Wind-InducedVibrationResponseofanInspection...

Research ArticleWind-Induced Vibration Response of an InspectionVehicle for Main Cables Based on Computer Simulation

Lu Zhang 12 Shaohua Wang12 Peng Guo 12 and Qunsheng Wang 3

1School of Mechanical Engineering Southwest Jiaotong University Chengdu 610031 China2Technology and Equipment of Rail Transit Operation and Maintenance Key Laboratory of Sichuan ProvinceChengdu 610031 China3State Key Laboratory of Traction Power Southwest Jiaotong University Chengdu 610031 China

Correspondence should be addressed to Lu Zhang jd_zhanglu163com and Peng Guo pengguo318gmailcom

Received 24 June 2019 Revised 18 September 2019 Accepted 10 October 2019 Published 30 October 2019

Academic Editor Evgeny Petrov

Copyright copy 2019 Lu Zhang et alis 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 isproperly cited

is paper presents a simulation approach based on the finite element method (FEM) to analyze the wind-induced vibrationresponse of an inspection vehicle for main cables First two finite element (FE) models of a suspension bridge and a main cable-inspection vehicle coupled system are established using MIDAS Civil software and ANSYS software respectively Second themean wind speed distribution characteristics at a bridge site are analyzed and the wind field is simulated based on the spectralrepresentation method (SRM)ird a modal analysis and a wind-induced vibration response transient analysis of the suspensionbridge FE model are completed Fourth the vibration characteristics of the inspection vehicle are analyzed by applying fluctuatingwind conditions andmain cable vibration displacements in the main cable-inspection vehicle coupled FEmodel Finally based onthe ISO2631-1-1997 standard a vehicle ride comfort evaluation is performed e results of the suspension bridge FE modalanalysis are in good accordance with those of the experimental modal test e effects of the working height number ofnonworking compressing wheels and number of nonworking driving wheels during driving are discussed When the averagewind speed is less than 133ms the maximum total weighted root mean square acceleration (av) is 01646ms2 and the vehicleride comfort level is classified as ldquonot uncomfortablerdquo is approach provides a foundation for the design and application ofinspection vehicles

1 Introduction

As the most important component of a suspension bridgethe main cable is corroded by the long-term exposure tonatural factors (eg wind rain freezing temperaturestemperature changes and humidity changes) which canendanger the security and reduce the service life of the bridge[1ndash3] erefore it is necessary to inspect and maintain themain cable regularly e traditional method of inspectingthe main cable is artificial climbing which has manyshortcomings such as having blind inspection areas diffi-culty in climbing at high altitudes low efficiency and po-tential safety hazards To improve the efficiency of cableinspection various types of crawling robots have been de-veloped [4ndash6] ese light crawling robots can perform

unmanned inspections of the sling and the cable but it isdifficult to inspect themain cable of a suspension bridge withcable bands and other ancillary structures or provide asuitable maintenance platform erefore it is of greatsignificance to develop an inspection vehicle suitable forlarge main cables

To inspect the main cable of a suspension bridge aninspection vehicle is designed and manufactured as shownin Figure 1 e inspection vehicle adopts the wheeledwalking scheme of ldquo10 sets of driving wheels +3 pairs ofcompressing wheels (driven wheels)rdquo to surround the maincable e vehicle body is a Π-shaped steel frame and theother parts are aluminum alloy trusses e whole vehicleweighs 85 t including a 1 t live load ree sets of lockdevices are installed on each pair of revolving plates at the

HindawiShock and VibrationVolume 2019 Article ID 1012987 13 pageshttpsdoiorg10115520191012987

bottom of the vehicle body to increase the rigidity of thevehicle body e inspection vehicle adopts automaticcontrol technology to perform the alternate lifting andlowering of the driving wheels the advancing and retractingof the compressing wheels the rotating of flaps and theswitching of lock devices by controlling the hydraulic cyl-inders to straddle obstacles such as cable bands and hangerse vehicle can identify cable bands automatically climbcable bands actively and crawl at a large angle (30deg) whenmanned

e inspection vehicle drives on the main cable whichis a typical wind-sensitive structure Wind-induced vi-bration directly affects the security of equipment and theefficiency of workers [7] erefore the dynamic prop-erties of the main cable-inspection vehicle coupled systemunder wind loads should be studied when the inspectionvehicle is designed Researchers have conducted numerousfield measurements to investigate the wind-induced vi-bration characteristics of suspension bridges [8ndash10] Fieldmeasurement is the most direct and reliable method toobtain site wind data [11ndash13] However this approachrequires a long period and is easily affected by environ-mental conditions Li et al [14] Chen et al [15] and Liet al [16] investigated the wind characteristics of differentbridge sites through wind tunnel tests to provide a basis forbridge design Although this method is not affected by thegeographical environment accurate models must be builtand the cost can be extremely expensive With the de-velopment of theoretical studies and computer technologysimulation experiments have been increasingly used tostudy the effects of various factors on bridge componentsat the initial stage of the research work to reduce thenumber of field measurements and tunnel tests [17 18]Field measurements and tunnel tests are usually used forfinal validation Bai et al [19] and Helgedagsrud et al [20]performed and validated simulation experiments bycomparing different simulation results with those of windtunnel tests However these studies focused on the wind-induced vibration of suspension bridges and few studieshave focused on the wind-induced vibration of mobiledevices on the main cable

e inspection vehicle was developed in the specializedfield of mobile robots In most previous studies researchersfocused on the design and vibration caused by the climbingof robots Kim et al [4] and Cho et al [5] manufactured awheel-based robot and a caterpillar-based robot for theinspection of a hanger rope and the climbing abilities ofboth robots were validated in indoor experimental envi-ronments Xu et al [6] designed a cable-climbing robot forcable-stayed bridges and the obstacle-climbing performanceof each robot was simulated and validated in the laboratoryHowever these robots are all tiny unmanned robots andonly structural safety must be considered For a mannedinspection vehicle the vibration of the vehicle may causediscomfort or annoy the workers and influence performance[21]ese factors must be studied in the design processewind-induced vibration of the inspection vehicle is acomplicated solid-wind-cable interaction problem and thecorresponding actionmechanism has not yet been effectivelystudied

e simulation of a random wind field is essential fortime-domain vibration analysis of the inspection vehicleunder wind loads Based on the Monte Carlo method thedigital filtering method and the spectral representationmethod (SRM) [22] are two basic approaches used tosimulate the random wind field SRM the method adoptedin this paper has been widely used in the engineeringcommunity due to its accuracy and simplicity [23 24] Inorder to improve the efficiency of SRM for the simulation ofmultidimensional wind fields Tao et al [23 25] Huang et al[24] and Xu et al [26] proposed different optimizationmethods for solving With the development of sensortechnology the study of wind fields has gradually beenextended from stationary fields to nonstationary fields es-pecially for extreme wind [27 28] However no empiricalmodel is available for nonstationary winds due to the dif-ficulties in mathematical treatments and nonergodic char-acteristics [28] erefore stationary wind is the objective ofthis paper

e purpose of this paper is to propose a method ofassessing the vibration response of a main cable-inspectionvehicle coupled system under fluctuating wind conditions

(a)

Guardrail

Cable band stanchi

Vehicle boday

Driving wheel

Working platform

Main cable

Cable band

Compressing wheel

Equipment box

Revolving plateLock device Hanger

(b)

