Design of TMD with nonlinear viscous fluid dampers with varying damping for6-Storey building with...

7/26/2019 Design of TMD with nonlinear viscous fluid dampers with varying damping for6-Storey building with two different

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JOURNAL OF STRUCTURAL ENGINEERING 169

Vol. 43, No. 2, JUNE - JULY 2016

Journal of Structural Engineering

Vol. 43, No. 2, June - July 2016 pp. 169-178 No. 43-1

Design of TMD with nonlinear viscous uid dampers with varying damping for

6-Storey building with two different structural damping

K. Rama Raju*,, M. Deepthi*, R.R. Aathish Narayanan* and V. Bhaskar Desai**

Email: [email protected]

*CSIR-Structural Engineering Research Centre, CSIR-Campus, Taramani, Chennai - 600113, INDIA.

**Department of civil Engineering, Jawaharlal Nehru Technological University Anantapuramu College of Engineering, Anantapuramu - 515 002, INDIA.

Received: 14 July 2015; Accepted: 03 August 2015

KEYWORDS: TMD; time histories; optimum tuning parameters; peak responses.

One of the main challenges faced by the structural

engineering, of the present decade is the necessity

to develop innovative design methods to protect the

civil engineering structures from damages, including

the material contents and human occupants, from the

hazards of strong earthquake and high wind loads.

Under these external excitations, undesirable vibrations

in a structure can be reduced by means of vibration

control systems.

Strong earthquakes cause damage to structures

and infrastructure. To reduce this seismic risk various

types of structural control technologies have been

developed to solve the safety and functional problems

for structures under the excitation of external forces

The vibration control methods include passive, active

semiactive, and the factors that affect the selection of

particular type of vibration control device are efciency

compactness and weight, capital cost and safety. Thi

makes earthquake actions fundamentally differenfrom any other imposed loads. Generally structure

have small stiffness and possess low inherent structura

damping. Due to excessive vibrations which may resul

in fatigue, damage or even failure of structures and lead

to overall failure of structure. The primary objectiv

of earthquake resistant design is to prevent building

collapse during earthquakes. Thus minimizing the risk

Dampers have become more popular for vibration control of structures, because of their safe, effective and economical

design. Tuned mass damper (TMD) is the most popular passive type of control system especially for buildings subjected

to earthquake/ high winds. The properties of the TMD required for optimum performance depends on stiffness, mass

and damping distribution of the structure/building or their components need to be isolated from vibrations. From

experimental results, the optimum parameters such as optimum tuning ratio (f) and optimum damping ratios (d) for

TMD were derived by two types of analytical formulations. A 6-Storey steel framed building with TMD is modeled in

3D using SAP2000. The 6-Storey building model is reduced to 6 DOF system and optimum parameters of TMD are

computed using the methods by two types of formulations. Two analytical formulation are found to give same optimum

tuning ratio, but optimum effective damping ratio are found to be differing. With the optimum tuning ratio and the

parameters of TMD obtained by the two methods, the damping in TMD is varied using nonlinear viscous uid dampers

(NVFD) for nding the responses of building in X-direction subjected to one near eld earthquake excitation (El Centro

with PGA of 4.417 m/s2) and two far eld earthquake excitations (Northridge, Kobe with PGA of 8.2676 and 8.1782 m/s2

respectively) with their PGA normalized to 0.35g. The effectiveness of the TMD in reducing the responses of structures

for two different structural damping of 2% and 5% by increasing effective damping of NVFD in TMD from 0.05 to 0.25is found.


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170 JOURNAL OF STRUCTURAL ENGINEERING


of death or injury to people in or around those buildings.

Conventional seismic design of structures relies on the

inherent ductility of the structure to dissipate seismic-

generated vibration energy while accepting a certain

level of structural damage. Recent R&D efforts are

directed to develop methods to enhance the structural

energy absorption capacity while avoiding/minimizing

damage in structural components.Passive dampers have become more popular

recently for vibration control of structures, because of

their safe, effective and economical design. TMD is

one of the most popular passive type of control system

especially for buildings subjected to earthquake/wind

loads. TMD is a passive energy absorbing device

consisting of a mass, a spring and a viscous damper

attached to a structure in order to reduce the dynamic

response of the structure. The inertial, resilient, and

dissipative elements in TMD are mass, spring and

dashpot (or material damping) for linear applications

and their rotary counterparts in rotational applications.

