PERFORMANCE IMPROVEMENT OF MULTI STORIED BUILDINGS … · and the structure through the damper. The mass, stiffness and damping of the new mass has to be tuned to achieve a state

© September 2016| IJIRT | Volume 3 Issue 4 | ISSN: 2349-6002

IJIRT 143920 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 1

PERFORMANCE IMPROVEMENT OF MULTI

STORIED BUILDINGS USING MULTIPLE TUNED

MASS DAMPERS

Deepu S. Hegden1, Lakshmi P2 1Master’s student, Department of Civil Engineering, Saintgits college of Engineering.

2Assistant Professor, Department of Civil Engineering, Saintgits college of Engineering

Abstract—Tuned mass damper (TMD) is one of the most

reliable vibration control devices for high rise buildings.

It utilizes a secondary mass attached to a main structure

through a spring-dashpot system to reduce the dynamic

response of the structure. Now a day, multiple tuned

mass dampers (MTMD) where more than one TMD is

tuned to different structural frequency are used to

control earthquake induced motion of high rise

buildings. In this work, a comparative analytical study is

done to check the effectiveness of multiple tuned mass

dampers to reduce translation structural vibration. A

typical multi storied building is considered and seismic

analysis is carried out without and with STMD or

MTMD using software ETABS. From the frequency

response analysis of the building to seismic excitations,

the mass, stiffness and damping of the tuned mass

damper is optimized. It is found that the damper can

reduce the displacement of the building to a considerable

extent and thus the safety and comfort of the occupants

can be ensured. It is found that increase in mass ratio

increases the effectiveness of TMD. The number of

damper in MTMD is varied and the response of the

structure is compared with the response of the structure

with STMD. It is found that the MTMD is more effective

in controlling the response of the structure compared to

the STMD having the same mass. Also, for a given

structural system and level of excitation there exists an

optimum value of the parameters (number of dampers in

MTMD, mass distribution and damping ratio) at which

the response of the structure attains its minimum value.

Index Terms—damping ratio, mass distribution, mass

ratio, Multiple Tuned Mass Dampers (MTMD), number

of dampers, Tuned Mass Dampers(TMD), structural

frequency, vibration control device.

I. INTRODUCTION

Now-a-days innumerable high rise building has been

constructed all over the world and the number is

increasing day by day. High rise buildings are more

prone to wind and seismic excitations which cause

damage to buildings and discomfort to occupants. For

the vibration control of these buildings, artificial

damping devices are used. Tuned Mass Damper

(TMD) is a passive vibration control device in which

a mass is connected to a structure by spring and

damping elements without any other support.

Frequency of the TMD is tuned to a particular

structural frequency, when that frequency is excited

the TMD will resonate out of phase and reduces the

building response. Mass is attached to the structure

with the help of a spring- dash pot system and energy

is released by the relative movement between the mass

and the structure through the damper. The mass,

stiffness and damping of the new mass has to be tuned

to achieve a state where the maximum amplitude

reached by the system is minimized. Since TMDs can

efficiently work only at a single mode of frequency,

the damper will be tuned to that frequency.

During earthquake or high wind, external lateral forces

are induced in the structure, as a result of which the

structure will oscillate. The spring which attaches the

structure to the mass, causes the mass to oscillate as

well. The damper will exert a force onto the structure

and at the same time, the structure will exert a force on

the damper system. This will gradually reduce the

oscillation of the structure.

The major limitation of a STMD is its lack of

effectiveness outside the narrow tuned frequency

band. A very small deviation from this tuned

frequency range can cause reduction in the

effectiveness of damper. Multiple tuned mass dampers

consist of several TMDs placed in parallel with

distributed natural frequencies around the control

tuning frequency. It gives better response control

compared to single TMD and it can dampen



oscillations in multiple directions and for multiple

modes.

The main objective of this study is to determine the

effect of Single and Multiple Tuned Mass Dampers on

the dynamic response of structures under seismic

excitations and to propose an effective MTMD for the

multi-storey building by determining the optimum

parameters namely mass ratio, number of TMD units,

mass distribution and damping ratio of damper to

reduce the displacement of the building.

