibration overall vibration and subway-induced vibration (a) Background vibration (b)Overall vibration (c) Subway-induced vibration

6 Shock and Vibration

Figure 8(a) Besides standard deviations and variation co-efficients of measured acceleration are varied greatly andsome of the values are large is is because of the randomcharacteristic of subway-induced vibration and the ran-domness originates from the different loads of passingmetros at different time and complexity of site soil etc

412 Frequency Domain Analysis In order to investigatethe propagation of vibration on free field from the view offrequency domain and energy the average smoothed powerspectral densities (PSDs) of 4 measuring points in threedirections were calculated and they were plotted in onefigure as presented in Figure 9

It is observed that the subway-induced vibration energyof point W1 in the frequency band which is greater than10Hz is dominant but the vibration energy of point W4 isreversely dominant in the frequency band that is less than10Hz in three directions the vibration energy of Y directionis obviously stronger than other directions and this can alsobe explained by the different features with between curvedand straight segment of metro line It is also observed thatthe dominant frequency of measuring points W1 W2 W3andW4 offset towards to left in X and Y direction as a wholebut there is local ldquorebound phenomenonrdquo such as thedominant frequency of measuring points W3 is on the rightside of W2 e dominant frequencies of four measuringpoints are essentially constant in Z direction

42 Vibration in the Vertical Shaft

421 Time Domain Analysis Statistical acceleration time-history results of subway-induced vibration of S1 and S2points are shown in Figure 10 due to length limitations Alsoonly 5 groupsrsquo effective data were collected in three di-rections because of weather problem and disturbance fromconstruction machinery etc e data of S1 and S2 (6channels S1-x S1-y S1-z and S2-x S2-y S2-z) were mea-sured simultaneously when metro passed

Figure 10 shows the comparison of average vibrationsbetween point S1 represented the pile top and point S2represented the site soil near pile in three directions It isobserved that the acceleration of pile top is larger than sitesoil in three directions no matter whatever from the peakvalues or the Rms values and this signifies that vibration ismore easily propagated along the pile than the soil for the

vibration of pile top the order of amplitude is Z gt Y gt X butas for the site soil the order is Y gt Z gt X which can be seeneasily through the peak values and Rms valuese order Z gtY gt X illustrates that the vertical vibration of top of pile ismore predominant than lateral vibration for propagatingalong the pile at the curved segment of metro line but theorder Y gt Z gt X of site soil is similar to the free field

422 Frequency Domain Analysis To investigate the vi-bration differences in the vertical shaft from the view offrequency and energy the average smoothed power spectraldensities (PSDs) of measuring points S1 and S2 in threedirections were calculated and fitted respectively esmoothed average acceleration PSDs of measuring points S1and S2 were plotted in one figure as shown in Figure 11

Figure 10 gives the comparison between smoothed PSDsof S1 and S2 in three directions It is observed that the subway-induced vibration energy of S1 is not always stronger than S2and reversed in some frequency bands for different directionsAs for the X direction the vibration energy of S1 is strongerthan S2 when the frequency is between 37Hz and 70Hz andthe situation turned over when frequency is less than 37Hzandmore than 70Hz for the Y direction the vibration energyof S1 is stronger than S2 almost in all frequency bands exceptfor 65sim77Hz for the Z direction 48Hz is the frequency ofturning point and the vibration energy of S1 is stronger thanS2 when the frequency is more than 48Hz and vibrationenergy of S1 becomes smaller than S2 when the frequency isless than 48Hz

5 Subway-Induced Vibration of the Building toBe Built

e building to be built is rightly over the zone of verticalshaft and the longitudinal direction of building is parallelwith direction of perpendicular to metro line (Y direction)

51 e Information of the Building and Structure Modele building will be used as the serviced apartment thatincludes three stories underground and ten stories above theground e function of three stories underground will be asparking lots and supermarkets and ten stories above theground will become luxury apartments e building plan ofthe typical story (6th story of the building) is shown asFigure 12

ndash10

ndash5

0

5

ndash5

5

ndash5

5

10

Acc

eler

atio

n (c

ms

2 )

X direction

Time (s)

ndash10

0

10Y direction

0 10 20 30 10 30 10 3040 0 20 40 0 20 40ndash10

0

10Z direction

Figure 7 e time-history of measuring point W1 in three directions for metro 1

Shock and Vibration 7

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

Figure 8 e average value of 3 indexes induced by subways on free eld (a) Acceleration (b) Velocity (c) Displacement

8 Shock and Vibration

Table 2 Mean values standard deviations and variation coeumlcients of peak and Rms values of accelerations induced by metros in threedirections

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Metro 1 2749 0981 0605 0771 0471 0183 0107 0143Metro 2 3525 0986 1720 0453 0739 0164 0354 0083Metro 3 3413 0771 0978 0421 0650 0146 0187 0084

Mean values 3229 0913 1101 0548 0620 0164 0216 0103Standard deviations 0420 0123 0567 0194 0136 0018 0126 0034Variation coeumlcients 0130 0135 0515 0353 0220 0112 0582 0328

Y direction

Metro 1 10798 1518 0800 0363 1504 0221 0133 0079Metro 2 7366 1150 1237 0746 1323 0223 0249 0142Metro 3 3524 0596 0940 0739 0550 0102 0197 0153Metro 4 12754 1420 0557 0395 1744 0230 0132 0072

Mean values 8611 1171 0884 0561 1281 0194 0178 0112Standard deviations 4057 0414 0284 0210 0516 0062 0056 0042Variation coeumlcients 0471 0353 0321 0374 0403 0318 0317 0374

Z direction

Metro 1 1794 0893 0402 0265 0309 0156 0077 0054Metro 2 1610 1140 0463 0538 0226 0160 0097 0100Metro 3 1841 1309 0532 0609 0275 0179 0099 0092Metro 4 1457 0996 0448 0508 0226 0160 0100 0106Metro 5 1666 1118 0530 0508 0226 0166 0102 0099

Mean values 1674 1091 0475 0486 0252 0164 0095 0090Standard deviations 0153 0157 0056 0130 0038 0009 0010 0021Variation coeumlcients 0091 0144 0118 0268 0151 0054 0107 0232

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Figure 9 e smoothed average acceleration PSDs of subway-induced vibration on free eld (a) X direction (b) Y direction (c) Zdirection

Shock and Vibration 9

e structure of underground part is reinforced concreteshear wall and the above part is reinforced concrete framee type of foundation of the building is the pile foundationFor the underground part typical column is circular forwhich diameter is 1000mm typical beam is rectangle ofwhich size is 800mm lowast 400mm the thickness of shear wall isamong 200ndash900mm and the thickness of slab is 600mm forthe part above the ground typical column is rectangle forwhich size is 600mm lowast 600mm typical beam is rectangle for

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

e structure model of the building was built bySAP2000 e mass in the model is considered as combi-nation of 10lowast dead load and 05lowast live load the stiness of allmembers is set as the elastic stiness the element meshingobeys the 18 wavelength principal and the damping isconsidered to follow Rayleigh damping approach About thedamping the 54 part will have a detail discussion In the

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

Figure 10 e average vibration acceleration of measuring points S1 and S2 induced by subway (a) Peak values (b) Rms values

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

Figure 11 e smoothed average acceleration PSD of measured points S1 and S2 induced by subway (a) X direction (b) Y direction (c) Zdirection

10 Shock and Vibration

model the beams and columns are simulated by line elementand the walls and slabs by elastic shell element e linearmodal time-history analysis method was adopted as cal-culation method and the rst 200 order modes were takene analysed SAP200 model is presented as Figure 13

52 e Excitation Was Inputted into the Model In thisresearch since it is assumed that the presence of the buildingdoes not aect the vibration generation source [20] thevibration measured is used as excitation source to thestructure e basement which is the negative third oor forparking cars that elevation is minus1500m is assumed to haveinnite stiness and hereby the SSI eect is ignoredMeanwhile the measured acceleration time-history re-sponse of point S1 is directly as the input of the building tosimulate the vibration induced by passage of metro eexcitation to be inputted into the basement of structure wasrandomly selected frommeasured accelerations time-historyof point S1 in the vertical shaft e detailed time anddomain information of the excitation are presented inFigure 14 e basement of building is pile foundation andsimplied as rigid body connected with the ground in thisanalysis In the SAP2000 model the selected time-history ofaccelerations in three directions was inputted into the base ofbuilding directly

e directions input to structure are in accord with thearrow direction in Figure 11 where X signies the shortdirection and Y signies long direction of the building

As is shown in Figure 14 the amplitude of excitation in Zdirection is maximum followed by Y direction and X di-rection is minimum from the perspective of time domainFrom the perspective of frequency domain the energy ofexcitation in X direction mainly distributes among60sim70Hz Y direction mainly distributes around 90Hz andZ direction mainly distributes among 60sim90Hz which iswider than other two directions

53 e Evaluation Indicators e vibration level is theusual indicator when evaluating all kinds of vibrations Here

two evaluation indicators are adopted which are accelera-tion vibration level La and velocity vibration level Lv

According to International Standard for Human Re-sponse to Whole-body Vibration (ISO2631) [28 29] theacceleration level is dened as follows

La 20 log10arms

a0 (5)

where a0 is the referenced acceleration its value is1 times 10minus6 ms2 based on ISO2631 arms is the root-mean-square value of acceleration with frequency weighting

e velocity level is an indicator that is mainly rec-ommended by Federal Transit Administration (FTA) criteria[30] e velocity level is dened as follows

Lv 20 log10vrms

v0 (6)

where v0 is the referenced acceleration its value is254 times 10minus8 ms vrms is the root-mean-square value of ac-celeration but with no frequency weighting

54 e Inuence of Damping Ratio on the Vibration Levele Rayleigh damping approach was followed in this re-search and the damping matrix [C] of the system can beexpressed as follows

[C] α[M] + β[K] (7)

where [M] and [K] are mass matrix and stiness matrixrespectively e α and β are combination coeumlcients ofmass matrix and stiness matrix respectively and they canbe determined by

α

β

2ξω1 + ω2

ω1ω2

1 (8)

where ω1 and ω2 are two frequencies of the system and ξ asthe key parameter is the damping ratio of the system

e value of ω1 always equals the fundamental frequencyof system and ω2 is generally selected from high frequencies

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

that have signicant eect on dynamic response In factdynamic response of structure is not only depending on thedynamic characteristics of structure but also the charac-teristics of frequency spectrum of vibration load Based onthe report of Idriss [31] on improving of above traditionalmethod ω1 and ω2 are set as 10Hz and 70Hz here

As the most important parameter in the Rayleighdamping approach the damping ratio ξ varies in dierentanalysis but it is in proportional to dynamic response ofstructure For example when the seismic analysis is carriedout it often set as 2 for steel structure but 5 for reinforcedconcrete structure When the issues of slab serviceability arefocused the ξ often takes 2 for reinforced concretestructure and less than 2 for steel structure In here thedamping ratios equating to 1 2 3 4 and 5 re-spectively were taken to study the inuence of dampingratio on the vibration level of the structure e inuence ofdamping ratio on acceleration level La and velocity level Lvin the frequency domain is pictured as Figures 15 and 16respectively

e average one-third octave spectrum of the acceler-ation level of typical story in three directions for dierent

damping ratios is shown in Figure 15 It is obvious that theacceleration level increases as the damping ratio reducesamong almost frequency range in all three directionsHowever the shapes of one-third octave spectra are variousfor dierent directions For example the peak values ap-pear around 5Hz and the acceleration level is almost below30 dB when frequency is beyond 10Hz for the X and Ydirections But for Z direction the peak values appeararound 63 Hz and the acceleration levels in all frequencyrange are above 30 dB ese are because that low-ordermodes of whole structure which mainly represent lateralmodes make remarkable contribution to the lateral vi-bration response while the high-order mode of wholestructure and local modes of slabs contribute to the verticalresponse much

Also the average one-third octave spectra of the velocitylevel of typical story in three directions for dierent dampingratio are shown in Figure 17 It can be found that there arealmost no dierences except the magnitude between averagevelocity level and acceleration level among one-third octavefrequency band erefore the same conclusions can bederived as same as Figure 14

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Figure 15 e average one-third octave spectra of the acceleration level of typical story (6th story) for dierent damping ratio (a) Xdirection (b) Y direction (c) Z direction

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

55 e Distribution of Acceleration Level along the Height-Wise In order to discern the distribution of accelerationindicators along the high-wise one-third octave spectra ofaccelerations of each evaluation point and their averagespectra were gained and pictured as Figure 16 en thedistribution of average maximum frequency acceleration

level Lamax along the high-wise was calculated and depictedas Figure 18 Here only the case of damping ratio equal to2 is showed due to limited space

It is observed from the curves of ldquoaverage valuesrdquo inFigure 16 that the spectral shapes are similar in X and Ydirection and the peak values all appear at 5Hz But for Z

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

Figure 16e one-third octave and average spectra of the accelerations of each evaluation point at typical story (6th story damping ratio 002) (a) X direction (b) Y direction (c) Z direction

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

Figure 17 e average one-third octave spectra of the velocity level of typical story (6th story) for dierent damping ratio (a) X direction(b) Y direction (c) Z direction

14 Shock and Vibration

direction the spectral shape is dierent from another twodirections and the peak value appears at 63Hz Based onthe curves of ldquoevaluation pointsrdquo of Figure 16 the spectralshapes of dierent evaluation points basically have uniformtrend among the whole frequency range in both X and Ydirections especially in X direction But for Z directionthere exists dierent situation that the spectral shapes ofdierent evaluation points are not as uniform as X directione above occurrence can be explained by the fact that thestiness in the lateral direction hardly changes for eachevaluation point but in the same story the stiness in thevertical direction is variable

e comparison of the distribution of maximum fre-quency acceleration level Lamax along the high-wise in threedirections is pictured as Figure 18 e Lamax for X di-rections decreases as the story number increases between 1stand 5th story and then increases zigzagged slightly above 5thstory e distribution of Lamax in Y direction is similar to Xdirection For Z direction the Lamax decreases as the storynumber increases and the values are obviously greater thanX and Y directions at each story is also states the verticalvibration induced by subway is prominent than other di-rections on the slabs of buildings