Figure 1 (a) An inspection vehicle for a main cable (b) Structure of the vehicle

2 Shock and Vibration

is paper is organized as follows In Section 2 the processfor establishing a suspension bridge finite element (FE)model and a main cable-inspection vehicle coupled FEmodel is introduced in detail Taking the Qingshui RiverBridge as an example the mean wind speed distributioncharacteristics at the bridge site are analyzed and the windfield is simulated in Section 3 Section 4 presents the ridecomfort evaluation method based on the ISO 2631-1-1997standard [21] A modal analysis of the suspension bridge FEmodel transient analysis of both FE models and ridecomfort evaluation of the vehicle are conducted in Section 5Finally the conclusions and future work are discussed inSection 6

2 Finite Element Model

e unit length mass of the inspection vehicle is muchsmaller than that of the suspension bridge e inspectionvehicle has little influence on the vibration amplitude andacceleration of the cable [29] erefore the influence ofthe inspection vehicle on the vibration response of thebridge is not considered in this study In order to simplifythe study the suspension bridge FE model and the maincable-inspection vehicle coupled FE model are estab-lished MIDAS Civil software is used for the suspensionbridge FE Model because of the accuracy and accessibilityof its built-in formulas For the main cable-inspectionvehicle coupled FE model ANSYS software is used due tothe variety of its element types and the flexibility of itsANSYS Parametric Design Language (APDL) e dy-namic displacement of the main cable which is recordedover time from the suspension bridge FE model is taken asthe excitation source for the main cable-inspection vehiclecoupled FE model to realize one-way coupling betweentwo FE models

21 SuspensionBridge FEModel eQingshui River Bridgelocated in Guizhou Province China is 27m wide with amain span of 1130m e structure is a single-span steeltruss suspension bridge located in a mountainous areaconnecting the expressway from Guizhou to Wengrsquoan asshown in Figure 2 xb is the axial direction of the bridge yb isthe direction of the bridge width and zb is the verticaldirection

e FE model of the Qingshui River Bridge was builtusing MIDAS Civil software as presented in Figure 3Beam elements are used for the bridge deck and towersTruss elements are used for the main cable and hangers andare tension-only elements e structural parameters ofthe bridge FE model are listed in Table 1 e bottom ofeach tower and each anchorage are fixed e bridge deckis connected to two main towers by elastic contacts in boththe y and z directions with ratings of 1000000 kNm Oneend of the bridge deck is constrained in the x directioneweight of the bridge deck two main cables and all hangersare added to the nodes of the bridge deck and main cablesin the form of a uniformly distributed mass load Fluc-tuating wind loads are applied to the bridge deck and the

main cables simultaneously on the elasticity center nodesin a given time sequence e damping ratio is defined as0005

22 Main Cable-Inspection Vehicle Coupled FE Modele structure of the main cable-inspection vehicle coupledsystem is shown in Figure 4 xv is the width direction of thebridge deck yv is the direction perpendicular to the tan-gential direction of the main cable centerline and zv is thetangential direction of the main cable centerline

e FE model of the main cable-inspection vehiclecoupled system was established in ANSYS software asshown in Figure 5 e main cable is defined as a rigid bodySHELL 63 elements are used for the vehicle body and BEAM188 elements are used for working platforms compressingwheel brackets and the equipment box truss e guardrailcompressing wheels driving wheels power system andcontrol system are omitted and the weight of each part isadded to the model by adjusting the material density of thelocal structure e parameters of the material are shown inTable 2 Between the driving wheels and main cable or thecompressing wheels and main cable are viscoelastic contactswhich are defined as spring-damping contacts e pa-rameters of the spring-damping contacts are shown in Ta-ble 3 Fluctuating wind loads are applied to the vehicle on thewindward nodes in a given time sequence e dynamicdisplacement of the main cable that is recorded over timefrom the suspension bridge FE model is taken as the ex-citation source

For consistency in the comparison of results the vi-bration of node P located at the bottom of the middle of theworking platform on the windward side (see Figure 5) isinvestigated in the following analysis

23 Coordinate Relationship e inspection vehicle drivesalong the main cable during work which results in changesin both the inclination angle (α) and working height (H) ofthe inspection vehicle According to the different heightsof the main cable from the bridge deck H is set at 5 m35m 65m 95m and 113me relation between H and αis shown in Table 4 According to the selected coordinatesystem when establishing the FE models the coordinaterelationships between the suspension bridge and in-spection vehicle and the vehicle and a worker are shown inFigure 6

e displacements obtained from the transient analysisof the suspension bridge FE model need to be transferred tothe main cable-inspection vehicle coupled FE model edisplacement relations in the two coordinate systems are asfollows

Dxv minus Dyb

Dyv Dxb middot sin α + Dzb middot cos α

Dzv minus Dxb middot cos α + Dzb middot sin α

(1)

where Dxv Dyv and Dzv are the displacements of the maincable in the X Y and Z directions of the vehicle coordinate

Shock and Vibration 3

system OvmdashXvYvZv respectively Additionally Dxb Dyband Dzb are the displacements of the main cable in the X Yand Z directions of the bridge coordinate systemObmdashXbYbZb respectively

e acceleration obtained from the transient analy-sis of the main cable-inspection vehicle coupled FE modelis transferred to the foot of the worker e accelerationrelations in the two coordinate systems are as follows

ax axv

ay ayv middot sin α minus azv middot cos α

az azv middot sin α + ayv middot cos α

(2)

where axv ayv and azv are the accelerations of the inspectionvehicle (node P) in the X Y and Z directions of the vehiclecoordinate system OvmdashXvYvZv respectively In addition axay and az are the accelerations transferred to the foot of the

worker in theX Y and Z directions of the worker coordinatesystem OmdashXYZ respectively

3 Wind Speed and Wind Load Simulation

31 Wind Speed Simulation e wind speed V(t) in natureover a given time interval is considered to be the sum ofmean wind speed V and fluctuating wind speed v(t)

V(t) V + v(t) (3)

To obtain the mean wind speed distribution character-istics for the Qingshui River Bridge a wind measurementtower was built approximately 100m away from the maintower of the bridge close to Guizhou An NRG 40C ane-mometer (produced by NRG Systems company) wasmounted 10m above the bridge deck to record 10-minmeanwind speeds (V10) Based on the records from 33 months(from January 2014 to September 2016) the frequency of

258 345

113

Zb

Xb

178 + 72 times 152 + 178 = 1130

Figure 2 Configuration of the Qingshui River Bridge (unit m)

Main cable

Hanger

Main towerBridge deck

Anchorage

Figure 3 e FE model of the suspension bridge

Table 1 Parameters of the suspension bridge

Part A (m2) Iy (m4) Iz (m4) ρ (kgm3) W (kNm) E (GPa)Main tower 560 7526 7623 2500 mdash 345Bridge deck 4594 678 22341 mdash 2560 205Main cable 03526 mdash mdash mdash 27679 192Hanger 00017 mdash mdash mdash 0134 192A cross-sectional area Iy vertical section moment of inertia Iz transverse section moment of inertia E Youngrsquos modulus ρ density W weight per unitlength


each mean wind speed interval was calculated as shown inFigure 7 e lognormal probability density distributionwhich is extensively used to fit the wind speed distribution

over land [30] is used to fit these wind speed data and isgiven as follows [31]

f(V) 1

Vσ2π

radic exp minus(ln(V) minus μ)2

2σ21113896 1113897 (4)

where σ and μ are the shape and scale parametersrespectively

According to the maximum likelihood estimator (MLE)method the shape and scale parameters are calculated asfollows [31]

μ 1

M1113944

M

i1ln vi( 1113857

σ

1M

1113944

M

i1ln vi( 11138571113858 1113859

2

11139741113972 (5)

where M is the total number of wind speed values and i 12 and vi is the wind speed at time step