II. METHODOLOGY

A. Scope of study

The study involves a case study of a 45 storied

residential cum commercial R.C.C. building with and

without TMD. Software ETABS is used for the three

dimensional modeling of building and damper. The

building is modeled to stand in Indian conditions by

following Indian Standard codes. The Time history

data of El- Centro earth quake is used for analysis and

conclusions are made from frequency response

analysis results with and without tuned mass dampers.

B. Methodology

A multi storied building is considered and is modeled

using software ETABS.

Fig.1 Typical plan of the considered building

The building is a residential cum commercial purpose

R.C.C. building. The beams of size 400x700mm,

columns of size 400x1000mm and slab thickness of

200mm are provided. M30 grade concrete and Fe415

grade steel reinforcements are used. Natural

frequencies and mode shapes of the structure are

determined by normal mode analysis. Stiffness of the

building and damping force are calculated by taking

damping ratio as per IS1893. TMD system is modeled

using linear damper link element. Normal mode

analysis of building with damper for varying mass

ratios is carried out to find the frequency of damper.

By tuning the damper to the natural frequency of the

building & making it out of phase, stiffness is

optimized. Mass of the damper is fixed in such a way

that response of the building is reduced to a reasonable

limit. The effect of damping of the damper is to be

studied by a frequency response analysis for the

building with and without damper. The best suited

STMD system is proposed for the considered building.

MTMDs are modeled with constant mass ratio and

varying other parameters such as number of dampers,

mass distribution, tuning frequency and damping ratio.

Frequency response analysis is performed to find the

best suited MTMD system for the considered building.

III. RESULTS AND DISCUSSIONS

The building is modeled using software ETABS.

Fig.2 Three dimensional model in ETABS

Normal mode analysis is carried out to find the natural

frequency and mode shapes which characterize the

basic dynamic behavior of the structure. Natural

frequency refers to the frequencies at which the

structure naturally tends to vibrate if it is subjected to

a disturbance. The deformed shape of the structure at

a specific natural frequency of vibration is termed its

normal mode of vibration. A structure can have many

modes of frequency, among that there will be a

particular frequency which is dominant for the whole

structure. This dominant frequency will produce the

maximum effect on the building compared to other



frequencies. This fundamental frequency is obtained

from normal mode analysis against first mode.

Table I. Normal mode analysis results

Mode No. Frequency(Hz)

1 0.321

2 0.339

3 0.361

4 1.049

5 1.068

6 1.129

7 1.543

8 1.913

9 1.935

10 1.971

From analysis results, fundamental frequency is

obtained as 0.321Hz or 2.01radians/second. As per IS

1893:2002, the structural damping ratio ξ of any

building can be taken as 5%. Hence the building when

considered as a SDOF system has a natural frequency

equal to 0.321cycles/second and damping ratio equal

to 5%. With these values the stiffness of the building

and also the damping force can be calculated.

Natural frequency ωn =2.01 rad/sec

Mass = 2.97 × 107 kg (modal mass for the first mode)

Damping ratio ξ =0.05 (As per IS 1893:2002)

Damping constant c= 2 ξ ωn m = 59814172 Nm/s

Stiffness k = m × ωn2 = 119990970 N/m

Damper is modeled as linear damper element in

ETABS. Mass, stiffness and damping coefficient are

provided in the property list and the damper is

provided at the top floor connecting with rigid beams.

Orientation of the damper is set to Y-direction as the

displacement is maximum along that direction.

Fig.3 Plan of the building with STMD

Mass of the damper is varied from 0.2% to 2% of the

modal mass of the building and the frequency of the

damper is obtained from normal mode analysis.

The frequency of damper is found to decrease with

increasing mass ratio. To reduce the response of the

building, damper is to be designed for the natural

frequency of the building. Also damper will be

effective only when it moves out of phase with the

building. By tuning, stiffness of damper was

optimized.