56 e Distribution of Vibration Level on Velocity Indicatoralong the Height-Wise Also in order to discern the

distribution of velocity indicator along the high-wise one-third octave spectra of velocities of each evaluation point atthe typical story and their average spectra were gained andpictured as Figure 19 en the distribution of averagemaximum frequency velocity level Lvmax along the high-wise was calculated and depicted as Figure 20 Also only thecase of damping ratio equal to 2 is showed due to thelimited space

From Figures 19 and 20 the similar observations andconclusions can be found and gained as same as Figures 16and 18 e only dierence between velocity level and theacceleration level is the dierence in amplitudes is isinevitable to calculate dierent indicators of vibrations

6 Conclusions

is paper mainly includes two parts the rst part hadpresented the results of subway-induced vibration measuredon a construction site at the curved section of ShenzhenMetro line No 1 in China e other part based on theresults of the eld measurement had calculated the dierentvibration indicators and investigated the distribution ofvibration level along the high-wise of the building to be builtover the site of vertical shaft Especially the inuence ofdamping ratio on the vibration level has been studied By theanalysis to the results of eld vibration measurement and thedynamic behaviour of the building model under the

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Figure 18 e distribution of maximum frequency acceleration level along the high-wise (damping ratio 002)

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

(1) In the time domain the subway-induced vibrationpropagation along direction of perpendicular sub-way line damped out on the free eld as a whole butthere is ldquorebound phenomenonrdquo at local zoneis isright for X and Z direction but not for Y direction Infrequency domain the vibration energy has dierent

distribution at dierent frequency sections in threedirections

(2) In vertical shaft the subway-induced vibration ofpile top is stronger than the soil site near the pilefrom view of time domain and this is right for allthree directions In frequency domain the vibrationenergy of two measuring points has its own high andlow at dierent frequency bands

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

Figure 19e 13 octave frequency band velocity level of the typical story (6th story damping ratio 002) (a) X direction (b) Y direction(c) Z direction

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

(3) For this curved section of the metro line the mostobvious feature is that the vibration in Y direction isstronger than the other directions on the free fieldBut for the measuring point of pile top in verticalshaft the vertical vibration level accords with thestraight sections of the metro line and greater thanthe other directions

(4) e vibration responses of two evaluation indicatorsincrease as the damping ratio in three directionsreduces and the vertical vibration spectral shapes areobviously different with the spectral shapes of twolateral directions

(5) For the acceleration level and velocity level thevertical vibration is more dominant than anothertwo directions at each story of the building and themaximum frequency vibration levels decrease as thestory number increases in vertical direction But inthe two lateral directions it decreases first thenincreases and then decreases again as the number ofstories increase in vertical direction

Data Availability

e data used to support the findings of this study areavailable from the corresponding author or bailigang2008126com upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

[1] X He ldquoEnvironmental vibration induced by urban rail transitsystemrdquo Journal of Northern Jiaotong University vol 21 no 2pp 84ndash88 1999

[2] O Hassan Train-Induced Groundborne Vibration and Noisein Buildings Multi Science Publishing Co Ltd BrentwoodUK 2007

[3] Y B Yang and H H Hung ldquoSoil vibrations caused by un-derground moving trainsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 134 no 11 pp 1633ndash1644 2008

[4] A Eitzenberger Train-Induced Vibrations in Tunnels a Re-view Lulea Tekniska Universitet Lulea Sweden 2008

[5] G Kouroussis L V Parys C Conti and O VerlindenldquoPrediction of ground vibrations induced by urban railwaytraffic an analysis of the coupling assumptions between ve-hicle track soil and buildingrdquo International Journal ofAcoustics and Vibration vol 18 no 4 pp 163ndash172 2013

[6] P J Remington L G Kurzweil and D A Towers ldquoLow-frequency noise and vibrations from trainsrdquo in TransportationNoise Reference Book Butterworths London UK 1987

[7] L G Kurzweil ldquoGround-borne noise and vibration fromunderground rail systemsrdquo Journal of Sound and Vibrationvol 66 no 3 pp 363ndash370 1979

[8] S Chen X Ling Z Zhu F Zhang and W Ma ldquoFieldmonitoring on train-induced vibration in the seasonallyfrozen region of daqing in springrdquo in Proceedings of In-ternational Conference on Transportation EngineeringChengdu China July 2009

[9] D Wei W Shi R Han and S Zhang ldquoMeasurement andresearch on subway induced vibration in tunnels and buildingnearby in Shanghairdquo in Proceedings of International Con-ference on Multimedia Technology (ICMT 2011) HangzhouChina July 2011

[10] W M Yan ldquoVertical vibration measurement and analysis ofbuildings on metro train platformsrdquo Journal of Beijing Uni-versity of Technology vol 34 no 8 pp 836ndash841 2008

[11] C Zou YWang J A Moore andM Sanayei ldquoTrain-inducedfield vibration measurements of ground and over-trackbuildingsrdquo Science of the Total Environment vol 575pp 1339ndash1351 2017

[12] C Zou Y Wang P Wang and J Guo ldquoMeasurement ofground and nearby building vibration and noise induced bytrains in a metro depotrdquo Science of the Total Environmentvol 536 pp 761ndash773 2015

[13] Z Cao T Guo and Z Zhang ldquoVibration measurement ina metro depot with trains running in the top storyrdquo Journal ofVibroengineering vol 19 no 1 pp 502ndash519 2017

[14] Z Cao T Guo and Z Zhang ldquoMeasurement and analysisof vibrations in a residential building constructed on anelevated metro depotrdquo Measurement vol 125 no 1pp 394ndash405 2018

[15] H Zhou W He and W Xie ldquoResearch on vibration ser-viceability of over-track buildingsrdquo in Proceedings of SecondInternational Conference on Transportation Information andSafety pp 621ndash626 Wuhan China June 2013

[16] P Lopes P A Costa R Calccedilada and A S Cardoso ldquoIn-fluence of soil stiffness on building vibrations due to railwaytraffic in tunnels numerical studyrdquo Computers and Geo-technics vol 61 pp 277ndash291 2014

[17] P Lopes P A Costa R Calccedilada and A S Cardoso ldquoNu-merical modeling of vibrations induced by railway traffic intunnels from the source to the nearby buildingsrdquo Soil Dy-namics and Earthquake Engineering vol 61-62 pp 269ndash2852014

[18] P Lopes J F Ruiz P A Costa R Calccedilada and A S CardosoldquoVibrations inside buildings due to subway railway trafficExperimental validation of a comprehensive predictionmodelrdquo Science of the Total Environment vol 568pp 1333ndash1343 2016

[19] D Lopez-Mendoza A Romero D P Connolly andP Galvın ldquoScoping assessment of building vibration inducedby railway trafficrdquo Soil Dynamics and Earthquake Engineeringvol 93 pp 147ndash161 2017

[20] P Coulier G Lombaert and G Degrande ldquoe influence ofsourcendashreceiver interaction on the numerical prediction ofrailway induced vibrationsrdquo Journal of Sound and Vibrationvol 333 no 12 pp 2520ndash2538 2014

[21] S Gupta G Degrande and G Lombaert ldquoExperimentalvalidation of a numerical model for subway induced vibra-tionsrdquo Journal of Sound and Vibration vol 321 no 3ndash5pp 786ndash812 2009

[22] D P Connolly G Kouroussis O Laghrouche C L Ho andM C Forde ldquoBenchmarking railway vibrationsndashtrack ve-hicle ground and building effectsrdquo Construction and BuildingMaterials vol 92 pp 64ndash81 2015

Shock and Vibration 17

[23] J P Yang P Z Li and Z Lu ldquoNumerical simulation and in-situ measurement of ground-borne vibration due to subwaysystemrdquo Sustainability vol 10 no 7 p 2439 2018

[24] Y Wang Research on the Acquisition and Procession ofStrutural Vibration Signal School of Civil Engineering TongjiUniversity Shanghai China 2006

[25] V H Nguyen J Mahowald S Maas and J C Golinval ldquoUseof time- and frequency-domain approaches for damage de-tection in civil engineering structuresrdquo Shock and Vibrationvol 2014 Article ID 872492 9 pages 2014

[26] R Shao W Hu and J Li ldquoMulti-fault feature extraction anddiagnosis of gear transmission system using time-frequencyanalysis and wavelet threshold de-noising based on EMDrdquoShock and Vibration vol 20 no 4 pp 763ndash780 2013

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

[28] Pennsylvania State University Mechanical Vibration andShock-Evaluation of Human Exposure to Whole-BodyVibration-Part 1 General Requirements Pennsylvania StateUniversity Harrisburg PA USA 1997

[29] M Vibration ldquoShock-evaluation of human exposure towhole-body vibrationndashpart 2 vibrations in buildings (1 to 80Hz)rdquo International Standard ISO Geneva Switzerland 2003

[30] C E Hanson D A Towers and L D Meister Transit Noiseand Vibration Impact Assessment Federal Transit Adminis-tration Office of Planning and Environment WashingtonDC USA 2006

[31] I Idriss Quad-4 A Computer Program for Evaluating theSeismic Response of Soil Structures by Variable Damping FineteElement Procedures University of California Berkeley CAUSA 1973

18 Shock and Vibration

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speed of 15sim20 km per hour where it caused the complaintfrom the occupants [1]

Environmental vibration induced by subway or other railtraffic is a type of vibration between the deterministic andrandom vibration e determinacy is that marshalling andmodel of train are almost unchanged and the sleeper spacingis also determinede randomness is that tread of wheel andtrack is distributed randomly and underground geotechnicalcondition is complex and the weight of the train is alsochanged It is difficult to accurately determine the impact ofthe environment vibration induced by metro meanwhile theanalysis should be combined with field measurement

Hassan [2] investigated the propagation of ground-borne vibration due to surface trains and subway It wasfound that the vibration propagates mainly through com-pression waves with particle motion in the direction ofpropagation shear waves with particle motion perpendic-ular to the direction of propagation and surface waves withthe elliptical particle motion in a vertical plane Yang andHung [3] reported that many factors cause the vibration ofthe tunnel structure when the subway passed through thetunnel including the load generation mechanism of thetrain-track system the geometry and location of the tunnelstructure and the irregularity of the soil layers e mag-nitude of the vibration from the soil into the building de-pends on the degree of coupling between the soil and thefoundation When the vibration propagates from the soil tothe foundation the energy of the interface is reflected due tothe mismatch or changing of impedances between twomedium which results in a decrease of the vibration level[4 5] When the base plate of building and soil is in fullcontact the coupling loss is determined to be 0 dB forfrequencies lower than the resonance frequency of the plateand the vibration of the base plate is similar to the soil [6]e coupling loss for lightweight buildings and buildingssupported directly on rock is 0 dB and for other base types itchanges among 2sim15 dB due to the diversity of the frequencydomain and base types [7] is explained the reason thatvibration levels inside some buildings are lower compared tomeasurements in open fields

Some field vibration measurements are carried out ondifferent zones For example Chen et al [8] shed new lighton the acceleration characteristics of vibration induced bytrain in the seasonally frozen region of Daqing in China andconveyed that the vertical component is prominent Weiet al [9] measured the subway-induced vibration fora tunnel and a 6-story masonry building over the tunnel inShanghai and reached the similar conclusion e subway-induced vibration in a building on the subway platform wasmeasured to find that vibration signal propagates mainlyalong the pile-column path to upper floors [10] e aboveresearch studies were all focused on subway-induced vi-bration at straight segment of metro line and the verticalcomponent is conspicuous For a curved section of themetroline subway-induced vibration of a free field or structuralbase potentially has different situations and the horizontalcomponent of subway-induced vibration is also necessary tobe noteworthy concerned On the metro-induced field vi-bration measurements several researchers investigated the

vibration transmission in themetro depot and the over-trackbuilding or nearby building [11ndash14] e research on vi-bration of over-track building related the curved section ofmetro line but the vibration is not obvious because the speedof metro is less than 10 km per hour

Also many numerical studies had been done on thesubway-induced vibration Zhou et al [15] made a numer-ical study on an over-track building and shown that vi-bration serviceability of the first floor cannot meet therequirement and some vibration reductionmeasures shouldbe taken e substructuring approach one of 3D FEMmethods was adopted to predict vibrations of the buildingdue to subway traffic e coupling of the building to theground is established by taking into account the soil-structure interaction (SSI) [16ndash18] Lopez-Mendoza et al[19] presented a scoping model that can predict ground-borne railway vibration levels within building typically re-quired to analyse a complex SSI problem and thus providea practical tool to rapidly analyse the vibration response ofnumerous buildings near railway lines Also a coupled finiteelement-boundary element methodology was employed toanalyse the interaction between a building and a railwaytunnel at the surface of a homogeneous half space re-spectively [20] Although these above numerical methods ormodels are relatively accurate the computational cost is toohigh e research studies on combination between nu-merical simulation and in situ measurement were carried onthe problem of subway-induced vibration [21ndash23]

is research mainly includes two parts In the first partfirstly the vibration measurements were carried out ona construction field over a curved segment of ShenzhenMetroline No 1 and measurement points were set on free field andin the vertical shaft Secondly the measured acceleration wasoperated by reasonable data processing technology includingremoval of background vibration which was emphasised andthen the dynamic time-history responses of accelerationvelocity and displacement at themeasurement points in threedirections were obtained Fourier transform technology (FFT)was used to gain the vibration characteristics of time-frequency domain of measurement points Finally fromthe perspectives of time and frequency domain the vibrationprorogation trend of free field in three directions was ana-lysed and the subway-induced vibration between pile top andsoil site near the pile is compared In the second part theanalysis was concentrated on the vibration analysis of thesubstructure Based on the structure model of the building tobe built over the vertical shaft and the measured accelerationsof the pile as the excitation to the base the influence ofdamping ratio on average vibration level of the evaluationpoints at each floor was studied e distribution of theaverage vibration level along the high-wise of the building wasalso reported

2 Field Vibration Measurement

Although there was already a lot of field measurements on thevibration induced by rail transit it is well known that thecomplexity of the soil itself the variability of the regional sitesand the randomness of the rail transit vibration will cause local