Depending on the application, these devices are sized

from a few grams to many tons. Other congurations

such as pendulum absorbers/dampers, and sloshing

liquid absorbers/dampers have also been realized for

vibration mitigation applications.

The TMD concept was rst applied by Frahm1 in

1909 to reduce the rolling motion of ships as well as

ship hull vibrations. A theory for the TMDwas presented

later in the paper by Ormondroyd and Den Hartog2

in1928 and a detailed discussion of optimal tuning and

damping parameters was given by Den Hartog3. The

natural frequency of the damper is tuned to a frequency

near to the natural frequency of main system. The

vibration of main system causes the TMDto vibrate in

resonance and results in vibration energy dissipation

through damping of TMD. Taniguchi et al.4investigated

the effectiveness of tuned mass damper on base

isolated structure to reduce displacement demand and

determines optimal parameters for the design of Tuned

Mass Dampers (TMD). Both base isolated structureand TMD are modeled as single degree of freedom

and linear oscillators. To determine the response of

base isolated structure with and without TMD when

it is subjected to white noise base acceleration using

stochastic analysis is used. Stochastic dynamic analysis

reveals that depending on mass, damping and frequency

characteristics of TMD, displacement demand on the

base isolated structure can be reduced by 15-25%. It is t

be shown that TMDis more effective for lightly damped

isolators. Time history analysis is also carried out for fa

and near eld ground motions of base isolated structur

with and without TMD. Variation of accelerations an

displacements for six different types of earthquakes ar

shown for far and near eld ground motions. Result

shows that the effectiveness of TMDfor far eld groundmotion is similar to that predicted by stochastic analysis

For near eld ground motions, the effectiveness of TMD

is not more than 10%. Jangid and Datta5 presente

the dynamic response behavior of structure which i

torsionally coupled with Multiple Tuned Mass Damper

(MTMD) subjected to lateral seismic excitations tha

is modeled as broad band stationary random process

It describes that Multiple Tuned Mass Damper i

more advantageous than single TMD because of it

sensitivity to error in calculating natural frequency. Th

effectiveness of a TMDis reduced signicantly by notuning to optimum damping in TMD. Objective of thei

study is to differentiate between dynamic behaviors o

torsionally coupled and uncoupled system withMTMD

to investigate how the optimum frequency bandwidth

for translational and torsional responses of torsionally

coupled system varies. A simple eccentric model i

considered having 2DOF and parametric study is als

considered to investigate the effectiveness of MTMD

on reducing the response of torsionally coupled system

It is shown that effectiveness of MTMDin controlling

translational response is less for an asymmetric system

than symmetric system, if it is designed withou

considering the effects of torsional coupling, since, th

effectiveness of MTMD is overestimated. Optimum

frequency bandwidth ofMTMDchanges with change in

eccentricity of asymmetric system, if it is computed by

ignoring torsional coupling may not control the respons

of asymmetric building. The increase in damping o

MTMDdecreases optimum frequency bandwidth which

leads to reduction in the effectiveness ofMTMD.

In the present study, a design methodology ipresented for the design of TMD using NVFD for

6-Storey 3D steel building using SAP2000 (Fig. 1). Th

building 3D model (Fig. 2) is reduced to MDOF system

with 6 degrees of freedom (Fig. 3). The mass ratio () o

the tuning damper is assumed to be 0.01. The optimum

parameters of TMDfor the model, tuning ratio (f) an

damping ratio (d) are computed using the method


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given by Tsai et al.6 and Sadek et al.7with structural

damping () 0.02 and 0.05. From these parameters,

corresponding, mass of the TMD (md), frequency of

damper (d), stiffness of damper (kd) and damping

of damper (cd) are found by the two methods. Except

damping ratio (opt) all other parameters with both the

methods are found to be almost equal. Even through the

Optimum damping ratio (opt) obtained by two methodsare varying, for structural damping (), 0.02 and 0.05