Figure 7 shows that the maximum daily mean windspeed is 133ms Because a real-time wind speed alarmsystem is installed on the inspection vehicle the influence ofheight on wind speed is neglected erefore the designmaximum working mean wind speed of the inspectionvehicle is 133ms (Vmax 133ms)

e Davenport power spectrum [32] is used to simulatethe fluctuating wind field along the bridge because the in-fluence of height on wind speed is neglected e Davenportpower spectrum is expressed as follows [32]

Sv(n) 4kV210

x2

n 1 + x2( )43 (6)

3540

3110 35

40

1926

472

800

600

600

600 500 500 500 500

24002400

800 600 600800

18161344

3110

S1

S2

S6

S1

S7

S5

S4

S1 S2 S3 S3 S8 S6 S7

3726

kd

kc

cd

cc

3

40 60 80

22 5

120

120

40 60 80

236

45402400 2913

749

120

8

88

8

88

kd cd

S3

Oslash30 Oslash34Oslash45

300 times 200 times 10

Figure 4 Configuration of the main cable-inspection vehicle coupled system (unit mm)

P

Y

XZ

Figure 5 e main cable-inspection vehicle coupled FE model

Table 2 e parameters of the material used in the coupled FEmodel

Part E (MPa) ] ρ (kgm3)Main cable Rigid body mdash mdashVehicle body 205times105 03 7850Drivingcompression wheel 205times105 03 60000Working platform 69times104 033 4000Equipment box 69times104 033 85000E Youngrsquos modulus ] Poissonrsquos ratio ρ density

Table 3 e parameters of the spring-damping contacts used inthe coupled FE model

Parameters kd (Nmm) cd (Nmiddotsmm) kc (Nmm) cc (Nmiddotsmm)Value 2853 02 1500 02kd and cd are the spring stiffness and viscous damping coefficient of thecontact between the driving wheels and main cable respectively kc and ccare the spring stiffness and viscous damping coefficient of the contactbetween the compressing wheels and main cable respectively

Table 4 e relation between H and αH 5m 35m 65m 95m 113mα 0deg 121deg 168deg 202deg 213deg


where x 1200nV10 k is a coefficient that depends on theroughness of the surface and n is the fluctuating windfrequency

e wind field of suspension bridges in each direction canbe considered as a one-dimensionalm-variable (1D-mV) zero-mean homogeneous random process V(t) [V1(t)

V2(t) Vm(t)]T [23] where T is a transpose indicatorecross power spectral density (CPSD) matrix of V(t) can bedescribed as follows

S(n)

S11(n) S12(n) middot middot middot S1m(n)

S21(ω) S22(n) middot middot middot S2m(n)

⋮ ⋮ ⋱ ⋮

Sm1(n) Sm2(n) middot middot middot Smm(n)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)

e CPSD between any two components Vj(t) and Vp(t)can be expressed as

Siq(n) Sj(n)Sq(n)

1113969cjq(n)e

iθjq(n) (8)

where cjq(n) is the coherence function the Davenportempirical function [33] is used j q 1 2 m and θjq(n) isthe corresponding phase angle [34]

e CPSD matrix can be factorized into the followingproduct with the Cholesky decomposition

S(n) H(n)HTlowast(n) (9)

where the superscript lowast indicates the matrix should beconjugate and H(n) is a lower triangular matrix

According to SRM the fluctuating wind speed for anypoint vj(t) is given as follows [22]

vj(t) 2Δn

radic1113944

j

l11113944

N

k1Hjl nlk( 1113857

11138681113868111386811138681113868

11138681113868111386811138681113868cos nlkt minus θ nlk( 1113857 + ϕlk1113858 1113859

nlk kΔn minus 1 minusl

m1113888 1113889Δn

θ nlk( 1113857 tanminus 1 Im Hlk nlk( 11138571113858 1113859

Re Hlk nlk( 11138571113858 11138591113896 1113897

(10)

where N is the total number of frequency intervalsΔn nuN nu is the cutoff frequency nlk is the double-indexfrequency Hjl (nlk) are the elements of matrix H(n) θ(nlk)is the phase angle of the complex element in H(n) at fre-quency nlk and ϕlk is a random phase angle uniformlydistributed from 0 to 2π

Referring to the JTGT D60-01-2004 standard [35] thebridge site is classified as Class D k is taken as 001291 andthe ground roughness index is taken as 03 Using fastFourier transform (FFT) and the random number generatorin MATLAB wind speed curves in the time domain can besimulated irty-seven simulation points are uniformlydistributed along the length of the bridge deck is paperonly considers the effect of the cross-bridge wind and the

Main cable

Inspection vehicle

Zb

Zv

Yb

Ob

Xb

Yv

Ov

Xv

H

α

(a)

Zv

Z

Xv

Ov

O

Yv

Y

X α

(b)

Figure 6 Coordinate relationship (a) Bridge and vehicle (b) Vehicle and worker

000

005

010

015

020

025

Prob

abili

ty d

ensit

y

measured wind speedLog normal fit (μ = 01700 σ = 03409)

1 2 3 4 5 6 7 8 9 10 11 12 13 140Maximum daily mean wind speed (ms)

Figure 7 Probability distribution of the maximum daily meanwind speed


angle between the incoming wind direction and primaryflow plane is taken as 0deg e simulated fluctuating windspeed time history at the middle-span position (z 10mV10 133ms) for the bridge is presented in Figure 8

32 Wind Load Simulation Wind load on a bridge can beclassified into three parts static wind load buffeting loadand self-excited load Chen et al found that the effect of theself-excited force is limited when the wind speed is lowerthan the design basic wind speed [36] erefore only staticwind load and buffeting load on the bridge are considered inthis paper

e wind loads per unit length including the static windand buffeting loads acting at the elasticity center of thebridge deckcable or acting on the windward nodes of theinspection vehicle are defined as follows

Lw(t) 12ρHCLV(t)

2

Dw(t) 12ρBCDV(t)

2

Mw(t) 12ρB

2CMV(t)

2

(11)

where Lw(t) Dw(t) and Mw(t) are the lift drag and torquewind force respectively ρ is the air density H is the height ofthe bridge deck or diameter of the main cable or windwardprojection height of the inspection vehicle and CL CD andCM are the lift drag and torque wind force coefficients re-spectively All three forces are considered for the deck butonly drag force is considered for the cables and the vehicleAccording to the section model tests of the bridge deck in thewind tunnel completed by Wang et al [37] CL CD and CMfor the deck are taken as 02 15 and 002 respectivelyReferring to the JTGT D60-01-2004 standard [35] CL for thecables and the vehicle are taken as 07 and 18 respectively

4 Comfort Evaluation

With the increasing awareness of human physiological andbehavioral responses to vibration the comfort problem in thevibration environment has extended from the ride comfort ofautomobiles to the operating comfort of engineeringequipment and has received increased attention [38 39] Inthis paper the evaluation method recommended by theISO2631-1-1997 standard [21] is used to evaluate the per-ception and ride comfort of a worker driving an inspectionvehicle under vibration According to the standard the ac-celeration time history signals in all directions transmittedfrom the working platform floor to a worker through the feetare transformed into the frequency domain using FFT efrequency-weighted root mean square (rms) acceleration aw

is determined by weighting and the appropriate addition ofone-third octave band data as follows [21]

aw 1113944k

Wkak( 11138572⎡⎣ ⎤⎦

12

(12)

whereWk is the weighting factor of the kth one-third octaveband given by the ISO 2631-1-1997 standard and ak is therms acceleration of the kth one-third octave band

In orthogonal coordinates the vibration total value ofthe weighted rms acceleration av is calculated by aw in threedirections as follows [21]

av k2xa

2wx + k

2ya

2wy + k

2za

2wz1113872 1113873

12 (13)

where awx awy and awz are the frequency-weighted ac-celerations with respect to orthogonal coordinate axes x yand z respectively and kx ky and kz are the multiplyingfactors given by the ISO 2631-1-1997 standard [21]

e relationship between av and subjective sensorycomfort is shown in Table 5 [21] After calculating av it isconvenient to quantitatively evaluate the ride comfort of theinspection vehicle