2 Shock and Vibration

dierences of subway-induced vibrations Carrying out eldvibration measurement is quite necessary in order to morereliably predict the vibration level of the proposed building

21 Arrangement of Measuring Points e vibration mea-surement was executed and the measuring points werearranged on the free eld and in vertical shaft of a constructionsite over the curved segment of Shenzhen Metro line No 1where a building complex will be built e vibration mea-surement includes two parts e rst part was executed ona free eld that its elevation is plusmn000m and the specicmeasuring point diagram is shown in Figure 1 Four mea-suring points were arranged along the radial direction ofmetro line which is perpendicular to forward direction ofmetro line e distances from the 4 measuring points (W1W2W3 andW4) to the right metro line (the upper line in theFigure 1) are 15m 27m 36m and 45m respectively esecond part was executed in vertical shaft where bearing test ofuplift pile was carried on e elevation of top of uplift pile isminus1200m and the specic measuring point diagram is alsoshown in Figure 1 and the eldmeasurement photo in verticalshaft is shown in Figure 2 Two measuring points (S1 and S2)were arranged on the vertical shafte S1 point was set on thetop of the uplift pile that the diameter is 1000mm and S2point was set on the original soil away from the S1 point 4mFor this curved section of metro line the curve radiuses of leftand right line are 415m and 400m respectively e depthfrom soil surface to tunnelrsquos top is about 17m and the soilparameters of dierent soil layers are shown in Table 1

When subway is been driving o on this curved section ofmetro line No1 the speed is under 40 km per hour For leftline the running direction of metro is from down to up and itis exactly the opposite for right line as shown as Figure 1 erunning metrorsquos type is the A-type which has ability to carry2500 people maximum has 6 compartments with 36-tonweight of each one and has 140m length e exible softsleeper was adopted as the wheel base to reduce the vibrationeect on running metro e diameter of tunnel is 6mthickness of tunnel segment is 30 cm and tunnel depth isabout 138sim1745m among this section of metro line

Each of the measuring points was mounted three ac-celeration sensors labelled with X Y and Z that are theidentiers of directions which are parallel to metro lineperpendicular to metro line and vertical to ground re-spectively e following chapters all obey this naming rule

22 Measuring Instrumentation e instrumentation usedthe SVSA data acquisition and signal processing system inthis measurement is system that was initially developedindependently by our research team in 2006 [24] has manyadvantages such as high sampling frequency long workingduration portable to carry etc It can not only acquire thehigh-precision vibration signal but also fully meet the testrequirements of rail transit environment vibration bypowerful data processing functions

Lance LC0132 T piezoelectric accelerometers (withsensitivity 4967Vg amplitude range plusmn01 g frequencyrange 005ndash500Hz resolution ratio 00000006 g weight

1200 g and using gravity to mount) are used All acceler-ometers were calibrated before the eld measurement edominant energy of targeted eld is generally below 100Hzand focused sensitive frequencies of vibration serviceabilityevaluation are in range 1sim80Hz Based on sampling theory(Nyquist theory) the sample frequency is set as 200Hzwhich can satisfy with the requirementse whole vibrationtest system mainly consisted of accelerometers and theSVSA data acquisition instrument is presented as Figure 3

3 Data Processing

e data or signal acquired by the vibration test systemneeds to be preprocessed to gain the probable time domaininformation of relative indexes such as acceleration velocityand displacement e frequency domain information of

W1

W2W3

W4Free field

S1S2

Vertical shaft

Right line

Left line

Figure 1 Measuring points of construction site

Figure 2 Photo of measuring points in vertical shaft

Shock and Vibration 3

relative indexes is obtained with an appropriate time-frequency analysis method after preprocessing the data[25 26] e classic Fourier transform (FFT) method wasadopted in this data processing

31DataPreprocessing Data preprocessing is the foundationof assessing environmental vibrations correctly e evalua-tion results will be inaccurate if the preprocessing steps are notappropriate or the impact of subjective human factors isintroduced According to the analysis needs of this researchthe preprocessing step is displayed as Figure 4 is wholepreprocessing step is developed in MATLAB software [27]e most commonly used signal processing methods such asdata interception low-pass filtering in the frequency domainsmoothing removal of the trend can be easily achieved withrelative Toolbox of MATLAB software But removing back-ground vibration as a key step has to be self-programmed toachieve it Each signal is intercepted to 40 seconds in thisresearch Section 32 and 33 will introduce the theory andexample of removing background vibration in detail

32 eory of Removing Background Vibration e Earthpulsates as a phenomenon of inherent environmentalvibration is called background vibration which is dom-inant in low frequency e vibration measured on fieldshows a tendency that components of low frequency isenhanced and high frequency is weakened as the distancebetween the measuring point and the vibration source(subway line) increases erefore removal of back-ground vibration from the vibration measured directly isnecessary In this section A signifies the subway-induced

vibration B signifies the background vibration and A + Bsignifies the overall vibration consisting of subway-induced vibration and background vibration e fol-lowing steps depict the process of removing the back-ground vibration

(i) Firstly for the acceleration time-history aA+B(t) andaB(t) acceleration frequency spectrum of AA+B(ω)AB(ω) is gained by Equation (1) respectively N isthe number of measured data ω is the frequency

A(ω) 1113944

Nminus1

t0a(t)eminusiωt2πN

(ω 0 1 2 Nminus 1)

(1)

(ii) Secondly AA+B(ω) and AB(ω) are substituted intoEquation (2) and the phase θω are eliminated to get|AA+B(ω)| and |AB(ω)| respectively

|A(ω)| A(ω)eminusiθω (ω 0 1 2 Nminus 1) (2)

(iii) irdly the difference between |AA+B(ω)| and|AB(ω)| is calculated to get absolute amplitude|AA(ω)| and then AA(ω) is gained through adoptingphase θω by

AA(ω) AA+B(ω)1113868111386811138681113868minus AB(ω)

11138681113868111386811138681113868111386811138681113868

1113868111386811138681113868 11138731113872 eiθω

(ω 0 1 2 Nminus 1)(3)

(iv) Lastly the discrete Fourier inverse transform isexecuted on AA(ω) by Equation (4) e real part isreserved and aA(t) of subway-induced vibration isgained finally

Table 1 Soil parameters of different soil layers

Soil layer no Soil type Water content () ickness (m) Depth (m) Density (kgm3) Shear wave velocity (ms)1 Filled Earth 406 120 120 1930 722 Mucky clay 536 340 460 1720 923 Clay 251 220 680 1940 844 Sandy clay 322 1030 1710 1950 115

Accelerometer

Signal line

PC

SVSA data acquisition instrument

Data line

Figure 3 SVSA vibration test system

4 Shock and Vibration

aA(t) 1N

1113944

Nminus1

t0AA(ω)a(t)e

iωt2πN

(ω 0 1 2 Nminus 1)

(4)

33 Example of Removing Background Vibration e cor-responding MATLAB computer program is compiledbased on the above theory Vertical vibration of measuringpoint W4 that is farthest from the metro line is taken as anexample and the acceleration time-history and Fourieramplitude spectrum of background vibration overall vi-bration and subway-induced vibration are presented asFigure 5

In Figure 5 the up row is time-history of vibration andthe down row is the Fourier amplitude spectrum forbackground overall and subway-induced vibration re-spectively e difference between overall and subway-induced vibration from time domain and frequency do-main is shown in Figures 5(b) and 5(c) us the evaluationresults may exit error if the background vibration cannot beremoved from overall vibrationis conclusion is especiallyimportant for the research focused on the low-frequencycomponent of vibrations or vibration where the measuringpoints are far from the source of vibration

4 Results of Field Vibration Measurement

Firstly the data of field vibration measurement were col-lected by the SVSA vibration test system shown in Figure 3en the field data were preprocessed though the illustrativesteps presented as Figure 4 e time domain information ofthree indexes such as acceleration velocity and displace-ment was gained e accelerations from field measurementare real but velocity and displacement were estimated basedon acceleration by frequency domain integral method Fi-nally the FFT was adopted to calculate the frequency do-main information based on the real acceleration data

More than one subway-induced vibration data werecollected when the field measurement was taken e sta-tistical results of peak value and root-mean-square (rms)value for all time-history signals of each measuring pointwere analysed

41 Propagation of Vibration on Free Field

411 Time Domain Analysis In order to illustrate the vi-bration on the free field the acceleration time-histories andcorresponding PSD of measuring point W1 in Z direction asthe typical example as Figure 6 and the time-histories ofmeasuring point W1 in three directions for metro 1 as thetypical example was shown as Figure 7 e results ofsubway-induced vibration of W1simW4 points on the freefield where the piles are not driven are shown as Figure 8and Table 2 e Figure 8 not only gives the statistical resultsof accelerations but also the statistical results of velocitiesand displacements estimated from the acceleration enumber of effective acceleration data in X Y and Z directionis limited because of the weather problem and disturbancefrom construction machinery etc which are 3 4 and 5 inthree directions respectively Statistical results of meanvalues standard deviations and variation coefficients ofpeak and Rms values of subway-induced vibrations in threedirections are presented in the Table 1 and only statisticalresults of acceleration were given due to length limitations

It can be found from Figure 6 that there are some dif-ferences on the amplitudes of vibrations measured whendifferent metros were passing off but the dominant fre-quencies have certain regularity is states the subway-induced vibration featured with randomness and regularityFigure 7 shows the general order of acceleration magnitudein three directions on the free field and the vibration of Ydirection is obviously dominant

Figure 8 shows propagation trend of average vibrationson free field in three directions e average accelerationvibrations in three directions as a whole are decaying as thedistance of measuring points away from the right line in-creases however there is ldquorebound phenomenonrdquo in localzone the average acceleration vibration of Y direction ismore significant than other two directionse reason is thatthe site lies at the curved segment over the metro line andthe average vibration perpendicular to metro line is pre-dominant which is caused by obvious lateral wheel-railinteraction is is very different from the vibration ofstraight segment of metro line where the vertical vibration ispredominant but the differences of vibrations in three di-rections are gradually disappeared as the distances ofmeasuring points away from the right line increase the

Data interception

Measured acceleration

data

Low-pass filtering in frequency

domain

Smoothing

Removal of trend

Removal of background

vibration

Plotting acceleration time history

Frequency-domain integral

1 time

Frequency-domain integral

2 times

Removal of trend

Removal of trend

Plotting displacement time history

Plotting velocity time

history

Figure 4 Preprocessing step of measured data

Shock and Vibration 5

average vibrations judged by the velocity and displacementestimated based on measured acceleration data also have thesimilar propagation trend and characteristics the maximumof peak velocities is quite small and no more than 200 micromsand the displacements are too small to measure with or-dinary displacement meter for which the maximum of peak

displacements is no more than 5 microm Whatever from theindexesrsquo peak value or Rms value the propagation trend andcharacteristics of vibration on the free eld are same exceptfrom the value of amplitude

Table 2 shows the detailed measured accelerations in-duced by subways and same results can be gained as the

Metro 1

0 20 40

Acc

eler

atio

n (c

ms

2 )

ndash2

ndash1

0

1

2Metro 2

0 20 40ndash2

ndash1

0

1

2Metro 3

Time (s)0 20 40

ndash2

ndash1

0

1

2Metro 4

0 20 40ndash2

ndash1

0

1

2Metro 5

0 20 40ndash2

ndash1

0

1

2

(a)

Metro 1

PSD

(cm

2 s3 )

1000

500

50 1000

0

2000

2500

1500

Metro 2

1000

500

50 1000

0

2000

2500

1500

Metro 3

1000

500

50 1000

0

2000

2500

1500

Metro 4

1000

500

50 1000

0

2000

2500

1500

Metro 5

0

1000

500

50 1000

2000

2500

1500

Frequency (Hz)

(b)

Figure 6 e acceleration signals of measuring point W1 in Z direction (a) Time-history curves of acceleration (b) PSD curves ofacceleration

006

004

002

000

ndash002

ndash004

ndash0060 10 20 30 40

Time (s)

4

3

2

1

00 20 40 60 80 100

Frequency (Hz)

a B (t

) (cm

s2 )

A B (ω

) (cm

s)

times10ndash3

(a)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0002

00 20 40 60 80 100

Frequency (Hz)

0004a A

+B (

t) (c

ms

2 )A A

+B (

ω) (c

ms

)

(b)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0004

0002

00 20 40 60 80 100

Frequency (Hz)

a A (t

) (cm

s2 )

A A (ω

) (cm

s)

(c)

Figure 5 Signal comparison of background vibration overall vibration and subway-induced vibration (a) Background vibration (b)Overall vibration (c) Subway-induced vibration

6 Shock and Vibration

Figure 8(a) Besides standard deviations and variation co-efficients of measured acceleration are varied greatly andsome of the values are large is is because of the randomcharacteristic of subway-induced vibration and the ran-domness originates from the different loads of passingmetros at different time and complexity of site soil etc

412 Frequency Domain Analysis In order to investigatethe propagation of vibration on free field from the view offrequency domain and energy the average smoothed powerspectral densities (PSDs) of 4 measuring points in threedirections were calculated and they were plotted in onefigure as presented in Figure 9

It is observed that the subway-induced vibration energyof point W1 in the frequency band which is greater than10Hz is dominant but the vibration energy of point W4 isreversely dominant in the frequency band that is less than10Hz in three directions the vibration energy of Y directionis obviously stronger than other directions and this can alsobe explained by the different features with between curvedand straight segment of metro line It is also observed thatthe dominant frequency of measuring points W1 W2 W3andW4 offset towards to left in X and Y direction as a wholebut there is local ldquorebound phenomenonrdquo such as thedominant frequency of measuring points W3 is on the rightside of W2 e dominant frequencies of four measuringpoints are essentially constant in Z direction

42 Vibration in the Vertical Shaft

421 Time Domain Analysis Statistical acceleration time-history results of subway-induced vibration of S1 and S2points are shown in Figure 10 due to length limitations Alsoonly 5 groupsrsquo effective data were collected in three di-rections because of weather problem and disturbance fromconstruction machinery etc e data of S1 and S2 (6channels S1-x S1-y S1-z and S2-x S2-y S2-z) were mea-sured simultaneously when metro passed