the tuning ratio, mass of the damper, frequency of the

damper, stiffness of TMDare found to be almost same for

both the methods (Tables 1-2). ThePGAof the 6-storey

building where building located is assumed to be 0.35. In

the present study, the effective damping ratio of TMDis

varied inNVFDfrom 0.05 to 0.25 base shears are found

using nonlinear modal time history analysis of 6-Storey

building in X-direction is subjected the two near eld

earthquake excitation (El Centro with PGA of 4.417 m/

s2) and two far eld earthquake excitations (Northridge,Kobe withPGAof 8.2676 and 8.1782 m/s2respectively)

with PGA normalized to 0.35g using SAP2000. It is

observed that, the base shear reduction beyond effective

damping 0.25 is negligible. The peak responses such as

displacement, acceleration and inter-storey drifts along

the height of the building with TMD with effective

damping of 0.25 are found. The percentage of reduction

in peak displacements, accelerations and inter-storey

drifts in 6-Storey building in X-direction with structural

damping 0.02 and 0.05 subjected to the one near eld

earthquakes (El Centro) and two far eld earthquake

excitation (Northridge, Kobe) with PGA normalized to

0.35 inX- direction usingNVFDwith effective damping

of 0.25 are compared.

DESIGN OF TMD FOR 6-STOREY BUILDING

WITH 0.02 AND 0.05 STRUCTURAL DAMPING

A 6-Storey steel building as bare frame/with pendulum

type TMD taken from Tuned Mass Damper is taken

for study9. A 6-Storey steel building frame with Tuned

Mass Damper (TMD) is simplied as multiple degree

of freedom (6 DOF) system with (TMD) as shown in

Fig. 38,9. Since, earthquake accelerations are taken in

X-direction, the properties of the building corresponding

to translation mode corresponding to X-direction are

taken, i.e., fourth mode in 3D model for modelling the

6DOFbuilding model. The plan and elevation of 3D

model are shown in Fig. 1.

TABLE 1

RANGE OF PARAMETERS CONSIDERED IN THE

PRESENT STUDY

Structure Type Steel Framed Structure

No. of storey G+5

Typical storey height 3 m

Seismic zone V

Soil Type Medium

Material Properties

Young modulus of concrete,Ec 25 106kN/m2

Poissons Ratio concrete 0.2

Density of Concrete 24 kN/m3

Young modulus of steel,Es 2 108 kN/m2

Poissons Ratio steel 0.3

Density of Steel 76.8 kN/m3

Section Properties

Primary beam W27102Secondary beam W1430

Column W14193

Thickness of slab (shell) 250mm

Thickness of wall (shell) 250mm

Thickness of plank (membrane) 250mm

Thickness of deck (membrane) 88.9mm

The properties of the TMD required for optimum

performance depends on stiffness, mass and dampin

distribution of the structure/building or their component

need to be isolated from vibrations. The performancof the building with TMDvary with the characteristic

of the excitations such as frequency of excitations and

near eld and far eld. From experimental results, th

optimum parameters such as optimum tuning ratio (f

and optimum damping ratios (d) for TMDwere derive

by Tsai et al.6and Sadek et al.7are used and results ar

tabulated in Table 2. Using these formulations, for a 6

DOFmodel of the building9, the optimum parameter

such as optimum tuning ratio (f) and optimum damping

ratios (d) for TMD are found. The optimum tuning

(frequency) ratio for two structural damping ratios (

is almost same, but optimum damping ratio for Sadek

et al. for effective structural damping () 0.02 and 0.0

are found to be more in comparison with Tsai et al6

Only for deriving optimum parameters for TMD,

DOFthe model given in Fig. 2 is used8. The damping

matrix C in Eq. (3) is required, if the responses of

DOFsystem are required. Since, response calculation


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are calculated with optimum damping parameters

obtained by two method by varying damping using

NLVDusing 3D model, the damping matrix C in Eq.

(3) is not used.