5 Results and Analysis

51 Suspension Bridge FE Model Verification e block-Lanczos method was used in the modal analysis of a sus-pension bridge to verify the correctness of the proposedsuspension bridge FE model To measure the modal char-acteristics of the suspension bridge a full-bridge aeroelasticmodel was constructed that was scaled to C 1100 of theoriginal According to the similarity criterion suggested inthe JTGT D60-01-2004 standard [35] the major designparameters of the model are listed in Table 6 e full-bridgeaeroelastic elastic model was composed of the bridge deckmain towers main cables hangers and bases e modelmain beam adopted aluminum chords and plastic diagonalse bridge deck consisted of 37 sections with a 2mm gapbetween each section and a U connection between twosections Each tower contained a steel core beam andwooden boards that provided an aerodynamic shape Steelstrand provided stiffness of cable and an iron block wasenwrapped outside the cable to control the weight Eachhanger consisted of a steel wire without shear stiffness butwith high tension stiffness Lead blocks were used to adjustthe weight of the model and were installed inside the bridgedeck model Plastic boards were used to simulate theaeroelastic shape of the deck rail e test was conducted inthe Industrial Wind Tunnel (XNJD-3) of Southwest JiaotongUniversity as shown in Figure 9 e dynamic response of

Win

d ve

loci

ty (m

s)

8

10

12

14

16

18

20

22

10 20 30 40 50 60 70 80 90 1000Time (s)

Figure 8 Simulated wind speed time history at the middle-spanposition


the model was measured by the forced oscillation method[14] Two laser displacement sensors were used to obtain thevibration signal in the test A comparison of the results of theFE modal analysis and experiment modal test of the first 4vibration modes is presented in Table 7e table shows thatthe modes of vibration are fully consistent and the differ-ence in frequency values is less than 5 erefore the FEmodel of the suspension bridge has high accuracy and caneffectively reflect the dynamic characteristics of the sus-pension bridge

52 Wind-Induced Vibration Response of the Main CableAfter validation the suspension bridge FE model can beused to analyze the vibration characteristics of the maincable with fluctuating winds as the excitation sourceFigure 10 shows the vibration displacement history of thenode at the middle-span position which is 5m above thebridge deck surface in the bridge coordinate systemObmdashXbYbZb e vibration frequency of the main cable is00815 which is consistent with the first-order frequency ofthe suspension bridge e results are also consistent withthe conclusion of Huang et al [40] e main vibrationdirection of the main cable is the Y direction (lateral di-rection) e peak value of the Y-direction vibration dis-placement is 1887mm and the peak values of X-directionand Z-direction vibration displacement are less than01mm erefore only the Y-direction vibration of themain cable node is considered in the study of the wind-induced vibration response in the main cable-inspectionvehicle coupled FE model As the height of the main cablenode increases the constraint on the node from the cablesaddle becomes stronger and the peak value of the Y-di-rection vibration displacement of the node gradually de-creases as shown in Figure 11

53 Wind-Induced Vibration Response of the InspectionVehicle e transient analysis of the main cable-inspectionvehicle coupled FE model was performed with the fluc-tuating wind and the displacement of the main cable nodeas the excitation sources Figure 12 shows the vibrationacceleration time history of the inspection vehicle node P ata height of 5m in the moving coordinate systemOvmdashXvYvZv At this time all the driving wheels andcompressing wheels of the inspection vehicle are in contactwith the main cable e vibration of the inspection vehiclehas a large impact from 0 s to 10 s which is due to theimpact of gravity applied during simulation is phe-nomenon will not occur during the operation of the

inspection vehicle erefore all subsequent accelerationstatistics start from 10 s to maintain accuracy e peakvalue of the X-direction vibration acceleration (axv) at nodeP at a height of 5m is the largest at 786ms2 and the peakvalue of the Z-direction vibration acceleration (azv) is thesmallest at 055ms2 e peak value of the Y-directionvibration acceleration (ayv) is 381ms2 erefore themain vibrations of the inspection vehicle are X-directionvibration and Y-direction vibration

When the inspection vehicle climbs along the maincable the working height (H) and inclination angle (α) of theinspection vehicle increase simultaneously Due to the in-fluence of the constraint on the nodes of the cable from themain cable saddle strength and the increase in the gravitycomponent in the Z direction of the inspection vehicle thepeak values of the X-direction and Y-direction vibrationacceleration of the inspection vehicle gradually decrease andthe peak value of the Z-direction vibration accelerationinitially increases and then decreases as shown in Figure 13

When the inspection vehicle crosses the cable bandthe driving wheels need to be lifted and the compressingwheels need to be alternately opened Lifting the drivingwheels or opening the compressing wheels will change thecoupling relationship between the inspection vehicle andthe main cable and will reduce the contact stiffness be-tween them resulting in simultaneous reductions in themain frequency and the main frequency amplitude asshown in Figure 14 As the number of nonworkingcompression wheels increases the vertical and lateralcontact stiffness values between the inspection vehicle andthe main cable simultaneously decrease resulting in agradual decrease in the peak values of both the X-directionand Y-direction vibration acceleration of the inspectionvehicle and an initial increase and subsequent decrease inthe peak value of the Z-direction vibration acceleration asshown in Figure 15 As the number of nonworking drivingwheels increases the vertical contact stiffness between theinspection vehicle and the main cable decreases resultingin a gradual decrease in the peak value of the X-directionvibration acceleration of the inspection vehicle a non-obvious change in the peak value of the Y-direction vi-bration acceleration and a slow increase in the peak valueof the Z-direction vibration acceleration as shown inFigure 16

54 Ride Comfort Evaluation of the Inspection Vehiclee inspection vehicle is a type of aerial work equipmentVibration of the vehicle can not only induce psychologicalpanic in workers but also affect the work efficiency andhealth of workers [21] erefore it is necessary to analyzethe ride comfort of the vehicle rough coordinate trans-formation the vibration acceleration transmitted to the footof a worker in the inspection vehicle is obtained and thevehicle ride comfort is further analyzed Figure 17 illustratesthe variation curves of the vibration total values of theweighted rms acceleration (av)

Figure 17(a) shows that as the working height of theinspection vehicle increases the value of av decreases

Table 5 Subjective criteria for ride comfort

av (ms2) Comfort level

lt0315 Not uncomfortable0315sim063 A little uncomfortable05sim10 Fairly uncomfortable08sim16 Uncomfortable125sim25 Very uncomfortablegt20 Extremely uncomfortable


slowly first and then sharply and the maximum reductionratio of av is 990 e ride comfort of the inspectionvehicle is improved due to the vehicle acceleration changedescribed in Section 53 When the inspection vehicleworks at the middle-span position (H 5m) the value ofav reaches a maximum of 01478ms2 which is less than0315ms2 and the vehicle ride comfort level is ldquonotuncomfortablerdquo

Figure 17(b) shows that when one pair of compressingwheels at the end of the vehicle is opened the value of av

reaches a maximum of 01646ms2 which is less than0315ms2 us the vehicle comfort level is ldquonot un-comfortablerdquo because as the number of open compressingwheel pairs increases the main frequency of vehicle vi-bration decreases In this case the frequency graduallyapproaches the sensitive frequency of the human body and

the vehicle acceleration changes as described in Section53 As the number of nonworking driving wheels in-creases the value of av slowly decreases and the vehicleride comfort improves due to the decreases in the mainfrequency and amplitude of the main frequency describedin Section 53 When all the driving wheels contact themain cable the value of av is the largest at 01478ms2 lessthan 0315ms2 erefore the vehicle ride comfort level isldquonot uncomfortablerdquo