Figure 10 shows the comparison of average vibrationsbetween point S1 represented the pile top and point S2represented the site soil near pile in three directions It isobserved that the acceleration of pile top is larger than sitesoil in three directions no matter whatever from the peakvalues or the Rms values and this signifies that vibration ismore easily propagated along the pile than the soil for the

vibration of pile top the order of amplitude is Z gt Y gt X butas for the site soil the order is Y gt Z gt X which can be seeneasily through the peak values and Rms valuese order Z gtY gt X illustrates that the vertical vibration of top of pile ismore predominant than lateral vibration for propagatingalong the pile at the curved segment of metro line but theorder Y gt Z gt X of site soil is similar to the free field

422 Frequency Domain Analysis To investigate the vi-bration differences in the vertical shaft from the view offrequency and energy the average smoothed power spectraldensities (PSDs) of measuring points S1 and S2 in threedirections were calculated and fitted respectively esmoothed average acceleration PSDs of measuring points S1and S2 were plotted in one figure as shown in Figure 11

Figure 10 gives the comparison between smoothed PSDsof S1 and S2 in three directions It is observed that the subway-induced vibration energy of S1 is not always stronger than S2and reversed in some frequency bands for different directionsAs for the X direction the vibration energy of S1 is strongerthan S2 when the frequency is between 37Hz and 70Hz andthe situation turned over when frequency is less than 37Hzandmore than 70Hz for the Y direction the vibration energyof S1 is stronger than S2 almost in all frequency bands exceptfor 65sim77Hz for the Z direction 48Hz is the frequency ofturning point and the vibration energy of S1 is stronger thanS2 when the frequency is more than 48Hz and vibrationenergy of S1 becomes smaller than S2 when the frequency isless than 48Hz

5 Subway-Induced Vibration of the Building toBe Built

e building to be built is rightly over the zone of verticalshaft and the longitudinal direction of building is parallelwith direction of perpendicular to metro line (Y direction)

51 e Information of the Building and Structure Modele building will be used as the serviced apartment thatincludes three stories underground and ten stories above theground e function of three stories underground will be asparking lots and supermarkets and ten stories above theground will become luxury apartments e building plan ofthe typical story (6th story of the building) is shown asFigure 12

ndash10

ndash5

0

5

ndash5

5

ndash5

5

10

Acc

eler

atio

n (c

ms

2 )

X direction

Time (s)

ndash10

0

10Y direction

0 10 20 30 10 30 10 3040 0 20 40 0 20 40ndash10

0

10Z direction

Figure 7 e time-history of measuring point W1 in three directions for metro 1

Shock and Vibration 7

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

Figure 8 e average value of 3 indexes induced by subways on free eld (a) Acceleration (b) Velocity (c) Displacement

8 Shock and Vibration

Table 2 Mean values standard deviations and variation coeumlcients of peak and Rms values of accelerations induced by metros in threedirections

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Metro 1 2749 0981 0605 0771 0471 0183 0107 0143Metro 2 3525 0986 1720 0453 0739 0164 0354 0083Metro 3 3413 0771 0978 0421 0650 0146 0187 0084

Mean values 3229 0913 1101 0548 0620 0164 0216 0103Standard deviations 0420 0123 0567 0194 0136 0018 0126 0034Variation coeumlcients 0130 0135 0515 0353 0220 0112 0582 0328

Y direction

Metro 1 10798 1518 0800 0363 1504 0221 0133 0079Metro 2 7366 1150 1237 0746 1323 0223 0249 0142Metro 3 3524 0596 0940 0739 0550 0102 0197 0153Metro 4 12754 1420 0557 0395 1744 0230 0132 0072

Mean values 8611 1171 0884 0561 1281 0194 0178 0112Standard deviations 4057 0414 0284 0210 0516 0062 0056 0042Variation coeumlcients 0471 0353 0321 0374 0403 0318 0317 0374

Z direction

Metro 1 1794 0893 0402 0265 0309 0156 0077 0054Metro 2 1610 1140 0463 0538 0226 0160 0097 0100Metro 3 1841 1309 0532 0609 0275 0179 0099 0092Metro 4 1457 0996 0448 0508 0226 0160 0100 0106Metro 5 1666 1118 0530 0508 0226 0166 0102 0099

Mean values 1674 1091 0475 0486 0252 0164 0095 0090Standard deviations 0153 0157 0056 0130 0038 0009 0010 0021Variation coeumlcients 0091 0144 0118 0268 0151 0054 0107 0232

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Figure 9 e smoothed average acceleration PSDs of subway-induced vibration on free eld (a) X direction (b) Y direction (c) Zdirection

Shock and Vibration 9

e structure of underground part is reinforced concreteshear wall and the above part is reinforced concrete framee type of foundation of the building is the pile foundationFor the underground part typical column is circular forwhich diameter is 1000mm typical beam is rectangle ofwhich size is 800mm lowast 400mm the thickness of shear wall isamong 200ndash900mm and the thickness of slab is 600mm forthe part above the ground typical column is rectangle forwhich size is 600mm lowast 600mm typical beam is rectangle for

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

e structure model of the building was built bySAP2000 e mass in the model is considered as combi-nation of 10lowast dead load and 05lowast live load the stiness of allmembers is set as the elastic stiness the element meshingobeys the 18 wavelength principal and the damping isconsidered to follow Rayleigh damping approach About thedamping the 54 part will have a detail discussion In the

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

Figure 10 e average vibration acceleration of measuring points S1 and S2 induced by subway (a) Peak values (b) Rms values

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

Figure 11 e smoothed average acceleration PSD of measured points S1 and S2 induced by subway (a) X direction (b) Y direction (c) Zdirection

10 Shock and Vibration

model the beams and columns are simulated by line elementand the walls and slabs by elastic shell element e linearmodal time-history analysis method was adopted as cal-culation method and the rst 200 order modes were takene analysed SAP200 model is presented as Figure 13

52 e Excitation Was Inputted into the Model In thisresearch since it is assumed that the presence of the buildingdoes not aect the vibration generation source [20] thevibration measured is used as excitation source to thestructure e basement which is the negative third oor forparking cars that elevation is minus1500m is assumed to haveinnite stiness and hereby the SSI eect is ignoredMeanwhile the measured acceleration time-history re-sponse of point S1 is directly as the input of the building tosimulate the vibration induced by passage of metro eexcitation to be inputted into the basement of structure wasrandomly selected frommeasured accelerations time-historyof point S1 in the vertical shaft e detailed time anddomain information of the excitation are presented inFigure 14 e basement of building is pile foundation andsimplied as rigid body connected with the ground in thisanalysis In the SAP2000 model the selected time-history ofaccelerations in three directions was inputted into the base ofbuilding directly

e directions input to structure are in accord with thearrow direction in Figure 11 where X signies the shortdirection and Y signies long direction of the building

As is shown in Figure 14 the amplitude of excitation in Zdirection is maximum followed by Y direction and X di-rection is minimum from the perspective of time domainFrom the perspective of frequency domain the energy ofexcitation in X direction mainly distributes among60sim70Hz Y direction mainly distributes around 90Hz andZ direction mainly distributes among 60sim90Hz which iswider than other two directions

53 e Evaluation Indicators e vibration level is theusual indicator when evaluating all kinds of vibrations Here

two evaluation indicators are adopted which are accelera-tion vibration level La and velocity vibration level Lv

According to International Standard for Human Re-sponse to Whole-body Vibration (ISO2631) [28 29] theacceleration level is dened as follows

La 20 log10arms

a0 (5)

where a0 is the referenced acceleration its value is1 times 10minus6 ms2 based on ISO2631 arms is the root-mean-square value of acceleration with frequency weighting

e velocity level is an indicator that is mainly rec-ommended by Federal Transit Administration (FTA) criteria[30] e velocity level is dened as follows

Lv 20 log10vrms

v0 (6)

where v0 is the referenced acceleration its value is254 times 10minus8 ms vrms is the root-mean-square value of ac-celeration but with no frequency weighting

54 e Inuence of Damping Ratio on the Vibration Levele Rayleigh damping approach was followed in this re-search and the damping matrix [C] of the system can beexpressed as follows

[C] α[M] + β[K] (7)

where [M] and [K] are mass matrix and stiness matrixrespectively e α and β are combination coeumlcients ofmass matrix and stiness matrix respectively and they canbe determined by

α

β

2ξω1 + ω2

ω1ω2

1 (8)

where ω1 and ω2 are two frequencies of the system and ξ asthe key parameter is the damping ratio of the system

e value of ω1 always equals the fundamental frequencyof system and ω2 is generally selected from high frequencies

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

that have signicant eect on dynamic response In factdynamic response of structure is not only depending on thedynamic characteristics of structure but also the charac-teristics of frequency spectrum of vibration load Based onthe report of Idriss [31] on improving of above traditionalmethod ω1 and ω2 are set as 10Hz and 70Hz here

As the most important parameter in the Rayleighdamping approach the damping ratio ξ varies in dierentanalysis but it is in proportional to dynamic response ofstructure For example when the seismic analysis is carriedout it often set as 2 for steel structure but 5 for reinforcedconcrete structure When the issues of slab serviceability arefocused the ξ often takes 2 for reinforced concretestructure and less than 2 for steel structure In here thedamping ratios equating to 1 2 3 4 and 5 re-spectively were taken to study the inuence of dampingratio on the vibration level of the structure e inuence ofdamping ratio on acceleration level La and velocity level Lvin the frequency domain is pictured as Figures 15 and 16respectively

e average one-third octave spectrum of the acceler-ation level of typical story in three directions for dierent

damping ratios is shown in Figure 15 It is obvious that theacceleration level increases as the damping ratio reducesamong almost frequency range in all three directionsHowever the shapes of one-third octave spectra are variousfor dierent directions For example the peak values ap-pear around 5Hz and the acceleration level is almost below30 dB when frequency is beyond 10Hz for the X and Ydirections But for Z direction the peak values appeararound 63 Hz and the acceleration levels in all frequencyrange are above 30 dB ese are because that low-ordermodes of whole structure which mainly represent lateralmodes make remarkable contribution to the lateral vi-bration response while the high-order mode of wholestructure and local modes of slabs contribute to the verticalresponse much

Also the average one-third octave spectra of the velocitylevel of typical story in three directions for dierent dampingratio are shown in Figure 17 It can be found that there arealmost no dierences except the magnitude between averagevelocity level and acceleration level among one-third octavefrequency band erefore the same conclusions can bederived as same as Figure 14

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Figure 15 e average one-third octave spectra of the acceleration level of typical story (6th story) for dierent damping ratio (a) Xdirection (b) Y direction (c) Z direction

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

55 e Distribution of Acceleration Level along the Height-Wise In order to discern the distribution of accelerationindicators along the high-wise one-third octave spectra ofaccelerations of each evaluation point and their averagespectra were gained and pictured as Figure 16 en thedistribution of average maximum frequency acceleration

level Lamax along the high-wise was calculated and depictedas Figure 18 Here only the case of damping ratio equal to2 is showed due to limited space

It is observed from the curves of ldquoaverage valuesrdquo inFigure 16 that the spectral shapes are similar in X and Ydirection and the peak values all appear at 5Hz But for Z

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

Figure 16e one-third octave and average spectra of the accelerations of each evaluation point at typical story (6th story damping ratio 002) (a) X direction (b) Y direction (c) Z direction

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

Figure 17 e average one-third octave spectra of the velocity level of typical story (6th story) for dierent damping ratio (a) X direction(b) Y direction (c) Z direction

14 Shock and Vibration

direction the spectral shape is dierent from another twodirections and the peak value appears at 63Hz Based onthe curves of ldquoevaluation pointsrdquo of Figure 16 the spectralshapes of dierent evaluation points basically have uniformtrend among the whole frequency range in both X and Ydirections especially in X direction But for Z directionthere exists dierent situation that the spectral shapes ofdierent evaluation points are not as uniform as X directione above occurrence can be explained by the fact that thestiness in the lateral direction hardly changes for eachevaluation point but in the same story the stiness in thevertical direction is variable

e comparison of the distribution of maximum fre-quency acceleration level Lamax along the high-wise in threedirections is pictured as Figure 18 e Lamax for X di-rections decreases as the story number increases between 1stand 5th story and then increases zigzagged slightly above 5thstory e distribution of Lamax in Y direction is similar to Xdirection For Z direction the Lamax decreases as the storynumber increases and the values are obviously greater thanX and Y directions at each story is also states the verticalvibration induced by subway is prominent than other di-rections on the slabs of buildings

56 e Distribution of Vibration Level on Velocity Indicatoralong the Height-Wise Also in order to discern the

distribution of velocity indicator along the high-wise one-third octave spectra of velocities of each evaluation point atthe typical story and their average spectra were gained andpictured as Figure 19 en the distribution of averagemaximum frequency velocity level Lvmax along the high-wise was calculated and depicted as Figure 20 Also only thecase of damping ratio equal to 2 is showed due to thelimited space

From Figures 19 and 20 the similar observations andconclusions can be found and gained as same as Figures 16and 18 e only dierence between velocity level and theacceleration level is the dierence in amplitudes is isinevitable to calculate dierent indicators of vibrations

6 Conclusions

is paper mainly includes two parts the rst part hadpresented the results of subway-induced vibration measuredon a construction site at the curved section of ShenzhenMetro line No 1 in China e other part based on theresults of the eld measurement had calculated the dierentvibration indicators and investigated the distribution ofvibration level along the high-wise of the building to be builtover the site of vertical shaft Especially the inuence ofdamping ratio on the vibration level has been studied By theanalysis to the results of eld vibration measurement and thedynamic behaviour of the building model under the

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Figure 18 e distribution of maximum frequency acceleration level along the high-wise (damping ratio 002)

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

(1) In the time domain the subway-induced vibrationpropagation along direction of perpendicular sub-way line damped out on the free eld as a whole butthere is ldquorebound phenomenonrdquo at local zoneis isright for X and Z direction but not for Y direction Infrequency domain the vibration energy has dierent

distribution at dierent frequency sections in threedirections

(2) In vertical shaft the subway-induced vibration ofpile top is stronger than the soil site near the pilefrom view of time domain and this is right for allthree directions In frequency domain the vibrationenergy of two measuring points has its own high andlow at dierent frequency bands

