© 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
© September 2016| IJIRT | Volume 3 Issue 4 | ISSN: 2349-6002
IJIRT 143920 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 2
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
© September 2016| IJIRT | Volume 3 Issue 4 | ISSN: 2349-6002
IJIRT 143920 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 3
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.
© September 2016| IJIRT | Volume 3 Issue 4 | ISSN: 2349-6002
IJIRT 143920 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 4
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
Fig.6 Frequency response graphs for varying mass ratio
with 10% damping ratio
Fig.7 Frequency response graphs for varying mass ratio
with 20% 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.
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IJIRT 143920 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 5
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
© September 2016| IJIRT | Volume 3 Issue 4 | ISSN: 2349-6002
IJIRT 143920 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 6
Fig.9 Frequency response graph for varying number of
damper units with 10% damping ratio
Fig.10 Frequency response graph for varying number of
damper units with 20% 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%
© September 2016| IJIRT | Volume 3 Issue 4 | ISSN: 2349-6002
IJIRT 143920 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 7
A response reduction of up to 74% was obtained for
the multiple tuned mass dampers with the above
parameters.
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