6 Conclusions

In this paper an FE model of a suspension bridge and acoupled FE model of a main cable-inspection vehicle cou-pled system were established by MIDAS Civil software andANSYS software respectively and the two systems were

Table 6 Major design parameters of the full-bridge aeroelastic model

Parameter Unit Similarity ratio Value of the real bridge Value of the modelLength

Total length of bridge deck (L)

m C

1130 113Width of bridge deck (B) 27 027Height of bridge deck (H) 7 007Height of main tower (Ht) 230 23

StiffnessVertical stiffness of bridge deck EIy

Nm2 C5

139times1012 139times102

Transverse stiffness of bridge deck EIz 458times1013 458times103

Along-bridge direction stiffness of the bottom ofmain tower EIy


Transverse stiffness of the bottom of main tower EIz 1260times1013 1260times103

Figure 9 Test model of the suspension bridge

Table 7 Comparison of vibration modes

Modeno

FrequencyMode of vibration RemarkExperiment modal test

(Hz)FE modal analysis

(Hz)Difference

()

1 00844 00818 31 Symmetric lateralvibration

2 01660 01608 31 Antisymmetric verticalvibration

3 01777 01812 20 Symmetric verticalvibration

4 02435 02542 44 Antisymmetric lateralvibration


connected by the vibration displacement of the main cableAn experimental modal test of the suspension bridge wascompleted and the dynamic responses of both the sus-pension bridge and the inspection vehicle were analyzed

X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250

X directionY directionZ direction

Figure 10 Vibration displacement time history of the node 5mabove the main cable

20 40 60 80 100 120The height of main cable node (mm)

The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250

Figure 11 e peak Y-direction displacement vs the height of themain cable node

10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )

ndash12ndash8ndash404812

axv

ayv

azv

Figure 12 Vibration acceleration time history of the inspectionvehicle at a height of 5m

20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10


Figure 13 Amplitude of vibration acceleration vs the workingheight of the inspection vehicle

5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

0 pair of nonworkingcompressing wheels


2 pairs of nonworkingcompressing wheels


(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)

0 set of nonworkingdriving wheels

1 sets of nonworkingdriving wheels



(b)

Figure 14 One-sided power spectrum density (PSD) of the vi-bration acceleration of the inspection vehicle vs (a) the number ofnonworking compression wheels and (b) the number of non-working driving wheels


using two FE models under fluctuating wind conditionssimulated by MATLAB software e main conclusionsdrawn from the study results are as follows

(1) By comparing the results of the FE modal analysisand modal test of the first 4 vibration modes thevibration modes are fully consistent and the differ-ence in frequency values between them is less than5 e validity of the FE model of the suspensionbridge is verified

(2) rough the transient analysis under fluctuating windconditions the main vibration direction of the maincable is the lateral direction and the main vibrationdirections of the inspection vehicle are the X directionand Y direction e increase in the working heightwill lead to a significant reduction in the vibrationdisplacement amplitude of the main cable node and asignificant reduction in the vibration response of theinspection vehicle An increase in the number ofnonworking compressing wheels or nonworkingdriving wheels will result in a decrease in the main

frequency and slowly reduce the vibration response ofthe inspection vehicle

(3) e vehicle ride comfort evaluation under differentworking conditions shows that an increase in theworking height improves the vehicle ride comfortdue to the reduction in the vibration response of theinspection vehicle e increase in the number ofnonworking compressing wheels affects the vibra-tion amplitude and frequency of the vehicle whichresults in an initial deterioration and subsequentimprovement in vehicle ride comforte increase inthe number of nonworking driving wheels will leadto improved vehicle ride comfort

(4) e vehicle ride comfort analysis shows that whenthe average wind speed of the inspection vehicle isbelow 133ms the maximum value of av for thevehicle is 01646ms2 and the vehicle ride comfortlevel is ldquonot uncomfortablerdquo which meets the usersrsquorequirements

e simulation results presented demonstrate that thenumerical analysis method proposed in this paper can beimplemented to evaluate wind-induced vibration charac-teristics for other similar devices working on the main cableHowever comparisons and experimental tests on the in-fluence of the long-term driving of the inspection vehicle onthe main cable protective layer have yet to be achievedeseissues remain potential topics of future work

0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )

1 2 30Number of nonworking compression wheels (pair)


Figure 15 Amplitude of displacement vs the number of non-working compression wheels of the inspection vehicle

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10

1 2 30Number of nonworking driving wheels (set)


Figure 16 Amplitude of displacement vs the number of non-working driving wheels of the inspection vehicle

a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020

1 2 30Number of nonworking wheels (pair or set)

Compressing wheelDriving wheel

(b)

Figure 17 e variation curves of the av value vs (a) the workingheight and (b) the number of nonworking compressingdrivingwheels


Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by the National Natural ScienceFoundation of China (no 51675450) and the GuizhouScience and Technology Special Project (no 20156001)

References

[1] C Cocksedge T Hudson B Urbans and S Baron ldquoM48severn bridgemdashmain cable inspection and rehabilitationrdquoProceedings of the Institution of Civil EngineersmdashBridge En-gineering vol 163 no 4 pp 181ndash195 2010

[2] M L Bloomstine ldquoMain cable corrosion protection by de-humidification experience optimization and new develop-mentrdquo in Proceedings of the 6th New York City BridgeConference vol 2115 New York City NY USA July 2011

[3] R M Mayrbaurl and S Camo NCHRPV Report 534Guidelines for Inspection and Strength Evaluation of Sus-pension Bridge Parallel Wire Cables Transportation ResearchBoard of the National Academies Washington DC USA2004

[4] H M Kim K H Cho Y H Jin F Liu J C Koo andH R Choi ldquoDevelopment of cable climbing robot formaintenance of suspension bridgesrdquo in Proceedings of 2012IEEE International Conference on Automation Science andEngineering vol 415 Seoul Republic of Korea August 2012

[5] K H Cho Y H Jin H M Kim H Moon J C Koo andH R Choi ldquoCaterpillar-based cable climbing robot for in-spection of suspension bridge hanger roperdquo in Proceedings of2013 IEEE International Conference on Automation Scienceand Engineering vol 217 pp 1059ndash1062 Madison WI USAAugust 2013

[6] F Xu J Shen and G Jiang ldquoKinematic and dynamic analysisof a cable-climbing robotrdquo International Journal of AdvancedRobotic Systems vol 12 no 7 pp 1ndash17 2015

[7] F Xu X Wang and G Jiang ldquoExperimental studies on thedynamic behaviour of a robot cable-detecting systemrdquoTransactions of the Institute of Measurement and Controlvol 38 no 3 pp 338ndash347 2016

[8] Oslash W Petersen O Oslashiseth and E-M Lourens ldquoe use ofinverse methods for response estimation of long-span sus-pension bridges with uncertain wind loading conditionspractical implementation and results for the HardangerBridgerdquo Journal of Civil Structural Health Monitoring vol 9no 1 pp 21ndash36 2019

[9] H Wang A Li T Guo and T Tao ldquoEstablishment andapplication of the wind and structural health monitoringsystem for the Runyang Yangtze River Bridgerdquo Shock andVibration vol 2014 Article ID 421038 15 pages 2014

[10] Y L Xu L D Zhu K Y Wong and K W Y Chan ldquoFieldmeasurement results of Tsing Ma suspension bridge duringtyphoon Victorrdquo Structural Engineering and Mechanicsvol 10 no 6 pp 545ndash559 2000