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

Figure 19e 13 octave frequency band velocity level of the typical story (6th story damping ratio 002) (a) X direction (b) Y direction(c) Z direction

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

(3) For this curved section of the metro line the mostobvious feature is that the vibration in Y direction isstronger than the other directions on the free fieldBut for the measuring point of pile top in verticalshaft the vertical vibration level accords with thestraight sections of the metro line and greater thanthe other directions

(4) e vibration responses of two evaluation indicatorsincrease as the damping ratio in three directionsreduces and the vertical vibration spectral shapes areobviously different with the spectral shapes of twolateral directions

(5) For the acceleration level and velocity level thevertical vibration is more dominant than anothertwo directions at each story of the building and themaximum frequency vibration levels decrease as thestory number increases in vertical direction But inthe two lateral directions it decreases first thenincreases and then decreases again as the number ofstories increase in vertical direction

Data Availability

e data used to support the findings of this study areavailable from the corresponding author or bailigang2008126com upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

[1] X He ldquoEnvironmental vibration induced by urban rail transitsystemrdquo Journal of Northern Jiaotong University vol 21 no 2pp 84ndash88 1999

[2] O Hassan Train-Induced Groundborne Vibration and Noisein Buildings Multi Science Publishing Co Ltd BrentwoodUK 2007

[3] Y B Yang and H H Hung ldquoSoil vibrations caused by un-derground moving trainsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 134 no 11 pp 1633ndash1644 2008

[4] A Eitzenberger Train-Induced Vibrations in Tunnels a Re-view Lulea Tekniska Universitet Lulea Sweden 2008

[5] G Kouroussis L V Parys C Conti and O VerlindenldquoPrediction of ground vibrations induced by urban railwaytraffic an analysis of the coupling assumptions between ve-hicle track soil and buildingrdquo International Journal ofAcoustics and Vibration vol 18 no 4 pp 163ndash172 2013

[6] P J Remington L G Kurzweil and D A Towers ldquoLow-frequency noise and vibrations from trainsrdquo in TransportationNoise Reference Book Butterworths London UK 1987

[7] L G Kurzweil ldquoGround-borne noise and vibration fromunderground rail systemsrdquo Journal of Sound and Vibrationvol 66 no 3 pp 363ndash370 1979

[8] S Chen X Ling Z Zhu F Zhang and W Ma ldquoFieldmonitoring on train-induced vibration in the seasonallyfrozen region of daqing in springrdquo in Proceedings of In-ternational Conference on Transportation EngineeringChengdu China July 2009

[9] D Wei W Shi R Han and S Zhang ldquoMeasurement andresearch on subway induced vibration in tunnels and buildingnearby in Shanghairdquo in Proceedings of International Con-ference on Multimedia Technology (ICMT 2011) HangzhouChina July 2011

[10] W M Yan ldquoVertical vibration measurement and analysis ofbuildings on metro train platformsrdquo Journal of Beijing Uni-versity of Technology vol 34 no 8 pp 836ndash841 2008

[11] C Zou YWang J A Moore andM Sanayei ldquoTrain-inducedfield vibration measurements of ground and over-trackbuildingsrdquo Science of the Total Environment vol 575pp 1339ndash1351 2017

[12] C Zou Y Wang P Wang and J Guo ldquoMeasurement ofground and nearby building vibration and noise induced bytrains in a metro depotrdquo Science of the Total Environmentvol 536 pp 761ndash773 2015

[13] Z Cao T Guo and Z Zhang ldquoVibration measurement ina metro depot with trains running in the top storyrdquo Journal ofVibroengineering vol 19 no 1 pp 502ndash519 2017

[14] Z Cao T Guo and Z Zhang ldquoMeasurement and analysisof vibrations in a residential building constructed on anelevated metro depotrdquo Measurement vol 125 no 1pp 394ndash405 2018

[15] H Zhou W He and W Xie ldquoResearch on vibration ser-viceability of over-track buildingsrdquo in Proceedings of SecondInternational Conference on Transportation Information andSafety pp 621ndash626 Wuhan China June 2013

[16] P Lopes P A Costa R Calccedilada and A S Cardoso ldquoIn-fluence of soil stiffness on building vibrations due to railwaytraffic in tunnels numerical studyrdquo Computers and Geo-technics vol 61 pp 277ndash291 2014

[17] P Lopes P A Costa R Calccedilada and A S Cardoso ldquoNu-merical modeling of vibrations induced by railway traffic intunnels from the source to the nearby buildingsrdquo Soil Dy-namics and Earthquake Engineering vol 61-62 pp 269ndash2852014

[18] P Lopes J F Ruiz P A Costa R Calccedilada and A S CardosoldquoVibrations inside buildings due to subway railway trafficExperimental validation of a comprehensive predictionmodelrdquo Science of the Total Environment vol 568pp 1333ndash1343 2016

[19] D Lopez-Mendoza A Romero D P Connolly andP Galvın ldquoScoping assessment of building vibration inducedby railway trafficrdquo Soil Dynamics and Earthquake Engineeringvol 93 pp 147ndash161 2017

[20] P Coulier G Lombaert and G Degrande ldquoe influence ofsourcendashreceiver interaction on the numerical prediction ofrailway induced vibrationsrdquo Journal of Sound and Vibrationvol 333 no 12 pp 2520ndash2538 2014

[21] S Gupta G Degrande and G Lombaert ldquoExperimentalvalidation of a numerical model for subway induced vibra-tionsrdquo Journal of Sound and Vibration vol 321 no 3ndash5pp 786ndash812 2009

[22] D P Connolly G Kouroussis O Laghrouche C L Ho andM C Forde ldquoBenchmarking railway vibrationsndashtrack ve-hicle ground and building effectsrdquo Construction and BuildingMaterials vol 92 pp 64ndash81 2015

Shock and Vibration 17

[23] J P Yang P Z Li and Z Lu ldquoNumerical simulation and in-situ measurement of ground-borne vibration due to subwaysystemrdquo Sustainability vol 10 no 7 p 2439 2018

[24] Y Wang Research on the Acquisition and Procession ofStrutural Vibration Signal School of Civil Engineering TongjiUniversity Shanghai China 2006

[25] V H Nguyen J Mahowald S Maas and J C Golinval ldquoUseof time- and frequency-domain approaches for damage de-tection in civil engineering structuresrdquo Shock and Vibrationvol 2014 Article ID 872492 9 pages 2014

[26] R Shao W Hu and J Li ldquoMulti-fault feature extraction anddiagnosis of gear transmission system using time-frequencyanalysis and wavelet threshold de-noising based on EMDrdquoShock and Vibration vol 20 no 4 pp 763ndash780 2013

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

[28] Pennsylvania State University Mechanical Vibration andShock-Evaluation of Human Exposure to Whole-BodyVibration-Part 1 General Requirements Pennsylvania StateUniversity Harrisburg PA USA 1997

[29] M Vibration ldquoShock-evaluation of human exposure towhole-body vibrationndashpart 2 vibrations in buildings (1 to 80Hz)rdquo International Standard ISO Geneva Switzerland 2003

[30] C E Hanson D A Towers and L D Meister Transit Noiseand Vibration Impact Assessment Federal Transit Adminis-tration Office of Planning and Environment WashingtonDC USA 2006

[31] I Idriss Quad-4 A Computer Program for Evaluating theSeismic Response of Soil Structures by Variable Damping FineteElement Procedures University of California Berkeley CAUSA 1973

18 Shock and Vibration

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Shock and Vibration

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dierences of subway-induced vibrations Carrying out eldvibration measurement is quite necessary in order to morereliably predict the vibration level of the proposed building

21 Arrangement of Measuring Points e vibration mea-surement was executed and the measuring points werearranged on the free eld and in vertical shaft of a constructionsite over the curved segment of Shenzhen Metro line No 1where a building complex will be built e vibration mea-surement includes two parts e rst part was executed ona free eld that its elevation is plusmn000m and the specicmeasuring point diagram is shown in Figure 1 Four mea-suring points were arranged along the radial direction ofmetro line which is perpendicular to forward direction ofmetro line e distances from the 4 measuring points (W1W2W3 andW4) to the right metro line (the upper line in theFigure 1) are 15m 27m 36m and 45m respectively esecond part was executed in vertical shaft where bearing test ofuplift pile was carried on e elevation of top of uplift pile isminus1200m and the specic measuring point diagram is alsoshown in Figure 1 and the eldmeasurement photo in verticalshaft is shown in Figure 2 Two measuring points (S1 and S2)were arranged on the vertical shafte S1 point was set on thetop of the uplift pile that the diameter is 1000mm and S2point was set on the original soil away from the S1 point 4mFor this curved section of metro line the curve radiuses of leftand right line are 415m and 400m respectively e depthfrom soil surface to tunnelrsquos top is about 17m and the soilparameters of dierent soil layers are shown in Table 1

When subway is been driving o on this curved section ofmetro line No1 the speed is under 40 km per hour For leftline the running direction of metro is from down to up and itis exactly the opposite for right line as shown as Figure 1 erunning metrorsquos type is the A-type which has ability to carry2500 people maximum has 6 compartments with 36-tonweight of each one and has 140m length e exible softsleeper was adopted as the wheel base to reduce the vibrationeect on running metro e diameter of tunnel is 6mthickness of tunnel segment is 30 cm and tunnel depth isabout 138sim1745m among this section of metro line

Each of the measuring points was mounted three ac-celeration sensors labelled with X Y and Z that are theidentiers of directions which are parallel to metro lineperpendicular to metro line and vertical to ground re-spectively e following chapters all obey this naming rule

22 Measuring Instrumentation e instrumentation usedthe SVSA data acquisition and signal processing system inthis measurement is system that was initially developedindependently by our research team in 2006 [24] has manyadvantages such as high sampling frequency long workingduration portable to carry etc It can not only acquire thehigh-precision vibration signal but also fully meet the testrequirements of rail transit environment vibration bypowerful data processing functions

Lance LC0132 T piezoelectric accelerometers (withsensitivity 4967Vg amplitude range plusmn01 g frequencyrange 005ndash500Hz resolution ratio 00000006 g weight

1200 g and using gravity to mount) are used All acceler-ometers were calibrated before the eld measurement edominant energy of targeted eld is generally below 100Hzand focused sensitive frequencies of vibration serviceabilityevaluation are in range 1sim80Hz Based on sampling theory(Nyquist theory) the sample frequency is set as 200Hzwhich can satisfy with the requirementse whole vibrationtest system mainly consisted of accelerometers and theSVSA data acquisition instrument is presented as Figure 3

3 Data Processing

e data or signal acquired by the vibration test systemneeds to be preprocessed to gain the probable time domaininformation of relative indexes such as acceleration velocityand displacement e frequency domain information of

W1

W2W3

W4Free field

S1S2

Vertical shaft

Right line

Left line

Figure 1 Measuring points of construction site

Figure 2 Photo of measuring points in vertical shaft

Shock and Vibration 3

relative indexes is obtained with an appropriate time-frequency analysis method after preprocessing the data[25 26] e classic Fourier transform (FFT) method wasadopted in this data processing

31DataPreprocessing Data preprocessing is the foundationof assessing environmental vibrations correctly e evalua-tion results will be inaccurate if the preprocessing steps are notappropriate or the impact of subjective human factors isintroduced According to the analysis needs of this researchthe preprocessing step is displayed as Figure 4 is wholepreprocessing step is developed in MATLAB software [27]e most commonly used signal processing methods such asdata interception low-pass filtering in the frequency domainsmoothing removal of the trend can be easily achieved withrelative Toolbox of MATLAB software But removing back-ground vibration as a key step has to be self-programmed toachieve it Each signal is intercepted to 40 seconds in thisresearch Section 32 and 33 will introduce the theory andexample of removing background vibration in detail

32 eory of Removing Background Vibration e Earthpulsates as a phenomenon of inherent environmentalvibration is called background vibration which is dom-inant in low frequency e vibration measured on fieldshows a tendency that components of low frequency isenhanced and high frequency is weakened as the distancebetween the measuring point and the vibration source(subway line) increases erefore removal of back-ground vibration from the vibration measured directly isnecessary In this section A signifies the subway-induced

vibration B signifies the background vibration and A + Bsignifies the overall vibration consisting of subway-induced vibration and background vibration e fol-lowing steps depict the process of removing the back-ground vibration

(i) Firstly for the acceleration time-history aA+B(t) andaB(t) acceleration frequency spectrum of AA+B(ω)AB(ω) is gained by Equation (1) respectively N isthe number of measured data ω is the frequency

A(ω) 1113944

Nminus1

t0a(t)eminusiωt2πN

(ω 0 1 2 Nminus 1)

(1)

(ii) Secondly AA+B(ω) and AB(ω) are substituted intoEquation (2) and the phase θω are eliminated to get|AA+B(ω)| and |AB(ω)| respectively

|A(ω)| A(ω)eminusiθω (ω 0 1 2 Nminus 1) (2)

(iii) irdly the difference between |AA+B(ω)| and|AB(ω)| is calculated to get absolute amplitude|AA(ω)| and then AA(ω) is gained through adoptingphase θω by

AA(ω) AA+B(ω)1113868111386811138681113868minus AB(ω)

11138681113868111386811138681113868111386811138681113868

1113868111386811138681113868 11138731113872 eiθω

(ω 0 1 2 Nminus 1)(3)

(iv) Lastly the discrete Fourier inverse transform isexecuted on AA(ω) by Equation (4) e real part isreserved and aA(t) of subway-induced vibration isgained finally

Table 1 Soil parameters of different soil layers

Soil layer no Soil type Water content () ickness (m) Depth (m) Density (kgm3) Shear wave velocity (ms)1 Filled Earth 406 120 120 1930 722 Mucky clay 536 340 460 1720 923 Clay 251 220 680 1940 844 Sandy clay 322 1030 1710 1950 115

Accelerometer

Signal line

PC

SVSA data acquisition instrument

Data line

Figure 3 SVSA vibration test system

4 Shock and Vibration

aA(t) 1N

1113944

Nminus1

t0AA(ω)a(t)e

iωt2πN

(ω 0 1 2 Nminus 1)

(4)