Secondary

beam (W14 30)

Main

Beam (W27 102)

Column section

(W14 193)

2@6m

2@6m

6@3m

2@6m

Plan

Elevation

y

x

Fig. 1 Plan and elevation view of six storey building

Fig. 2 3D model of 6-Storey building with TMD

Instead of using optimum damping ratios, damping

ratios with variation from 0.05 to 0.25 with an incremen

of 0.05 is applied using NVFD. The response ratio

of base shear with increasing effective damping fo

the 3D model of building subjected to one near eld

earthquake excitation (El Centro and Taft) and one fa

eld excitation (Northridge) reduced to PGA of 0.35g

in X-direction are shown in Fig. 4. At effective thexcitations damping of 0.25 the reduction in base shea

for both is maximum.

u1+u

g u

2+u

g u

3+u

g u

4+u

g u

5+u

g u

6+u

g u

6+u

g+u

dug

k1

m1

m2

m3

m4

m5

m6

md

p1

k2

p2

k3

p3

k4

p4

k5

p5

k6

p6

kd

c1

c2

c3

c4

c5

c6

cd

6DOF system with TMD

Fig. 3 6-Storey building model with TMD

Note: m1, m2, m3, m4, m5and m6 = Mass of each storey; k1

k2, k3, k4, k5and k6= Stiffness of each storey; c1, c2, c3, c4c5and c6= Damping of each storey;p1,p2,p3,p4,p5andp

= Force acting on primary mass.

At effective damping of TMD, 0.25, the respons

reductions in roof displacement, acceleration response

of the 6-Storey building inX-direction with and withou

TMD with optimum tuning frequency subjected to

three different ground excitations, i.e., El Centro, Kob

and Northridge inX-direction with PGA normalized to

0.35g and compared the same using the two damping

ratios of structure (0.02 and 0.05). The methodology

involves the nonlinear time history modal analysis o

building with/without TMDwithNVFD.

Mass of each storey, m= 56650 kN-s2/m

Column Section = W14193

Elastic modulus of steel = 2.07 108kNm2

Moment of inertia of section = 0.0009984m4

Length of each storey = 3m

Number of columns in each storey (n) = 9

Stiffness of each storey, k = n12EI/L3= 826700.

kN/mMasses of rst 5 storey (m1, m2, m3, m4and m5) ar

assumed to be m and mass of six oor (m6) is assumed

to be half the other storey, i.e., m/2;

All storey have the same stiffness of all storey (k1k2, k3, k4, k5and k6) are assumed to be equal to k; Mas

and stiffness matrix of 6-Storey building [M] and [K

are as given below:


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M

m

m

m

m

m

m

1

2

3

4

5

6

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

(1)

(2)

Time period in rst mode, T1 = 0.2075s

Structural effective damping of the building assume

to be two types, they are 1 = 0.05 and 1 = 0.02

Damping is assumed to be proportional to stiffness

cx = Kand where,

T1 ; For two cases, is varied

as 0.02 and 0.05.

All stories (c1, c2, c3, c4, c5 and c6) have th

same damping for two types of structural damping

considered; Corresponding structural damping matrix

is found using Eq. (3)

=

1 + 2 2 0 0 0 0

2 2 + 3 3 0 0 0

0 3 3 + 4 4 0 0

0 0 4 4 + 5 5 0

0 0 0 5 5 + 6 6

0 0 0 0 6 6

(3

0.80

0.85

0.90

0.95

1.00

0.05 0.10 0.15 0.20 0.25

Baseshearresponseratio

Effective Damping of TMD (

Base shear response ratio vs effective damping

for =0.02

Base shear response ratio vs effective damping

for =0.05

Base shear vs effective damping for =0.02 Base shear vs effective damping for =0.05

d

)

d) d)

d)

Structural damping(2%)

NR EL KO

0.90

0.92

0.94

0.96

0.98

1.00

0.05 0.10 0.15 0.20 0.25

Baseshearresponseratio



NR EL KO

2000

2500

3000

3500

4000

4500

5000

0.00 0.05 0.10 0.15 0.20 0.25

Bas

eshear(kN)



NR EL KO

2000

2200

2400

2600

2800

3000

3200

3400

3600

0.00 0.05 0.10 0.15 0.20 0.25

Bas

eshear(kN)



NR EL KO

Fig. 4 Variation of base shear and base shear response ratios with different effective dampings (d) in TMD


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Properties of six storey frame:

Mass ratio () = 0.01; Damping ratios considered

for the structure () =0.02 and 0.05

First mode of the 6 DOF corresponds to translation

bending mode in X-direction (4thmode) of 3D model

of the building SAP2000 model, the natural frequencies

of the same are given in Table 2.