[11] Q S Li X Li Y He and J Yi ldquoObservation of wind fieldsover different terrains and wind effects on a super-tall

building during a severe typhoon and verification of windtunnel predictionsrdquo Journal of Wind Engineering and In-dustrial Aerodynamics vol 162 pp 73ndash84 2017

[12] H Wang T Tao Y Gao and F Xu ldquoMeasurement of windeffects on a kilometer-level cable-stayed bridge during ty-phoon Haikuirdquo Journal of Structural Engineering vol 144no 9 Article ID 04018142 2018

[13] T Tao H Wang and T Wu ldquoComparative study of the windcharacteristics of a strong wind event based on stationary andnonstationary modelsrdquo Journal of Structural Engineeringvol 143 no 5 Article ID 04016230 2017

[14] G H Li W J Wang X C Ma L B Zuo F B Wang andT Z Li ldquoWind tunnel test study on pipeline suspensionbridge via aeroelastic model with π connectionrdquo Journal ofPipeline Systems Engineering and Practice vol 10 no 1Article ID 04018025 2019

[15] Z Chen C Zhang X Wang and C Ma ldquoWind tunnelmeasurements for flutter of a long-afterbody bridge deckrdquoSensors vol 17 no 2 p 335 2017

[16] Y Li X Xu M Zhang and Y Xu ldquoWind tunnel test andnumerical simulation of wind characteristics at a bridge site inmountainous terrainrdquo Advances in Structural Engineeringvol 20 no 8 pp 1123ndash1223 2017

[17] Y Yang Y Gang FWei andW Qin ldquoBuffeting performanceof long-span suspension bridge based on measured wind datain a mountainous regionrdquo Journal of Vibroengineeringvol 20 no 1 pp 621ndash635 2018

[18] L Zhao and Y Ge ldquoCross-spectral recognition method ofbridge deck aerodynamic admittance functionrdquo EarthquakeEngineering and Engineering Vibration vol 14 no 4pp 595ndash609 2015

[19] Y Bai Y Zhang T Liu T Liu D Kennedy and F WilliamldquoNumerical predictions of wind-induced buffeting vibrationfor structures by a developed pseudo-excitation methodrdquoJournal of Low Frequency Noise Vibration and Active Controlvol 38 no 2 pp 510ndash526 2019

[20] T A Helgedagsrud I Akkerman Y Bazilevs ASCEK M Mathisen and O A Oslashiseth ldquoIsogeometric modelingand experimental investigation of moving-domain bridgeaerodynamicsrdquo Journal of Engineering Mechanics vol 145no 5 Article ID 04019026 2019

[21] International Organization for Standardization ISO 2631-11997 Mechanical Vibration and Shock-Evaluation of HumanExposure to Whole-Body Vibration-Part 1 General Re-quirements International Organization for StandardizationGeneva Switzerland 1997

[22] M Shinozuka and C-M Jan ldquoDigital simulation of randomprocesses and its applicationsrdquo Journal of Sound and Vi-bration vol 25 no 1 pp 111ndash128 1972

[23] T Tao H Wang C Yao X He and A Kareem ldquoEfficacy ofinterpolation-enhanced schemes in random wind field sim-ulation over long-span bridgesrdquo Journal of Bridge Engineeringvol 23 no 3 Article ID 04017147 2018

[24] G Huang H Liao and M Li ldquoNew formulation of Choleskydecomposition and applications in stochastic simulationrdquoProbabilistic Engineering Mechanics vol 34 pp 40ndash47 2013

[25] T Tao H Wang and A Kareem ldquoReduced-Hermite bifold-interpolation assisted schemes for the simulation of randomwind fieldrdquo Probabilistic Engineering Mechanics vol 53pp 126ndash142 2018

[26] Y-L Xu L Hu and A Kareem ldquoConditional simulation ofnonstationary fluctuating wind speeds for long-span bridgesrdquoJournal of Engineering Mechanics vol 140 no 1 pp 61ndash732014


[27] T Tao and H Wang ldquoModelling of longitudinal evolutionarypower spectral density of typhoon winds considering high-frequency subrangerdquo Journal of Wind Engineering and In-dustrial Aerodynamics vol 193 Article ID 103957 2019

[28] G Huang H Zheng Y Xu and Y Li ldquoSpectrum models fornonstationary extreme windsrdquo Journal of Structural Engi-neering vol 141 no 10 Article ID 04015010 2015

[29] F Xu L Wang X Wang and G Jiang ldquoDynamic perfor-mance of a cable with an inspection robotmdashanalysis simu-lation and experimentsrdquo Journal of Mechanical Science andTechnology vol 27 no 5 pp 1479ndash1492 2013

[30] O Alavi A Sedaghat and A Mostafaeipour ldquoSensitivityanalysis of different wind speed distribution models withactual and truncated wind data a case study for KermanIranrdquo Energy Conversion and Management vol 120 pp 51ndash61 2016

[31] V L brano A Orioli G Ciulla and S Culotta ldquoQuality ofwind speed fitting distributions for the urban area of PalermoItalyrdquo Renewable Energy vol 36 no 3 pp 1026ndash1039 2011

[32] A G Davenport ldquoe spectrum of horizontal gustiness nearthe ground in high windsrdquo Quarterly Journal of the RoyalMeteorological Society vol 88 no 376 pp 197-198 2010

[33] A G Davenport ldquoe dependence of wind load upon me-teorological parametersrdquo in Proceedings of the InternationalResearch Seminar on Wind Effects on Building and Structurespp 19ndash82 University of Toronto Press Ottawa CanadaSeptember 1968

[34] M Di Paola and I Gullo ldquoDigital generation of multivariatewind field processesrdquo Probabilistic Engineering Mechanicsvol 16 no 1 pp 1ndash10 2001

[35] Ministry of Transport of the Peoplersquos Republic of China JTGT-D60-01 2004 Wind-Resistent Design Specification forHighway Bridges Ministry of Transport of the Peoplersquos Re-public of China Beijing China 2014

[36] Z Q Chen Y Han X G Hua and Y Z Luo ldquoInvestigationon influence factors of buffeting response of bridges and itsaeroelastic model verification for Xiaoguan Bridgerdquo Engi-neering Structures vol 31 no 2 pp 417ndash431 2009

[37] K Wang H L Liao and M S Li ldquoFlutter performances of along-span suspension bridge with steel trusses based on windtunnel testingrdquo Journal of Vibration and Shock vol 34 no 15pp 175ndash194 2015

[38] M A Abdelkareem M M Makrahy A M Abd-El-TawwabA EL-Razaz M Kamal Ahmed Ali andMMoheyeldein ldquoAnanalytical study of the performance indices of articulatedtruck semi-trailer during three different cases to improve thedriver comfortrdquo Proceedings of the Institution of MechanicalEngineers Part K Journal of Multi-Body Dynamics vol 232no 1 pp 84ndash102 2018

[39] M Stankovic A Micovic A Sedmak and V PopovicldquoAnalysis of comfort parameters in special purpose vehiclesfrom technological development point of viewrdquo TehnickivjesnikmdashTechnical Gazette vol 25 no 2 pp 502ndash509 2018

[40] G Q Huang Y W Shu L L Peng C M Ma H L Liao andM S Li ldquoResponse analysis of long-span suspension bridgeunder mountainous windsrdquo Journal of Southwest JiaotongUniversity vol 50 no 4 pp 610ndash616 2015