33 Example of Removing Background Vibration e cor-responding MATLAB computer program is compiledbased on the above theory Vertical vibration of measuringpoint W4 that is farthest from the metro line is taken as anexample and the acceleration time-history and Fourieramplitude spectrum of background vibration overall vi-bration and subway-induced vibration are presented asFigure 5

In Figure 5 the up row is time-history of vibration andthe down row is the Fourier amplitude spectrum forbackground overall and subway-induced vibration re-spectively e difference between overall and subway-induced vibration from time domain and frequency do-main is shown in Figures 5(b) and 5(c) us the evaluationresults may exit error if the background vibration cannot beremoved from overall vibrationis conclusion is especiallyimportant for the research focused on the low-frequencycomponent of vibrations or vibration where the measuringpoints are far from the source of vibration

4 Results of Field Vibration Measurement

Firstly the data of field vibration measurement were col-lected by the SVSA vibration test system shown in Figure 3en the field data were preprocessed though the illustrativesteps presented as Figure 4 e time domain information ofthree indexes such as acceleration velocity and displace-ment was gained e accelerations from field measurementare real but velocity and displacement were estimated basedon acceleration by frequency domain integral method Fi-nally the FFT was adopted to calculate the frequency do-main information based on the real acceleration data

More than one subway-induced vibration data werecollected when the field measurement was taken e sta-tistical results of peak value and root-mean-square (rms)value for all time-history signals of each measuring pointwere analysed

41 Propagation of Vibration on Free Field

411 Time Domain Analysis In order to illustrate the vi-bration on the free field the acceleration time-histories andcorresponding PSD of measuring point W1 in Z direction asthe typical example as Figure 6 and the time-histories ofmeasuring point W1 in three directions for metro 1 as thetypical example was shown as Figure 7 e results ofsubway-induced vibration of W1simW4 points on the freefield where the piles are not driven are shown as Figure 8and Table 2 e Figure 8 not only gives the statistical resultsof accelerations but also the statistical results of velocitiesand displacements estimated from the acceleration enumber of effective acceleration data in X Y and Z directionis limited because of the weather problem and disturbancefrom construction machinery etc which are 3 4 and 5 inthree directions respectively Statistical results of meanvalues standard deviations and variation coefficients ofpeak and Rms values of subway-induced vibrations in threedirections are presented in the Table 1 and only statisticalresults of acceleration were given due to length limitations

It can be found from Figure 6 that there are some dif-ferences on the amplitudes of vibrations measured whendifferent metros were passing off but the dominant fre-quencies have certain regularity is states the subway-induced vibration featured with randomness and regularityFigure 7 shows the general order of acceleration magnitudein three directions on the free field and the vibration of Ydirection is obviously dominant

Figure 8 shows propagation trend of average vibrationson free field in three directions e average accelerationvibrations in three directions as a whole are decaying as thedistance of measuring points away from the right line in-creases however there is ldquorebound phenomenonrdquo in localzone the average acceleration vibration of Y direction ismore significant than other two directionse reason is thatthe site lies at the curved segment over the metro line andthe average vibration perpendicular to metro line is pre-dominant which is caused by obvious lateral wheel-railinteraction is is very different from the vibration ofstraight segment of metro line where the vertical vibration ispredominant but the differences of vibrations in three di-rections are gradually disappeared as the distances ofmeasuring points away from the right line increase the

Data interception

Measured acceleration

data

Low-pass filtering in frequency

domain

Smoothing

Removal of trend

Removal of background

vibration

Plotting acceleration time history

Frequency-domain integral

1 time

Frequency-domain integral

2 times

Removal of trend

Removal of trend

Plotting displacement time history

Plotting velocity time

history

Figure 4 Preprocessing step of measured data

Shock and Vibration 5

average vibrations judged by the velocity and displacementestimated based on measured acceleration data also have thesimilar propagation trend and characteristics the maximumof peak velocities is quite small and no more than 200 micromsand the displacements are too small to measure with or-dinary displacement meter for which the maximum of peak

displacements is no more than 5 microm Whatever from theindexesrsquo peak value or Rms value the propagation trend andcharacteristics of vibration on the free eld are same exceptfrom the value of amplitude

Table 2 shows the detailed measured accelerations in-duced by subways and same results can be gained as the

Metro 1

0 20 40

Acc

eler

atio

n (c

ms

2 )

ndash2

ndash1

0

1

2Metro 2

0 20 40ndash2

ndash1

0

1

2Metro 3

Time (s)0 20 40

ndash2

ndash1

0

1

2Metro 4

0 20 40ndash2

ndash1

0

1

2Metro 5

0 20 40ndash2

ndash1

0

1

2

(a)

Metro 1

PSD

(cm

2 s3 )

1000

500

50 1000

0

2000

2500

1500

Metro 2

1000

500

50 1000

0

2000

2500

1500

Metro 3

1000

500

50 1000

0

2000

2500

1500

Metro 4

1000

500

50 1000

0

2000

2500

1500

Metro 5

0

1000

500

50 1000

2000

2500

1500

Frequency (Hz)

(b)

Figure 6 e acceleration signals of measuring point W1 in Z direction (a) Time-history curves of acceleration (b) PSD curves ofacceleration

006

004

002

000

ndash002

ndash004

ndash0060 10 20 30 40

Time (s)

4

3

2

1

00 20 40 60 80 100

Frequency (Hz)

a B (t

) (cm

s2 )

A B (ω

) (cm

s)

times10ndash3

(a)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0002

00 20 40 60 80 100

Frequency (Hz)

0004a A

+B (

t) (c

ms

2 )A A

+B (

ω) (c

ms

)

(b)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0004

0002

00 20 40 60 80 100

Frequency (Hz)

a A (t

) (cm

s2 )

A A (ω

) (cm

s)

(c)

Figure 5 Signal comparison of background vibration overall vibration and subway-induced vibration (a) Background vibration (b)Overall vibration (c) Subway-induced vibration

6 Shock and Vibration

Figure 8(a) Besides standard deviations and variation co-efficients of measured acceleration are varied greatly andsome of the values are large is is because of the randomcharacteristic of subway-induced vibration and the ran-domness originates from the different loads of passingmetros at different time and complexity of site soil etc

412 Frequency Domain Analysis In order to investigatethe propagation of vibration on free field from the view offrequency domain and energy the average smoothed powerspectral densities (PSDs) of 4 measuring points in threedirections were calculated and they were plotted in onefigure as presented in Figure 9

It is observed that the subway-induced vibration energyof point W1 in the frequency band which is greater than10Hz is dominant but the vibration energy of point W4 isreversely dominant in the frequency band that is less than10Hz in three directions the vibration energy of Y directionis obviously stronger than other directions and this can alsobe explained by the different features with between curvedand straight segment of metro line It is also observed thatthe dominant frequency of measuring points W1 W2 W3andW4 offset towards to left in X and Y direction as a wholebut there is local ldquorebound phenomenonrdquo such as thedominant frequency of measuring points W3 is on the rightside of W2 e dominant frequencies of four measuringpoints are essentially constant in Z direction

42 Vibration in the Vertical Shaft

421 Time Domain Analysis Statistical acceleration time-history results of subway-induced vibration of S1 and S2points are shown in Figure 10 due to length limitations Alsoonly 5 groupsrsquo effective data were collected in three di-rections because of weather problem and disturbance fromconstruction machinery etc e data of S1 and S2 (6channels S1-x S1-y S1-z and S2-x S2-y S2-z) were mea-sured simultaneously when metro passed

Figure 10 shows the comparison of average vibrationsbetween point S1 represented the pile top and point S2represented the site soil near pile in three directions It isobserved that the acceleration of pile top is larger than sitesoil in three directions no matter whatever from the peakvalues or the Rms values and this signifies that vibration ismore easily propagated along the pile than the soil for the

vibration of pile top the order of amplitude is Z gt Y gt X butas for the site soil the order is Y gt Z gt X which can be seeneasily through the peak values and Rms valuese order Z gtY gt X illustrates that the vertical vibration of top of pile ismore predominant than lateral vibration for propagatingalong the pile at the curved segment of metro line but theorder Y gt Z gt X of site soil is similar to the free field

422 Frequency Domain Analysis To investigate the vi-bration differences in the vertical shaft from the view offrequency and energy the average smoothed power spectraldensities (PSDs) of measuring points S1 and S2 in threedirections were calculated and fitted respectively esmoothed average acceleration PSDs of measuring points S1and S2 were plotted in one figure as shown in Figure 11

Figure 10 gives the comparison between smoothed PSDsof S1 and S2 in three directions It is observed that the subway-induced vibration energy of S1 is not always stronger than S2and reversed in some frequency bands for different directionsAs for the X direction the vibration energy of S1 is strongerthan S2 when the frequency is between 37Hz and 70Hz andthe situation turned over when frequency is less than 37Hzandmore than 70Hz for the Y direction the vibration energyof S1 is stronger than S2 almost in all frequency bands exceptfor 65sim77Hz for the Z direction 48Hz is the frequency ofturning point and the vibration energy of S1 is stronger thanS2 when the frequency is more than 48Hz and vibrationenergy of S1 becomes smaller than S2 when the frequency isless than 48Hz

5 Subway-Induced Vibration of the Building toBe Built

e building to be built is rightly over the zone of verticalshaft and the longitudinal direction of building is parallelwith direction of perpendicular to metro line (Y direction)

51 e Information of the Building and Structure Modele building will be used as the serviced apartment thatincludes three stories underground and ten stories above theground e function of three stories underground will be asparking lots and supermarkets and ten stories above theground will become luxury apartments e building plan ofthe typical story (6th story of the building) is shown asFigure 12

ndash10

ndash5

0

5

ndash5

5

ndash5

5

10

Acc

eler

atio

n (c

ms

2 )

X direction

Time (s)

ndash10

0

10Y direction

0 10 20 30 10 30 10 3040 0 20 40 0 20 40ndash10

0

10Z direction

Figure 7 e time-history of measuring point W1 in three directions for metro 1

Shock and Vibration 7

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

Figure 8 e average value of 3 indexes induced by subways on free eld (a) Acceleration (b) Velocity (c) Displacement

8 Shock and Vibration

Table 2 Mean values standard deviations and variation coeumlcients of peak and Rms values of accelerations induced by metros in threedirections

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Metro 1 2749 0981 0605 0771 0471 0183 0107 0143Metro 2 3525 0986 1720 0453 0739 0164 0354 0083Metro 3 3413 0771 0978 0421 0650 0146 0187 0084

Mean values 3229 0913 1101 0548 0620 0164 0216 0103Standard deviations 0420 0123 0567 0194 0136 0018 0126 0034Variation coeumlcients 0130 0135 0515 0353 0220 0112 0582 0328

Y direction

Metro 1 10798 1518 0800 0363 1504 0221 0133 0079Metro 2 7366 1150 1237 0746 1323 0223 0249 0142Metro 3 3524 0596 0940 0739 0550 0102 0197 0153Metro 4 12754 1420 0557 0395 1744 0230 0132 0072

Mean values 8611 1171 0884 0561 1281 0194 0178 0112Standard deviations 4057 0414 0284 0210 0516 0062 0056 0042Variation coeumlcients 0471 0353 0321 0374 0403 0318 0317 0374

Z direction

Metro 1 1794 0893 0402 0265 0309 0156 0077 0054Metro 2 1610 1140 0463 0538 0226 0160 0097 0100Metro 3 1841 1309 0532 0609 0275 0179 0099 0092Metro 4 1457 0996 0448 0508 0226 0160 0100 0106Metro 5 1666 1118 0530 0508 0226 0166 0102 0099

Mean values 1674 1091 0475 0486 0252 0164 0095 0090Standard deviations 0153 0157 0056 0130 0038 0009 0010 0021Variation coeumlcients 0091 0144 0118 0268 0151 0054 0107 0232

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Figure 9 e smoothed average acceleration PSDs of subway-induced vibration on free eld (a) X direction (b) Y direction (c) Zdirection

Shock and Vibration 9

e structure of underground part is reinforced concreteshear wall and the above part is reinforced concrete framee type of foundation of the building is the pile foundationFor the underground part typical column is circular forwhich diameter is 1000mm typical beam is rectangle ofwhich size is 800mm lowast 400mm the thickness of shear wall isamong 200ndash900mm and the thickness of slab is 600mm forthe part above the ground typical column is rectangle forwhich size is 600mm lowast 600mm typical beam is rectangle for

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

e structure model of the building was built bySAP2000 e mass in the model is considered as combi-nation of 10lowast dead load and 05lowast live load the stiness of allmembers is set as the elastic stiness the element meshingobeys the 18 wavelength principal and the damping isconsidered to follow Rayleigh damping approach About thedamping the 54 part will have a detail discussion In the

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

Figure 10 e average vibration acceleration of measuring points S1 and S2 induced by subway (a) Peak values (b) Rms values

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

Figure 11 e smoothed average acceleration PSD of measured points S1 and S2 induced by subway (a) X direction (b) Y direction (c) Zdirection

10 Shock and Vibration

model the beams and columns are simulated by line elementand the walls and slabs by elastic shell element e linearmodal time-history analysis method was adopted as cal-culation method and the rst 200 order modes were takene analysed SAP200 model is presented as Figure 13

52 e Excitation Was Inputted into the Model In thisresearch since it is assumed that the presence of the buildingdoes not aect the vibration generation source [20] thevibration measured is used as excitation source to thestructure e basement which is the negative third oor forparking cars that elevation is minus1500m is assumed to haveinnite stiness and hereby the SSI eect is ignoredMeanwhile the measured acceleration time-history re-sponse of point S1 is directly as the input of the building tosimulate the vibration induced by passage of metro eexcitation to be inputted into the basement of structure wasrandomly selected frommeasured accelerations time-historyof point S1 in the vertical shaft e detailed time anddomain information of the excitation are presented inFigure 14 e basement of building is pile foundation andsimplied as rigid body connected with the ground in thisanalysis In the SAP2000 model the selected time-history ofaccelerations in three directions was inputted into the base ofbuilding directly

e directions input to structure are in accord with thearrow direction in Figure 11 where X signies the shortdirection and Y signies long direction of the building