Table II. Optimized stiffness of damper

Mass

ratio

(%)

Mass of

damper

(Kg)

Stiffness k

before

tuning(N/m)

Optimized

stiffness

(N/m)

0.2 59469 239872 244871

0.4 118939 479746 489743

0.6 178408 719617 734615

0.8 237878 959482 979486

1.0 297348 1199358 1224358

1.2 356817 1439230 1469230

1.4 416287 1679101 1714101

1.6 475757 1918974 1958973

1.8 535226 2158841 2201345

2.0 594696 2398714 2446216

Table III. Frequency of damper

Mass

ratio

(%)

Damper

frequency

before

tuning

(Hz)

Damper

frequency

after

tuning

(Hz)

Structure

frequency

before

tuning

(Hz)

0.2 0.311 0.321 0.321

0.4 0.301 0.32 0.321

0.6 0.293 0.319 0.321

0.8 0.286 0.318 0.321

1.0 0.280 0.318 0.321

1.2 0.275 0.317 0.321

1.4 0.271 0.316 0.321

1.6 0.268 0.315 0.321

1.8 0.266 0.314 0.321

2.0 0.265 0.313 0.321

Frequency response analysis is used to compute

structural response to steady state oscillatory

excitation. For fixing mass and damping of damper

frequency response analysis is done. The result of

analysis gives plots of displacement against frequency

values. The steady-state oscillatory response occurs at

the same frequency as the loading.



The response may be shifted in time due to damping

in the system. The shift in response is called a phase

shift because the peak loading and peak response no

longer occur at the same time. Analysis was done for

El-Centro earth quake excitation. Mass ratio was

varied from 0.2% to 2% and for each mass ratio,

damping ratio was varied from 5% to 25%. Analysis

results are obtained as graphs with frequency on X axis

and maximum displacement on Y axis. From the

graphs, the percentage reduction in the amplitude of

oscillation was calculated.

The input of earth quake analysis is provided as time

history data. The time history is the sequence of values

of any time-varying quantity (here ground motion

acceleration) measured at a set of fixed times.

Time history method is considered to be more realistic

compared to the response spectrum method. In this

study the time history for El-Centro California, NS

1940 with maximum recorded ground acceleration of

about 0.33g is used. The recorded acceleration was for

the first crucial 20seconds.

Fig.4 Time history graph of El-Centro earthquake

The frequency response graphs for varying mass ratio

with different levels of damping ratio obtained from

analysis results can be summarized as follows:

Fig.5 Frequency response graphs for varying mass ratio

with 5% damping ratio





From the frequency response analysis results, it is

clear that when the damper mass is equal to 1.2% of

the modal mass of the building and at a damping ratio

of 5%, the damper can decrease the amplitude of

displacement of the building by 42% and at a damping

ratio of 20%, the response reduction was found up to

65% when excited by seismic forces. Increasing

damping ratio was found to reduce the two peaks

which occur symmetrically about the natural

frequency at resonance. At 20% damping, the 2 peaks

get reduced by large amount and the graph become

continuous. Thus fixing 1.2% mass ratio, total weight

of damper is obtained as 357 tones.



Multiple tuned mass dampers consist of more than one

TMD whose frequencies are distributed around the

natural frequency of controlled mode of main

structure. A parabolic mass distribution is used

because the response curve is quiet closer to the

parabolic shape. The most effective mass ratio of 1.2%

obtained from STMD analysis is fixed. Number of

TMD units was varied from 2 to 12. Fractional

bandwidth β was fixed as 0.05. The tuning frequency

of each damper was distributed around the structural

frequency according to the equation:

ωj = ωT [1+{j-(n+1)/2}β/(n-1)] , where ωj is the natural

frequency of the jth damper, ωT is the structural

frequency and n is the number of TMD units. Damping

ratio of damper was varied from 5% to 25%.

Table IV. Mass and frequency of each damper unit of

different MTMD

Nu

mb

er o

f

da

mp

er u

nit

s

Ma

ss N

am

e

Wei

gh

t in

kg

Fre

qu

ency

na

me

Fre

qu

ency

in

Hz

2 m1 178408.5 ω1 0.312

m2 178408.5 ω2 0.329

Total 356817 Avg. 0.321

4 m1 53522.5 ω1 0.312

m2 124886 ω2 0.318

m3 124886 ω3 0.323

m4 53522.5 ω4 0.329

Total 356817 Avg. 0.321

6 m1 35681.7 ω1 0.312

m2 53522.5 ω2 0.316

m3 89204.2 ω3 0.319

m4 89204.2 ω4 0.322

m5 53522.5 ω5 0.325

m6 35681.7 ω6 0.329

Total 356817 Avg. 0.321

8 m1 17840.8 ω1 0.312

m2 35681.7 ω2 0.315

m3 53522.5 ω3 0.317

m4 71363.4 ω4 0.319

m5 71363.4 ω5 0.322

m6 53522.5 ω6 0.324

m7 35681.7 ω7 0.326

m8 17840.8 ω8 0.329

Total 356817 Avg. 0.321

10 m1 10704.5 ω1 0.312

m2 21409 ω2 0.314

m3 35681.7 ω3 0.316

m4 49954.3 ω4 0.318

m5 60658.8 ω5 0.320

m6 60658.8 ω6 0.322

m7 49954.3 ω7 0.323

m8 35681.7 ω8 0.325

m9 21409 ω9 0.327

m10 10704.5 ω10 0.329

Total 356817 Avg. 0.321

12 m1 3568.1 ω1 0.312

m2 14272.6 ω2 0.314

m3 24977.2 ω3 0.315

m4 39249.8 ω4 0.317

m5 46386.2 ω5 0.318

m6 49954.4 ω6 0.320

m7 49954.4 ω7 0.322

m8 46386.2 ω8 0.323

m9 39249.8 ω9 0.325

m10 24977.2 ω10 0.326

m11 14272.6 ω11 0.328

m12 3568.1 ω12 0.329

Total 356817 Avg. 0.321

The effect of increase in the number of TMD units in

MTMD obtained from the frequency response graphs

for different damping ratio can be summarized as

follows:

Fig.8 Frequency response graph for varying number of

damper units with 5% damping ratio







Table V. Response reduction for various TMD systems

Number of

damper

units

Percentage

response

reduction for

5% damping

Percentage

response

reduction for

20% damping

damping STMD 42% 65%

2 Damper 48% 70%

4 Damper 53% 72%

6 Damper 57% 73%

8 Damper 60% 74%

10 Damper 62% 75%

12 Damper 62% 75%

Increase in damping ratio tends to decrease the peaks

and at 20% damping, the 2 peaks get reduced by large

amount and the graph become continuous. As the

number of damper units in MTMD is increased

keeping the total mass same, there is a significant

decrease in response of the building. The reduction in

response of the building is significant up to MTMD

with n = 8, and after that the reduction in response is

very small or remains almost same. Hence 8 damper

MTMD can be suggested as most efficient for the

considered building.

Fig.11 Plan of the building showing position of eight

damper units in the most efficient MTMD

IV. CONCLUSION

Response of the building was found to reduce with the

increase in mass ratio and damping ratio of the

damper. The inclusion of a Single Tuned Mass

Damper with 1.2% mass ratio (357 tones weight) and

damping ratio of around 20% could reduce the

response of the building to around 65%. Multiple

Tuned Mass Dampers are much more effective to

reduce structural vibration when subjected to seismic

excitation than Single Tuned Mass Damper of same

mass ratio. The reduction in response of the building

increases with increase in number of dampers up to a

limit, and after that the reduction in response is very

small or remains almost same.

From the study, for the building considered an

effective Multiple Tuned Mass Damper was proposed

with the following parameters:

Number of TMD units = 8

Total weight = 357 tones (1.2% mass ratio)

Mass distribution – Parabolic

Fractional bandwidth = 0.05

Damping ratio of dampers = 20%



A response reduction of up to 74% was obtained for

the multiple tuned mass dampers with the above

parameters.

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Documents

PERFORMANCE IMPROVEMENT OF MULTI STORIED BUILDINGS … · and the structure through the damper. The mass, stiffness and damping of the new mass has to be tuned to achieve a state