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



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



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

bottom of the vehicle body to increase the rigidity of thevehicle body e inspection vehicle adopts automaticcontrol technology to perform the alternate lifting andlowering of the driving wheels the advancing and retractingof the compressing wheels the rotating of flaps and theswitching of lock devices by controlling the hydraulic cyl-inders to straddle obstacles such as cable bands and hangerse vehicle can identify cable bands automatically climbcable bands actively and crawl at a large angle (30deg) whenmanned

e inspection vehicle drives on the main cable whichis a typical wind-sensitive structure Wind-induced vi-bration directly affects the security of equipment and theefficiency of workers [7] erefore the dynamic prop-erties of the main cable-inspection vehicle coupled systemunder wind loads should be studied when the inspectionvehicle is designed Researchers have conducted numerousfield measurements to investigate the wind-induced vi-bration characteristics of suspension bridges [8ndash10] Fieldmeasurement is the most direct and reliable method toobtain site wind data [11ndash13] However this approachrequires a long period and is easily affected by environ-mental conditions Li et al [14] Chen et al [15] and Liet al [16] investigated the wind characteristics of differentbridge sites through wind tunnel tests to provide a basis forbridge design Although this method is not affected by thegeographical environment accurate models must be builtand the cost can be extremely expensive With the de-velopment of theoretical studies and computer technologysimulation experiments have been increasingly used tostudy the effects of various factors on bridge componentsat the initial stage of the research work to reduce thenumber of field measurements and tunnel tests [17 18]Field measurements and tunnel tests are usually used forfinal validation Bai et al [19] and Helgedagsrud et al [20]performed and validated simulation experiments bycomparing different simulation results with those of windtunnel tests However these studies focused on the wind-induced vibration of suspension bridges and few studieshave focused on the wind-induced vibration of mobiledevices on the main cable

e inspection vehicle was developed in the specializedfield of mobile robots In most previous studies researchersfocused on the design and vibration caused by the climbingof robots Kim et al [4] and Cho et al [5] manufactured awheel-based robot and a caterpillar-based robot for theinspection of a hanger rope and the climbing abilities ofboth robots were validated in indoor experimental envi-ronments Xu et al [6] designed a cable-climbing robot forcable-stayed bridges and the obstacle-climbing performanceof each robot was simulated and validated in the laboratoryHowever these robots are all tiny unmanned robots andonly structural safety must be considered For a mannedinspection vehicle the vibration of the vehicle may causediscomfort or annoy the workers and influence performance[21]ese factors must be studied in the design processewind-induced vibration of the inspection vehicle is acomplicated solid-wind-cable interaction problem and thecorresponding actionmechanism has not yet been effectivelystudied

e simulation of a random wind field is essential fortime-domain vibration analysis of the inspection vehicleunder wind loads Based on the Monte Carlo method thedigital filtering method and the spectral representationmethod (SRM) [22] are two basic approaches used tosimulate the random wind field SRM the method adoptedin this paper has been widely used in the engineeringcommunity due to its accuracy and simplicity [23 24] Inorder to improve the efficiency of SRM for the simulation ofmultidimensional wind fields Tao et al [23 25] Huang et al[24] and Xu et al [26] proposed different optimizationmethods for solving With the development of sensortechnology the study of wind fields has gradually beenextended from stationary fields to nonstationary fields es-pecially for extreme wind [27 28] However no empiricalmodel is available for nonstationary winds due to the dif-ficulties in mathematical treatments and nonergodic char-acteristics [28] erefore stationary wind is the objective ofthis paper

e purpose of this paper is to propose a method ofassessing the vibration response of a main cable-inspectionvehicle coupled system under fluctuating wind conditions

(a)

Guardrail

Cable band stanchi

Vehicle boday

Driving wheel

Working platform

Main cable

Cable band

Compressing wheel

Equipment box

Revolving plateLock device Hanger

(b)

Figure 1 (a) An inspection vehicle for a main cable (b) Structure of the vehicle













Dxv minus Dyb



(1)





ax axv



(2)





V(t) V + v(t) (3)


258 345

113

Zb

Xb

178 + 72 times 152 + 178 = 1130


Main cable

Hanger


Anchorage







f(V) 1

Vσ2π


2σ21113896 1113897 (4)



μ 1

M1113944

M

i1ln vi( 1113857

σ

1M

1113944

M

i1ln vi( 11138571113858 1113859

2

11139741113972 (5)




Sv(n) 4kV210

x2

n 1 + x2( )43 (6)

3540

3110 35

40

1926

472

800

600

600

600 500 500 500 500

24002400

800 600 600800

18161344

3110

S1

S2

S6

S1

S7

S5

S4

S1 S2 S3 S3 S8 S6 S7

3726

kd

kc

cd

cc

3

40 60 80

22 5

120

120

40 60 80

236

45402400 2913

749

120

8

88

8

88

kd cd

S3




P

Y

XZ











S(n)



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


Siq(n) Sj(n)Sq(n)

1113969cjq(n)e

iθjq(n) (8)






vj(t) 2Δn

radic1113944

j

l11113944

N

k1Hjl nlk( 1113857

11138681113868111386811138681113868



m1113888 1113889Δn


Re Hlk nlk( 11138571113858 11138591113896 1113897

(10)



Main cable

Inspection vehicle

Zb

Zv

Yb

Ob

Xb

Yv

Ov

Xv

H

α

(a)

Zv

Z

Xv

Ov

O

Yv

Y

X α

(b)


000

005

010

015

020

025

Prob

abili

ty d

ensit

y








Lw(t) 12ρHCLV(t)

2

Dw(t) 12ρBCDV(t)

2

Mw(t) 12ρB

2CMV(t)

2

(11)





aw 1113944k

Wkak( 11138572⎡⎣ ⎤⎦

12

(12)



av k2xa

2wx + k

2ya

2wy + k

2za

2wz1113872 1113873

12 (13)





Win

d ve

loci

ty (m

s)

8

10

12

14

16

18

20

22

10 20 30 40 50 60 70 80 90 1000Time (s)



















6 Conclusions





m C



Nm2 C5








Modeno



(Hz)Difference

()







X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













Dxv minus Dyb



(1)





ax axv



(2)





V(t) V + v(t) (3)


258 345

113

Zb

Xb

178 + 72 times 152 + 178 = 1130


Main cable

Hanger


Anchorage







f(V) 1

Vσ2π


2σ21113896 1113897 (4)



μ 1

M1113944

M

i1ln vi( 1113857

σ

1M

1113944

M

i1ln vi( 11138571113858 1113859

2

11139741113972 (5)




Sv(n) 4kV210

x2

n 1 + x2( )43 (6)

3540

3110 35

40

1926

472

800

600

600

600 500 500 500 500

24002400

800 600 600800

18161344

3110

S1

S2

S6

S1

S7

S5

S4

S1 S2 S3 S3 S8 S6 S7

3726

kd

kc

cd

cc

3

40 60 80

22 5

120

120

40 60 80

236

45402400 2913

749

120

8

88

8

88

kd cd

S3




P

Y

XZ











S(n)



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


Siq(n) Sj(n)Sq(n)

1113969cjq(n)e

iθjq(n) (8)






vj(t) 2Δn

radic1113944

j

l11113944

N

k1Hjl nlk( 1113857

11138681113868111386811138681113868



m1113888 1113889Δn


Re Hlk nlk( 11138571113858 11138591113896 1113897

(10)



Main cable

Inspection vehicle

Zb

Zv

Yb

Ob

Xb

Yv

Ov

Xv

H

α

(a)

Zv

Z

Xv

Ov

O

Yv

Y

X α

(b)


000

005

010

015

020

025

Prob

abili

ty d

ensit

y








Lw(t) 12ρHCLV(t)

2

Dw(t) 12ρBCDV(t)

2

Mw(t) 12ρB

2CMV(t)

2

(11)





aw 1113944k

Wkak( 11138572⎡⎣ ⎤⎦

12

(12)



av k2xa

2wx + k

2ya

2wy + k

2za

2wz1113872 1113873

12 (13)





Win

d ve

loci

ty (m

s)

8

10

12

14

16

18

20

22

10 20 30 40 50 60 70 80 90 1000Time (s)



















6 Conclusions





m C



Nm2 C5








Modeno



(Hz)Difference

()







X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




ax axv



(2)





V(t) V + v(t) (3)


258 345

113

Zb

Xb

178 + 72 times 152 + 178 = 1130


Main cable

Hanger


Anchorage







f(V) 1

Vσ2π


2σ21113896 1113897 (4)



μ 1

M1113944

M

i1ln vi( 1113857

σ

1M

1113944

M

i1ln vi( 11138571113858 1113859

2

11139741113972 (5)




Sv(n) 4kV210

x2

n 1 + x2( )43 (6)

3540

3110 35

40

1926

472

800

600

600

600 500 500 500 500

24002400

800 600 600800

18161344

3110

S1

S2

S6

S1

S7

S5

S4

S1 S2 S3 S3 S8 S6 S7

3726

kd

kc

cd

cc

3

40 60 80

22 5

120

120

40 60 80

236

45402400 2913

749

120

8

88

8

88

kd cd

S3




P

Y

XZ











S(n)



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


Siq(n) Sj(n)Sq(n)

1113969cjq(n)e

iθjq(n) (8)






vj(t) 2Δn

radic1113944

j

l11113944

N

k1Hjl nlk( 1113857

11138681113868111386811138681113868



m1113888 1113889Δn


Re Hlk nlk( 11138571113858 11138591113896 1113897

(10)



Main cable

Inspection vehicle

Zb

Zv

Yb

Ob

Xb

Yv

Ov

Xv

H

α

(a)

Zv

Z

Xv

Ov

O

Yv

Y

X α

(b)


000

005

010

015

020

025

Prob

abili

ty d

ensit

y








Lw(t) 12ρHCLV(t)

2

Dw(t) 12ρBCDV(t)

2

Mw(t) 12ρB

2CMV(t)

2

(11)





aw 1113944k

Wkak( 11138572⎡⎣ ⎤⎦

12

(12)



av k2xa

2wx + k

2ya

2wy + k

2za

2wz1113872 1113873

12 (13)





Win

d ve

loci

ty (m

s)

8

10

12

14

16

18

20

22

10 20 30 40 50 60 70 80 90 1000Time (s)



















6 Conclusions





m C



Nm2 C5








Modeno



(Hz)Difference

()







X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




f(V) 1

Vσ2π


2σ21113896 1113897 (4)



μ 1

M1113944

M

i1ln vi( 1113857

σ

1M

1113944

M

i1ln vi( 11138571113858 1113859

2

11139741113972 (5)




Sv(n) 4kV210

x2

n 1 + x2( )43 (6)

3540

3110 35

40

1926

472

800

600

600

600 500 500 500 500

24002400

800 600 600800

18161344

3110

S1

S2

S6

S1

S7

S5

S4

S1 S2 S3 S3 S8 S6 S7

3726

kd

kc

cd

cc

3

40 60 80

22 5

120

120

40 60 80

236

45402400 2913

749

120

8

88

8

88

kd cd

S3




P

Y

XZ











S(n)



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


Siq(n) Sj(n)Sq(n)

1113969cjq(n)e

iθjq(n) (8)






vj(t) 2Δn

radic1113944

j

l11113944

N

k1Hjl nlk( 1113857

11138681113868111386811138681113868



m1113888 1113889Δn


Re Hlk nlk( 11138571113858 11138591113896 1113897

(10)



Main cable

Inspection vehicle

Zb

Zv

Yb

Ob

Xb

Yv

Ov

Xv

H

α

(a)

Zv

Z

Xv

Ov

O

Yv

Y

X α

(b)


000

005

010

015

020

025

Prob

abili

ty d

ensit

y








Lw(t) 12ρHCLV(t)

2

Dw(t) 12ρBCDV(t)

2

Mw(t) 12ρB

2CMV(t)

2

(11)





aw 1113944k

Wkak( 11138572⎡⎣ ⎤⎦

12

(12)



av k2xa

2wx + k

2ya

2wy + k

2za

2wz1113872 1113873

12 (13)





Win

d ve

loci

ty (m

s)

8

10

12

14

16

18

20

22

10 20 30 40 50 60 70 80 90 1000Time (s)



















6 Conclusions





m C



Nm2 C5








Modeno



(Hz)Difference

()







X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





S(n)



⋮ ⋮ ⋱ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


Siq(n) Sj(n)Sq(n)

1113969cjq(n)e

iθjq(n) (8)






vj(t) 2Δn

radic1113944

j

l11113944

N

k1Hjl nlk( 1113857

11138681113868111386811138681113868



m1113888 1113889Δn


Re Hlk nlk( 11138571113858 11138591113896 1113897

(10)



Main cable

Inspection vehicle

Zb

Zv

Yb

Ob

Xb

Yv

Ov

Xv

H

α

(a)

Zv

Z

Xv

Ov

O

Yv

Y

X α

(b)


000

005

010

015

020

025

Prob

abili

ty d

ensit

y








Lw(t) 12ρHCLV(t)

2

Dw(t) 12ρBCDV(t)

2

Mw(t) 12ρB

2CMV(t)

2

(11)





aw 1113944k

Wkak( 11138572⎡⎣ ⎤⎦

12

(12)



av k2xa

2wx + k

2ya

2wy + k

2za

2wz1113872 1113873

12 (13)





Win

d ve

loci

ty (m

s)

8

10

12

14

16

18

20

22

10 20 30 40 50 60 70 80 90 1000Time (s)



















6 Conclusions





m C



Nm2 C5








Modeno



(Hz)Difference

()







X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Lw(t) 12ρHCLV(t)

2

Dw(t) 12ρBCDV(t)

2

Mw(t) 12ρB

2CMV(t)

2

(11)





aw 1113944k

Wkak( 11138572⎡⎣ ⎤⎦

12

(12)



av k2xa

2wx + k

2ya

2wy + k

2za

2wz1113872 1113873

12 (13)





Win

d ve

loci

ty (m

s)

8

10

12

14

16

18

20

22

10 20 30 40 50 60 70 80 90 1000Time (s)



















6 Conclusions





m C



Nm2 C5








Modeno



(Hz)Difference

()







X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















6 Conclusions





m C



Nm2 C5








Modeno



(Hz)Difference

()







X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



X Z

-disp

lace

men

t (m

m)

ndash005

000

005

010

015

020

025

20 40 60 80 1000Time (s)

Y-di

spla

cem

ent (

mm

)

ndash50

0

50

100

150

200

250




The p

eak

of Y

-dire

ctio

ndi

spla

cem

ent (

mm

)

0

50

100

150

200

250


10 20 30 40 50 60 70 80 90 1000Time (s)

Acc

eler

atio

n (m

s2 )


axv

ayv

azv


20 40 60 80 100 120H (m)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10



5 10 15 20 250Frequency (Hz)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06





(a)

Am

plitu

de o

f acc

eler

atio

n (m

s2 )

00

02

04

06

5 10 15 20 250Frequency (Hz)





(b)










0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









0

2

4

6

8

10

Am

plitu

de o

f acc

eler

atio

n(m

s2 )




Am

plitu

de o

f acc

eler

atio

n (m

s2 )

0

2

4

6

8

10




a v(m

s2 )

000

005

010

015

020

20 40 60 80 100 1200H (m)

(a)

a v(m

s2 )

000

005

010

015

020



(b)



Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Wind-InducedVibrationResponseofanInspection...

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Transcript of Wind-InducedVibrationResponseofanInspection...