As is shown in Figure 14 the amplitude of excitation in Zdirection is maximum followed by Y direction and X di-rection is minimum from the perspective of time domainFrom the perspective of frequency domain the energy ofexcitation in X direction mainly distributes among60sim70Hz Y direction mainly distributes around 90Hz andZ direction mainly distributes among 60sim90Hz which iswider than other two directions

53 e Evaluation Indicators e vibration level is theusual indicator when evaluating all kinds of vibrations Here

two evaluation indicators are adopted which are accelera-tion vibration level La and velocity vibration level Lv

According to International Standard for Human Re-sponse to Whole-body Vibration (ISO2631) [28 29] theacceleration level is dened as follows

La 20 log10arms

a0 (5)

where a0 is the referenced acceleration its value is1 times 10minus6 ms2 based on ISO2631 arms is the root-mean-square value of acceleration with frequency weighting

e velocity level is an indicator that is mainly rec-ommended by Federal Transit Administration (FTA) criteria[30] e velocity level is dened as follows

Lv 20 log10vrms

v0 (6)

where v0 is the referenced acceleration its value is254 times 10minus8 ms vrms is the root-mean-square value of ac-celeration but with no frequency weighting

54 e Inuence of Damping Ratio on the Vibration Levele Rayleigh damping approach was followed in this re-search and the damping matrix [C] of the system can beexpressed as follows

[C] α[M] + β[K] (7)

where [M] and [K] are mass matrix and stiness matrixrespectively e α and β are combination coeumlcients ofmass matrix and stiness matrix respectively and they canbe determined by

α

β

2ξω1 + ω2

ω1ω2

1 (8)

where ω1 and ω2 are two frequencies of the system and ξ asthe key parameter is the damping ratio of the system

e value of ω1 always equals the fundamental frequencyof system and ω2 is generally selected from high frequencies

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

that have signicant eect on dynamic response In factdynamic response of structure is not only depending on thedynamic characteristics of structure but also the charac-teristics of frequency spectrum of vibration load Based onthe report of Idriss [31] on improving of above traditionalmethod ω1 and ω2 are set as 10Hz and 70Hz here

As the most important parameter in the Rayleighdamping approach the damping ratio ξ varies in dierentanalysis but it is in proportional to dynamic response ofstructure For example when the seismic analysis is carriedout it often set as 2 for steel structure but 5 for reinforcedconcrete structure When the issues of slab serviceability arefocused the ξ often takes 2 for reinforced concretestructure and less than 2 for steel structure In here thedamping ratios equating to 1 2 3 4 and 5 re-spectively were taken to study the inuence of dampingratio on the vibration level of the structure e inuence ofdamping ratio on acceleration level La and velocity level Lvin the frequency domain is pictured as Figures 15 and 16respectively

e average one-third octave spectrum of the acceler-ation level of typical story in three directions for dierent

damping ratios is shown in Figure 15 It is obvious that theacceleration level increases as the damping ratio reducesamong almost frequency range in all three directionsHowever the shapes of one-third octave spectra are variousfor dierent directions For example the peak values ap-pear around 5Hz and the acceleration level is almost below30 dB when frequency is beyond 10Hz for the X and Ydirections But for Z direction the peak values appeararound 63 Hz and the acceleration levels in all frequencyrange are above 30 dB ese are because that low-ordermodes of whole structure which mainly represent lateralmodes make remarkable contribution to the lateral vi-bration response while the high-order mode of wholestructure and local modes of slabs contribute to the verticalresponse much

Also the average one-third octave spectra of the velocitylevel of typical story in three directions for dierent dampingratio are shown in Figure 17 It can be found that there arealmost no dierences except the magnitude between averagevelocity level and acceleration level among one-third octavefrequency band erefore the same conclusions can bederived as same as Figure 14

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Figure 15 e average one-third octave spectra of the acceleration level of typical story (6th story) for dierent damping ratio (a) Xdirection (b) Y direction (c) Z direction

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

55 e Distribution of Acceleration Level along the Height-Wise In order to discern the distribution of accelerationindicators along the high-wise one-third octave spectra ofaccelerations of each evaluation point and their averagespectra were gained and pictured as Figure 16 en thedistribution of average maximum frequency acceleration

level Lamax along the high-wise was calculated and depictedas Figure 18 Here only the case of damping ratio equal to2 is showed due to limited space

It is observed from the curves of ldquoaverage valuesrdquo inFigure 16 that the spectral shapes are similar in X and Ydirection and the peak values all appear at 5Hz But for Z

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

Figure 16e one-third octave and average spectra of the accelerations of each evaluation point at typical story (6th story damping ratio 002) (a) X direction (b) Y direction (c) Z direction

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

Figure 17 e average one-third octave spectra of the velocity level of typical story (6th story) for dierent damping ratio (a) X direction(b) Y direction (c) Z direction

14 Shock and Vibration

direction the spectral shape is dierent from another twodirections and the peak value appears at 63Hz Based onthe curves of ldquoevaluation pointsrdquo of Figure 16 the spectralshapes of dierent evaluation points basically have uniformtrend among the whole frequency range in both X and Ydirections especially in X direction But for Z directionthere exists dierent situation that the spectral shapes ofdierent evaluation points are not as uniform as X directione above occurrence can be explained by the fact that thestiness in the lateral direction hardly changes for eachevaluation point but in the same story the stiness in thevertical direction is variable

e comparison of the distribution of maximum fre-quency acceleration level Lamax along the high-wise in threedirections is pictured as Figure 18 e Lamax for X di-rections decreases as the story number increases between 1stand 5th story and then increases zigzagged slightly above 5thstory e distribution of Lamax in Y direction is similar to Xdirection For Z direction the Lamax decreases as the storynumber increases and the values are obviously greater thanX and Y directions at each story is also states the verticalvibration induced by subway is prominent than other di-rections on the slabs of buildings

56 e Distribution of Vibration Level on Velocity Indicatoralong the Height-Wise Also in order to discern the

distribution of velocity indicator along the high-wise one-third octave spectra of velocities of each evaluation point atthe typical story and their average spectra were gained andpictured as Figure 19 en the distribution of averagemaximum frequency velocity level Lvmax along the high-wise was calculated and depicted as Figure 20 Also only thecase of damping ratio equal to 2 is showed due to thelimited space

From Figures 19 and 20 the similar observations andconclusions can be found and gained as same as Figures 16and 18 e only dierence between velocity level and theacceleration level is the dierence in amplitudes is isinevitable to calculate dierent indicators of vibrations

6 Conclusions

is paper mainly includes two parts the rst part hadpresented the results of subway-induced vibration measuredon a construction site at the curved section of ShenzhenMetro line No 1 in China e other part based on theresults of the eld measurement had calculated the dierentvibration indicators and investigated the distribution ofvibration level along the high-wise of the building to be builtover the site of vertical shaft Especially the inuence ofdamping ratio on the vibration level has been studied By theanalysis to the results of eld vibration measurement and thedynamic behaviour of the building model under the

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Figure 18 e distribution of maximum frequency acceleration level along the high-wise (damping ratio 002)

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

(1) In the time domain the subway-induced vibrationpropagation along direction of perpendicular sub-way line damped out on the free eld as a whole butthere is ldquorebound phenomenonrdquo at local zoneis isright for X and Z direction but not for Y direction Infrequency domain the vibration energy has dierent

distribution at dierent frequency sections in threedirections

(2) In vertical shaft the subway-induced vibration ofpile top is stronger than the soil site near the pilefrom view of time domain and this is right for allthree directions In frequency domain the vibrationenergy of two measuring points has its own high andlow at dierent frequency bands

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

Figure 19e 13 octave frequency band velocity level of the typical story (6th story damping ratio 002) (a) X direction (b) Y direction(c) Z direction

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

(3) For this curved section of the metro line the mostobvious feature is that the vibration in Y direction isstronger than the other directions on the free fieldBut for the measuring point of pile top in verticalshaft the vertical vibration level accords with thestraight sections of the metro line and greater thanthe other directions

(4) e vibration responses of two evaluation indicatorsincrease as the damping ratio in three directionsreduces and the vertical vibration spectral shapes areobviously different with the spectral shapes of twolateral directions

(5) For the acceleration level and velocity level thevertical vibration is more dominant than anothertwo directions at each story of the building and themaximum frequency vibration levels decrease as thestory number increases in vertical direction But inthe two lateral directions it decreases first thenincreases and then decreases again as the number ofstories increase in vertical direction

Data Availability

e data used to support the findings of this study areavailable from the corresponding author or bailigang2008126com upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

[1] X He ldquoEnvironmental vibration induced by urban rail transitsystemrdquo Journal of Northern Jiaotong University vol 21 no 2pp 84ndash88 1999

[2] O Hassan Train-Induced Groundborne Vibration and Noisein Buildings Multi Science Publishing Co Ltd BrentwoodUK 2007

[3] Y B Yang and H H Hung ldquoSoil vibrations caused by un-derground moving trainsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 134 no 11 pp 1633ndash1644 2008

[4] A Eitzenberger Train-Induced Vibrations in Tunnels a Re-view Lulea Tekniska Universitet Lulea Sweden 2008

[5] G Kouroussis L V Parys C Conti and O VerlindenldquoPrediction of ground vibrations induced by urban railwaytraffic an analysis of the coupling assumptions between ve-hicle track soil and buildingrdquo International Journal ofAcoustics and Vibration vol 18 no 4 pp 163ndash172 2013

[6] P J Remington L G Kurzweil and D A Towers ldquoLow-frequency noise and vibrations from trainsrdquo in TransportationNoise Reference Book Butterworths London UK 1987

[7] L G Kurzweil ldquoGround-borne noise and vibration fromunderground rail systemsrdquo Journal of Sound and Vibrationvol 66 no 3 pp 363ndash370 1979

[8] S Chen X Ling Z Zhu F Zhang and W Ma ldquoFieldmonitoring on train-induced vibration in the seasonallyfrozen region of daqing in springrdquo in Proceedings of In-ternational Conference on Transportation EngineeringChengdu China July 2009

[9] D Wei W Shi R Han and S Zhang ldquoMeasurement andresearch on subway induced vibration in tunnels and buildingnearby in Shanghairdquo in Proceedings of International Con-ference on Multimedia Technology (ICMT 2011) HangzhouChina July 2011

[10] W M Yan ldquoVertical vibration measurement and analysis ofbuildings on metro train platformsrdquo Journal of Beijing Uni-versity of Technology vol 34 no 8 pp 836ndash841 2008

[11] C Zou YWang J A Moore andM Sanayei ldquoTrain-inducedfield vibration measurements of ground and over-trackbuildingsrdquo Science of the Total Environment vol 575pp 1339ndash1351 2017

[12] C Zou Y Wang P Wang and J Guo ldquoMeasurement ofground and nearby building vibration and noise induced bytrains in a metro depotrdquo Science of the Total Environmentvol 536 pp 761ndash773 2015

[13] Z Cao T Guo and Z Zhang ldquoVibration measurement ina metro depot with trains running in the top storyrdquo Journal ofVibroengineering vol 19 no 1 pp 502ndash519 2017

[14] Z Cao T Guo and Z Zhang ldquoMeasurement and analysisof vibrations in a residential building constructed on anelevated metro depotrdquo Measurement vol 125 no 1pp 394ndash405 2018

[15] H Zhou W He and W Xie ldquoResearch on vibration ser-viceability of over-track buildingsrdquo in Proceedings of SecondInternational Conference on Transportation Information andSafety pp 621ndash626 Wuhan China June 2013

[16] P Lopes P A Costa R Calccedilada and A S Cardoso ldquoIn-fluence of soil stiffness on building vibrations due to railwaytraffic in tunnels numerical studyrdquo Computers and Geo-technics vol 61 pp 277ndash291 2014

[17] P Lopes P A Costa R Calccedilada and A S Cardoso ldquoNu-merical modeling of vibrations induced by railway traffic intunnels from the source to the nearby buildingsrdquo Soil Dy-namics and Earthquake Engineering vol 61-62 pp 269ndash2852014

[18] P Lopes J F Ruiz P A Costa R Calccedilada and A S CardosoldquoVibrations inside buildings due to subway railway trafficExperimental validation of a comprehensive predictionmodelrdquo Science of the Total Environment vol 568pp 1333ndash1343 2016

[19] D Lopez-Mendoza A Romero D P Connolly andP Galvın ldquoScoping assessment of building vibration inducedby railway trafficrdquo Soil Dynamics and Earthquake Engineeringvol 93 pp 147ndash161 2017

[20] P Coulier G Lombaert and G Degrande ldquoe influence ofsourcendashreceiver interaction on the numerical prediction ofrailway induced vibrationsrdquo Journal of Sound and Vibrationvol 333 no 12 pp 2520ndash2538 2014

[21] S Gupta G Degrande and G Lombaert ldquoExperimentalvalidation of a numerical model for subway induced vibra-tionsrdquo Journal of Sound and Vibration vol 321 no 3ndash5pp 786ndash812 2009

[22] D P Connolly G Kouroussis O Laghrouche C L Ho andM C Forde ldquoBenchmarking railway vibrationsndashtrack ve-hicle ground and building effectsrdquo Construction and BuildingMaterials vol 92 pp 64ndash81 2015

Shock and Vibration 17

[23] J P Yang P Z Li and Z Lu ldquoNumerical simulation and in-situ measurement of ground-borne vibration due to subwaysystemrdquo Sustainability vol 10 no 7 p 2439 2018

[24] Y Wang Research on the Acquisition and Procession ofStrutural Vibration Signal School of Civil Engineering TongjiUniversity Shanghai China 2006

[25] V H Nguyen J Mahowald S Maas and J C Golinval ldquoUseof time- and frequency-domain approaches for damage de-tection in civil engineering structuresrdquo Shock and Vibrationvol 2014 Article ID 872492 9 pages 2014

[26] R Shao W Hu and J Li ldquoMulti-fault feature extraction anddiagnosis of gear transmission system using time-frequencyanalysis and wavelet threshold de-noising based on EMDrdquoShock and Vibration vol 20 no 4 pp 763ndash780 2013

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

[28] Pennsylvania State University Mechanical Vibration andShock-Evaluation of Human Exposure to Whole-BodyVibration-Part 1 General Requirements Pennsylvania StateUniversity Harrisburg PA USA 1997