Mode shape, 1 = [(0.002 0.0038 0.0053 0.0065

0.0073 0.0075)]T

Modal participation factor = Pm

mk

i

i

2163 012.

Modied mode shape, mod = Pk 1 = [(0.320.6194 0.8640 1.0596 1.19 1.2226)]T

TABLE 2

NATURAL FREQUENCY OF STRUCTURE IN FIRST

MODE,1

SAP 3D-Model 6 DOF Model

30.3 rad/s 4.82 Hz 31.28 rad/s 4.98 Hz

0

1

2

3

4

5

6

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Floor

Peak Displacement (m) at =0.25

WD_0.05

BF_0.05

WD_0.02

BF_0.02

1

1.52

2.5

3

3.5

4

4.5

5

5.5

6

0.0 0.2 0.4 0.6 0.8 1.0

Floor

Displacement (m) at = 0.25

Displacement RR_ 0.02

Displacement RR_ 0.05

0

1

2

3

4

5

6

0 5 10 15 20

Floor

Peak acceleration (m/s2) at = 0.25

BF_0.02BF_0.05WD_0.02WD_0.05

1

2

3

4

5

6

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Floor

Acceleration response ratio at = 0.25

Accleration RR_0.02Acceleration RR_0.05

0

1

2

3

4

5

6

0.004 0.014 0.024 0.034 0.044

Floor

Peak inter-storey drifts(m)

BF_0.02

BF_0.05

WD_0.02

0

1

2

3

4

5

6

0.92 0.94 0.96 0.98 1.00

F

loor

Peak inter-storey drift response ratio

at = 0.25

DRIFT RR_0.02DRIFT RR_0.05

Fig. 5 Peak response and response ratios (RR) at d= 0.25


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mod corresponds to maximum unit modal

participation factor, Pm

mk

mod

mod

21

First mode maximum amplitude, max = 1.2226

(maximum or dinote infmod)

TMD design for damped structure

The damper parameters, Mass ratio, m

M

d

; Mass of

damper m M M d mod T

mod

First mode maximum amplitude = max; Frequency

of damper, d= fi, where i = mode number, Stiffness

of damper, kd= mdd2; Damping of damper, cd= 2d

dmd

Tsai and Lin6 suggest equations for the optimal

parameters i.e., frequency ratio (f) and damping ratio

(d) of TMDfor SDOF is determined by curve tting

schemes by Eqs. (4) and (5)8,

f

1 0 5

11 2 1 2 375 1 034 0 426

3 73 1

2.

. . .

.

66 903 20 4962

. . (4)

d

3

8 1 1 0 50 151 0 170

0 163 4 98

2

2

.. .

. .

(5)

For nding tuning ratio (f) forMDOF,is replacedwith max in Eq. (4) and the damping ratio (d) in

Eq. (5) is multiplied with max, the parameters are

modied as given in Eqs. (6-7).

f

max

max

max

1 0 5

11 2 1

2 375 1 034 0 426

2.

. . .

max max

max max max

3 73 16 903 20 496 2. . . (6)

d max

3

8 1 1 0 50 151 0 170

0 163 4 98

2

2

.. .

. .

(7)

Sadek et al4 proposed the optimum parameters

of TMD which results in considerable reduction in

response of structures to seismic loading. The criteria

used to obtain the optimum parameters is to select fo

a given mass ratio, tuning ratio, damping ratio which

would result in equal and large modal damping in th

rst two modes of vibration. For a damped SDOF

structure, the approximate equations for TMD,

Tuning ratio, f

1

1

1

1

(8

Damping ratio,

d

1 1 (9

The approximate equations for TMD for dampe

MDOFstructure, the tuning ratio (f),is replaced with

maxin Eq. (8)

Tuning ratio, f

max

max

max

1

11

1

(10

The damping ratio of TMDforMDOFis also found

by multiplying the damping ratio computed for a SDOF

system (Eq. (9)) by max,

Damping ratio,

d

max

1 1 (11

TABLE 3

OPTIMUM PARAMETERS OF TMD OF 6-STOREY

BUILDING

Struc-

tural

damping

()

MethodsMass

ratio ()

Opti-

mum

tuning

ratio (f)

Opti-

mumdamping

ratio,

opt

max

0.02

Tsai et

al.60.01 0.9643 0.0862 1.222

Sadek et

al.70.01 0.9858 0.1459 1.222

0.05

Tsai et

al.60.01 0.9149 0.1008 1.222

Sadek et

al.70.01 0.9825 0.1822 1.222

The Optimum damping ratio, opt obtained by

two methods6,7 for structure with 0.02 and 0.0

effective damping are differing as shown in Table 3

The effective damping ratio (d) in TMD is varie

by using NVFD from 0.05 to 0.25 and correspondin

damping coefcients are not differing much as given in

Table 3. The above parameters are used for designing


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TMD, which involves nding the mass of damper (md),

frequency of damper(d), stiffness of damper (kd) and

damping of damper (cd) as mentioned in Eqs. (4)-(7)

are given in Table 3.

From Table 3, it is observed that the parameters

obtained for TMD i.e., md, d, kd, cdby the methods

Tsai et al. and Sadek et al. are almost equal. The damper

force is calculated using the equation,F= cdV, where,

=0.04. Further response studies are carried out using

nonlinear modal time history analysis of 6-Storey

building subjected to time histories of El Centro, Kobe

and Northridge normalized to 0.35g using SAP2000.

Since, base shear is found to be minimum at

d=0.25, all the responses like peak displacement,

peak acceleration and peak drifts are found at effective

damping d = 0.25. The peak responses to be used

for performance evolution are storey displacements,

accelerations, drifts are found from the following way.

Peak response ratio, x x tpeak t imax

i El CentroKobe

Northridge

Max

, (12)

Here, the variable xpeak can be storey peak

displacement, peak acceleration and peak drifts. In

Eq. (12), the time, t with time steps varying from 1

to number of time steps (n) in each of the earthquake

time histories considered, i represents the number of

storey along the height of the structure. The variation

of peak displacement, acceleration and drift response

ratios along height of the building and base shear along

X-direction with different ground excitations i.e., E

Centro, Kobe and Northridge earthquakes with PGA

normalized to 0.35 are found to be signicant fo

effective structural damping of 0.02 and insignican

(some times higher) for effective structural damping

of 0.05 as given in Table 4. The performance of the

building with TMDvary with the characteristics of th

excitations such as frequency of earthquake excitation

and their nature such as near eld and far eld. From

the studies carried out, it is found that the optimum

damping proposed by Tsai et al. and Sadek et al are

TABLE 4

THE PARAMETERS OF TMD USED STUDY OF 6-STOREY BUILDING

Structural

damping ()

md(kg-s/m2) d(rad/s) kd(t/m)d

cd (kg-s/m)

Tsai et al Sadek et al Tsai et al Sadek et al Tsai et al Sadek et al Tsai et al. Sadek et al.

0.02 265.53 265.46 30.16 30.83 241.32 252.5

0.05 801.2 818.7

0.10 1602 1637.3

0.15 2403 2456.2

0.20 3204.1 3274

0.25 4005.1 4093

0.05 265.53 265.46 28.62 28.23 217.53 250.45

0.05 760.3 816

0.10 1520 1631.9

0.15 2280.1 2447.9

0.20 3040.1 3263.8

0.25 3800.1 4079.8

Note: md is mass, d is frequency, kd is stiffness, dis damping ratios and cdis corresponding damping coefcients of nonlinear

viscous damper of TMD

TABLE 5

PERCENTAGE OF REDUCTION FOR RESPONSES FOR

= 0.02 & 0.05

%R Displacement (%) Acceleration

(%)

Drift (%)

SD =0.02 =0.05 =0.02 =0.05 =0.02 =0.05

EC

15.61

to15.95

3.61

to4.33

2.05

to15.16

-0.18

to4.08

14.18

to16.75

1.76

to4.27

KO

15.91

to

16.27

9.91

to

10.55

13.69

to

16.65

8.47

to

9.53

14.08

to

16.53

7.41

to

11.35

NR

5.19

to

5.8

5.44 to

5.74

-3.03

to

3.402

-3.6

to

2.55

4.26

to

6.11

4.65

to

5.74

Note: %: Percentage of reduction; SD: Structural Damping;

maximum and minimum reduction in bold letters.


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not useful while designing the TMD with NDFD for

different types earthquakes. The performance of the

building with TMDvary with the characteristics of the

excitations such as frequency of earthquake excitations

and their nature such as near eld and far eld. It is

observed that for far eld earthquakes the TMDis not

as effective of near eld earthquake.

CONCLUSIONS

The properties of the TMD required for optimum

performance depends on stiffness, mass and damping

distribution of the structure/building or their

components need to be isolated from vibrations. From

experimental results, the optimum parameters such as

optimum tuning ratio (f) and optimum damping ratios

(d) for TMDwere derived6,7. A 6-Storey steel framed

building with TMD is modeled in 3D using SAP2000.

The 6-Storey building model is reduced to 6 DOFsystem and optimum parameters of TMD are computed

using two different methods. In the present study these

formulations are used, for a 6 DOF building model of

the building, the optimum parameters such as optimum

tuning ratio (f) and optimum damping ratios (d) for

TMD are found. The optimum tuning (frequency) ratio

for two structural damping ratios () is almost same,

but optimum damping ratio obtained using the model

proposed by Sadek et al. for effective structural damping

() 0.02 and 0.05 are found to be more in comparison

with damping ratio obtained using the model proposed

by Tsai et al. Only for deriving optimum parameters for

TMD, 6 DOFthe model are used in the present study.

Two methods are found to give same optimum tuning

ratio, but optimum effective damping ratios are found

to be differing. With the optimum tuning ratio and the

parameters of TMDobtained by the two methods, the

damping in TMDis varied using nonlinear viscous uid

dampers (NVFD) for nding the responses of building

in X-direction subjected to one near eld earthquake

excitation (El Centro with PGA of 4.417 m/s2) andtwo far eld earthquake excitations (Northridge, Kobe

with PGA of 8.2676 and 8.1782 m/s2respectively) with

their PGA normalized to 0.35g. The effectiveness of

the TMD in reducing the responses of structures for

two different structural damping of 2% and 5% by

increasing effective damping of NVFD in TMD from

0.05 to 0.25 is found.

The variation of peak displacement, acceleration an

drift response ratios with increase in damping in TMD

along height of the building in X-direction subjecte

to one near eld earthquake excitation (El Centro

with PGA of 4.417 m/s2) and two far eld earthquak

excitations (Northridge, Kobe with PGA of 8.2676 and

8.1782 m/s2 respectively) with their PGA normalized

to 0.35g and base shear are found to be signicant foeffective structural damping of 0.02 and insignican

(some times higher in accelerations) for effectiv

structural damping of 0.05. Thus, the effectivenes

of increasing effective damping in TMD up to 0.25 i

more effective in structures with low structural damping

(2%) than high structural damping (5%). The reduction

in responses in near eld earthquake excitation (E

Centro) are signicant in comparison with response

with far eld earthquake excitations (Northridge

Kobe). The variation of base shear and base shea

response ratio for different effective damping of TMDfor the three earthquakes considered are found. Th

variations of peak displacement, peak acceleration and

peak inter-storey drifts for the bare frame and for th

frame with TMDwith damping ratio of 0.25 for the two

structural damping considered and respective respons

ratios are compared. From the studies carried out, it i

found that the optimum damping proposed by Tsai e

al. and Sadek et al are not useful while designing the

TMD with NDFD for different types of earthquakes

The performance of the building with TMDvary with

the characteristics of the excitations such as frequency

of earthquake excitations and their nature such as nea

eld and far eld.

ACKNOWLEDGMENT

This paper is being published with the kind permission

of Director, CSIR-Structural Engineering Research

Centre, Chennai-600113, India. The authors are very

much thankful to Dr. P. Kamatchi, Principal Scientis

for her help to enhance the quality of paper and

Ms. D. Nisha, Project Assistant, Vibration Contro

Group, CSIR-Structural Engineering research Centr

for her help and support while carrying out this work.

REFERENCES

Frahm, H., 1. Device for damping vibrations o

bodies, US Patent, 989958, 1909.


10/10



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(Discussion on this article must reach the editor befor

September 30, 2016)

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