[29] M Vibration ldquoShock-evaluation of human exposure towhole-body vibrationndashpart 2 vibrations in buildings (1 to 80Hz)rdquo International Standard ISO Geneva Switzerland 2003

[30] C E Hanson D A Towers and L D Meister Transit Noiseand Vibration Impact Assessment Federal Transit Adminis-tration Office of Planning and Environment WashingtonDC USA 2006

[31] I Idriss Quad-4 A Computer Program for Evaluating theSeismic Response of Soil Structures by Variable Damping FineteElement Procedures University of California Berkeley CAUSA 1973

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

A(ω) 1113944

Nminus1

t0a(t)eminusiωt2πN

(ω 0 1 2 Nminus 1)

(1)

|A(ω)| A(ω)eminusiθω (ω 0 1 2 Nminus 1) (2)

AA(ω) AA+B(ω)1113868111386811138681113868minus AB(ω)

11138681113868111386811138681113868111386811138681113868

1113868111386811138681113868 11138731113872 eiθω

(ω 0 1 2 Nminus 1)(3)

Table 1 Soil parameters of different soil layers

Accelerometer

Signal line

PC

SVSA data acquisition instrument

Data line

Figure 3 SVSA vibration test system

4 Shock and Vibration

aA(t) 1N

1113944

Nminus1

t0AA(ω)a(t)e

iωt2πN

(ω 0 1 2 Nminus 1)

(4)

4 Results of Field Vibration Measurement

41 Propagation of Vibration on Free Field

Data interception

Measured acceleration

data

Low-pass filtering in frequency

domain

Smoothing

Removal of trend

Removal of background

vibration

Plotting acceleration time history

Frequency-domain integral

1 time

Frequency-domain integral

2 times

Removal of trend

Removal of trend

Plotting displacement time history

Plotting velocity time

history

Figure 4 Preprocessing step of measured data

Shock and Vibration 5

Metro 1

0 20 40

Acc

eler

atio

n (c

ms

2 )

ndash2

ndash1

0

1

2Metro 2

0 20 40ndash2

ndash1

0

1

2Metro 3

Time (s)0 20 40

ndash2

ndash1

0

1

2Metro 4

0 20 40ndash2

ndash1

0

1

2Metro 5

0 20 40ndash2

ndash1

0

1

2

(a)

Metro 1

PSD

(cm

2 s3 )

1000

500

50 1000

0

2000

2500

1500

Metro 2

1000

500

50 1000

0

2000

2500

1500

Metro 3

1000

500

50 1000

0

2000

2500

1500

Metro 4

1000

500

50 1000

0

2000

2500

1500

Metro 5

0

1000

500

50 1000

2000

2500

1500

Frequency (Hz)

(b)

006

004

002

000

ndash002

ndash004

ndash0060 10 20 30 40

Time (s)

4

3

2

1

00 20 40 60 80 100

Frequency (Hz)

a B (t

) (cm

s2 )

A B (ω

) (cm

s)

times10ndash3

(a)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0002

00 20 40 60 80 100

Frequency (Hz)

0004a A

+B (

t) (c

ms

2 )A A

+B (

ω) (c

ms

)

(b)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0004

0002

00 20 40 60 80 100

Frequency (Hz)

a A (t

) (cm

s2 )

A A (ω

) (cm

s)

(c)

6 Shock and Vibration

42 Vibration in the Vertical Shaft

5 Subway-Induced Vibration of the Building toBe Built

ndash10

ndash5

0

5

ndash5

5

ndash5

5

10

Acc

eler

atio

n (c

ms

2 )

X direction

Time (s)

ndash10

0

10Y direction

0 10 20 30 10 30 10 3040 0 20 40 0 20 40ndash10

0

10Z direction

Figure 7 e time-history of measuring point W1 in three directions for metro 1

Shock and Vibration 7

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

8 Shock and Vibration

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Y direction

Z direction

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Shock and Vibration 9

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

10 Shock and Vibration

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

aA(t) 1N

1113944

Nminus1

t0AA(ω)a(t)e

iωt2πN

(ω 0 1 2 Nminus 1)

(4)

4 Results of Field Vibration Measurement

41 Propagation of Vibration on Free Field

Data interception

Measured acceleration

data

Low-pass filtering in frequency

domain

Smoothing

Removal of trend

Removal of background

vibration

Plotting acceleration time history

Frequency-domain integral

1 time

Frequency-domain integral

2 times

Removal of trend

Removal of trend

Plotting displacement time history

Plotting velocity time

history

Figure 4 Preprocessing step of measured data

Shock and Vibration 5

Metro 1

0 20 40

Acc

eler

atio

n (c

ms

2 )

ndash2

ndash1

0

1

2Metro 2

0 20 40ndash2

ndash1

0

1

2Metro 3

Time (s)0 20 40

ndash2

ndash1

0

1

2Metro 4

0 20 40ndash2

ndash1

0

1

2Metro 5

0 20 40ndash2

ndash1

0

1

2

(a)

Metro 1

PSD

(cm

2 s3 )

1000

500

50 1000

0

2000

2500

1500

Metro 2

1000

500

50 1000

0

2000

2500

1500

Metro 3

1000

500

50 1000

0

2000

2500

1500

Metro 4

1000

500

50 1000

0

2000

2500

1500

Metro 5

0

1000

500

50 1000

2000

2500

1500

Frequency (Hz)

(b)

006

004

002

000

ndash002

ndash004

ndash0060 10 20 30 40

Time (s)

4

3

2

1

00 20 40 60 80 100

Frequency (Hz)

a B (t

) (cm

s2 )

A B (ω

) (cm

s)

times10ndash3

(a)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0002

00 20 40 60 80 100

Frequency (Hz)

0004a A

+B (

t) (c

ms

2 )A A

+B (

ω) (c

ms

)

(b)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0004

0002

00 20 40 60 80 100

Frequency (Hz)

a A (t

) (cm

s2 )

A A (ω

) (cm

s)

(c)

6 Shock and Vibration

42 Vibration in the Vertical Shaft

5 Subway-Induced Vibration of the Building toBe Built

ndash10

ndash5

0

5

ndash5

5

ndash5

5

10

Acc

eler

atio

n (c

ms

2 )

X direction

Time (s)

ndash10

0

10Y direction

0 10 20 30 10 30 10 3040 0 20 40 0 20 40ndash10

0

10Z direction

Figure 7 e time-history of measuring point W1 in three directions for metro 1

Shock and Vibration 7

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

8 Shock and Vibration

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Y direction

Z direction

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Shock and Vibration 9

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

10 Shock and Vibration

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Metro 1

0 20 40

Acc

eler

atio

n (c

ms

2 )

ndash2

ndash1

0

1

2Metro 2

0 20 40ndash2

ndash1

0

1

2Metro 3

Time (s)0 20 40

ndash2

ndash1

0

1

2Metro 4

0 20 40ndash2

ndash1

0

1

2Metro 5

0 20 40ndash2

ndash1

0

1

2

(a)

Metro 1

PSD

(cm

2 s3 )

1000

500

50 1000

0

2000

2500

1500

Metro 2

1000

500

50 1000

0

2000

2500

1500

Metro 3

1000

500

50 1000

0

2000

2500

1500

Metro 4

1000

500

50 1000

0

2000

2500

1500

Metro 5

0

1000

500

50 1000

2000

2500

1500

Frequency (Hz)

(b)

006

004

002

000

ndash002

ndash004

ndash0060 10 20 30 40

Time (s)

4

3

2

1

00 20 40 60 80 100

Frequency (Hz)

a B (t

) (cm

s2 )

A B (ω

) (cm

s)

times10ndash3

(a)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0002

00 20 40 60 80 100

Frequency (Hz)

0004a A

+B (

t) (c

ms

2 )A A

+B (

ω) (c

ms

)

(b)

04

02

0

ndash02

ndash04

ndash060 10 20 30 40

Time (s)

0012

001

0008

0006

0004

0002

00 20 40 60 80 100

Frequency (Hz)

a A (t

) (cm

s2 )

A A (ω

) (cm

s)

(c)

6 Shock and Vibration

42 Vibration in the Vertical Shaft

5 Subway-Induced Vibration of the Building toBe Built

ndash10

ndash5

0

5

ndash5

5

ndash5

5

10

Acc

eler

atio

n (c

ms

2 )

X direction

Time (s)

ndash10

0

10Y direction

0 10 20 30 10 30 10 3040 0 20 40 0 20 40ndash10

0

10Z direction

Figure 7 e time-history of measuring point W1 in three directions for metro 1

Shock and Vibration 7

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

8 Shock and Vibration

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Y direction

Z direction

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Shock and Vibration 9

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

10 Shock and Vibration

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

42 Vibration in the Vertical Shaft

5 Subway-Induced Vibration of the Building toBe Built

ndash10

ndash5

0

5

ndash5

5

ndash5

5

10

Acc

eler

atio

n (c

ms

2 )

X direction

Time (s)

ndash10

0

10Y direction

0 10 20 30 10 30 10 3040 0 20 40 0 20 40ndash10

0

10Z direction

Figure 7 e time-history of measuring point W1 in three directions for metro 1

Shock and Vibration 7

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

8 Shock and Vibration

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Y direction

Z direction

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Shock and Vibration 9

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

10 Shock and Vibration

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

Acce

lera

tion

(cm

2 )Ac

cele

ratio

n (c

m2 )

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

05

1

15

0

05

1

15

0

05

1

15X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(a)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

Velo

city

(μm

s)

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0 0 0

10

20

30

10

20

30

10

20

30X-peak

W1 W2 W3 W4Y-peak

W1 W2 W3 W4Z-peak

W1 W2 W3 W4

X-rmsW1 W2 W3 W4

Y-rmsW1 W2 W3 W4

Z-rmsW1 W2 W3 W4

(b)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

Disp

lace

men

t (μm

)D

ispla

cem

ent (μm

)

X-peakW1 W2 W3 W4

0

1

2

3

4

5

Y-peakW1 W2 W3 W4

0

1

2

3

4

5

Z-peakW1 W2 W3 W4

0

1

2

3

4

5

X-rmsW1 W2 W3 W4

0

02

04

06

08

Y-rmsW1 W2 W3 W4

0

02

04

06

08

Z-rmsW1 W2 W3 W4

0

02

04

06

08

(c)

8 Shock and Vibration

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Y direction

Z direction

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Shock and Vibration 9

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

10 Shock and Vibration

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

IndexAcceleration (cms2)

Peak RmsMeasurement point W1 W2 W3 W4 W1 W2 W3 W4Distance to metro line (m) 5 17 26 35 5 17 26 35

X direction

Y direction

Z direction

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

100

105

PSD

(cm

2 s3 )

W1W2

W3W4

(c)

Shock and Vibration 9

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

10 Shock and Vibration

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

which size is (600mmsim700mm) lowast300mm and the thick-ness of slab is 100mm

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

5

10

15

Y directionS1 S2

0

5

10

15

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

Z directionS1 S2

0

5

10

15

(a)

Individualaccelerationof S1Individualaccelerationof S2

Averageaccelerationof S1Averageaccelerationof S2

X directionS1 S2

Acce

lera

tion

(cm

s2 )

0

05

1

15

2

25

3

Y directionS1 S2

0

05

1

15

2

25

3

Z directionS1 S2

0

05

1

15

2

25

3

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(a)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(b)

10 20 30 40 50 60 70 80 90 100Frequency (Hz)

S1S2

100

105

PSD

(cm

2 s3 )

(c)

10 Shock and Vibration

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

La 20 log10arms

a0 (5)

Lv 20 log10vrms

v0 (6)

[C] α[M] + β[K] (7)

α

β

2ξω1 + ω2

ω1ω2

1 (8)

Evaluationpoint

X

Y

Figure 12 e plan view of the evaluation points at typical story (6th story)

Shock and Vibration 11

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

0 10 20 30 40

0 50 100

10

0

ndash10

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(a)

0 50 100

0 10 20 30 40

20

0

ndash20

2

1

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times105

(b)

0 50 100

0 10 20 30 40

20

0

ndash20

10

5

0

Acce

lera

tion

(cm

s2 )

PSD

(cm

2 s3 )

Frequency (Hz)

Time (s)

times104

(c)

Figure 14 e excitations to be inputted (a) X direction (b) Y direction (c) Z direction

Figure 13 e SAP2000 model of the building

12 Shock and Vibration

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Acce

lera

tion

leve

l (dB

)

0

20

40

60

(c)

Frequency (Hz)100 101 102Ac

cele

ratio

n le

vel (

dB)

0102030405060

Evaluation pointAverage value

(a)

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(b)

Figure 16 Continued

Shock and Vibration 13

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Frequency (Hz)100 101 102

Evaluation pointAverage value

Acce

lera

tion

leve

l (dB

)

0102030405060

(c)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(a)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(b)

ξ = 001ξ = 002ξ = 003

ξ = 004ξ = 005

Frequency (Hz)100 101 102

Velo

city

leve

l (dB

)

0

20

40

60

(c)

14 Shock and Vibration

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

6 Conclusions

Lamax (dB)45 50 55 60 65

Stor

ey n

umbe

r

1

2

3

4

5

6

7

8

9

10

X directionY directionZ direction

Shock and Vibration 15

measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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measured accelerations the following main conclusionswere gained

distribution at dierent frequency sections in threedirections

100 101 102

Frequency (Hz)

010203040506070

Vel

ocity

leve

l (dB

)

Evaluation pointAverage value

(a)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203040506070

Vel

ocity

leve

l (dB

)

(b)

100 101 102

Frequency (Hz)

Evaluation pointAverage value

010203030506070

Vel

ocity

leve

l (dB

)

(c)

50 55 60 65 70 75Lvmax (dB)

123456789

10

Stor

ey n

umbe

r

X directionY directionZ direction

Figure 20 e distribution of velocity level along the high-wise (damping ratio 002)

16 Shock and Vibration

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Data Availability

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (no 51578273)

References

Shock and Vibration 17

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[27] MATLAB Version R2015a [Software] 2015 e Math WorksInc Natick MA USA 2015

18 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom