Genetic Algorithm Based Approach for Optimal Design of Multiple Tuned Mass Dampers (MTMDs) under Earthquake Excitation

Authors
M. Mohebbi
K. Shakeri
H. Majzoub
Abstract
To improve the behavior of building structures subjected to lateral loads, such as wind and
earthquake excitations, tuned mass damper (TMD) has been used extensively theoretically
and experimentally in previous researches. To increase the effectiveness of TMD mechanism,
different methods have been proposed to determine the optimal values of TMD parameters
including its mass, stiffness and damping. In using single TMD on the structures subjected to
external vibrations, the mistuning of TMD, variation of TMD damping and changes in
structural dynamic characteristics cause significant reduction in the effectiveness of TMD.
Multiple tuned mass dampers (MTMDs) have been proposed to overcome the shortcomings
of single TMD where each TMD has different dynamic characteristics. Based on the results of
different researches, it has been concluded that the performance of MTMDs is less sensitive
to uncertainty of structural dynamic parameters than that of a single TMD.
In the previous researches, for designing MTMDs on the linear structures subjected to various
external excitations, several methods have been proposed based on different kinds of design
criteria. In most of the proposed methods, to simplify the design procedure of MTMDs, some
limitations such as identical masses and damping ratios for TMDs or uniform distribution for
the frequency or damping of TMDs have been considered. Also these methods require
extensive numerical analysis. To generalize the design problem of MTMDs, in this paper, an
effective method has been proposed for optimal design of MTMDs on the multi-degree-offreedom
linear structures subjected to any desired excitation. In this method, an optimization
problem is defined for designing the optimal MTMDs. The minimization of the maximum
displacement of structure is considered as objective function and the parameters of TMDs are
considered as variables. Since the design problem includes a large number of variables, hence,
in this paper, it has been decided to use Genetic Algorithm (GA) for solving the optimization
problem.
To illustrate the procedure of the proposed method and also to assess the effectiveness of
MTMDs in improving the seismic behavior of structures, a ten–storey linear shear building
frame was subjected to white noise excitation and for different values of TMDs mass ratio
and TMDs number, optimal MTMDs were designed for minimizing the maximum
displacement of structure. To focus on the main objective of this paper and avoid the
complexity of the problem, TMDs were located on the top floor in parallel configuration. The
results of numerical simulations showed the capability of GA in solving complex MTMDsdesign problem with a large number of variables as well as the simplicity of the method under
any desired external excitation. Also it was concluded that increasing of the mass ratio of
TMDs could improve the effectiveness of MTMDs. To assess the performance of optimal
MTMDs under other earthquakes, which are different in characteristics with design record,
optimal structure-MTMDs was tested under near-fault and far-fault earthquakes and the
results have been reported.

Keywords

Kareem, A, and Klein, S., "Performance of
multiple tuned mass dampers under random
loadings", Journal of Structural Engineering,
ASCE, 121(2), 1995, 348-361.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Soong, T. and Dargush, G.F., Passive energy
dissipation systems in structural engineering,John Wiley & Sons, Chichester, 1997-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Xu, K. and Igusa, T., "Dynamic characteristics
of multiple substructures with closely spaced
frequencies", Earthquake Engineering &
Structural Dynamics, 21, 1992, 1059-1070.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Yamaguchi, H. and Harnpornchai, N.,
"Fundamental characteristics of multiple tuned
mass dampers for suppressing harmonically
forced oscillation", Earthquake Engineering &
Structural Dynamics, 22, 1993, 51-62.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Abe, M. and Fujino, Y., "Dynamic
characteristics of multiple tuned mass dampers
and some design formula", Earthquake
Engineering & Structural Dynamics, 23, 1994,
813-835.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Igusa, T. and Xu, K., "Vibration control using
multiple tuned mass damper", Journal of Sound
and Vibration, 175, 1994, 491-503.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Jangid, R.S., "Optimum multiple tuned mass
dampers for base excited undamped systems",
Earthquake Engineering & Structural
Dynamics, 28, 1999, 1041-1049.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Wu, J. and Chen, G., "Optimization of multiple
tuned mass dampers for seismic response
reduction", Proceeding of American Control
Conference, Chicago, Illinois, USA, June 2000,
519-523.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Chen, G. and Wu, J., "Optimal placement of
multiple tuned mass dampers for seismic
structures", Journal of Structural Engineering,
ASCE, 127(9), 2001, 1054-1062.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Li., C., "Optimum multi tuned mass dampers
for structures under the ground acceleration
based on DDMF and ADMF", Earthquake
Engineering & Structural Dynamics, 31, 2002,
897-919.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Zuo, L. and Nayfeh, S.A., "Optimization of the
individual stiffness and damping parameters in
multiple-tuned-mass-damper systems," Journalof Vibration and Acoustics, Transactions of
ASME, 127, 2005, 77-83.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Carneiro, R.B., Avila, S.M. and De Brito,
J.L.V., "Parametric study on multiple tuned
mass dampers using interconnected masses,"
International Journal of Structural Stability and
Dynamics, 8(1), 2008, 187-202.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
اعتماد سعید، ل، نراق ی س.ا و زهرایی س.م. "پ یش ]
بینی پارامترهای بهینه ی میراگرهای جرمی چندگانه با
استفاده از شبکه عصبی مصنوع ی و استنتاج فاز ی"،
. چهارمین کنگره مهندسی عمران، 1387-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Moon, K.S., "Vertically distributed multiple
tuned mass dampers in tall buildings:
performance and preliminary design", Structural
Design of Tall and Special Buildings, 19, 2010,
347-366.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Dehghan-Niri, E., Zahrai, S.M and Mohtat, A.,
"Effectiveness-robustness objectives in MTMD
system design: An evolutionary optimal design
methodology," Structural Control & Health
Monitoring, 17(2), 2010, 218-238.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Goldberg, D.E., Genetic algorithms in search,
optimization and machine Learning, Addison -
Wesley Publishing Co., Inc. Reading, Mass,
1989.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Michalewicz, Z., Genetic algorithms + data
structures=evolution programs, New York:
Springer –Verlag, 1996-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Bathe, K. J., Finite element procedures,
Prentice-Hall, Inc., 1996-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Joghataie, A. and Mohebbi, M., "Vibration
controller for confined masonry walls by
distributed genetic algorithms", Journal of
Structural Engineering, ASCE, 134(2), 2008,
300-309-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Holland, J.H., Adaptation in natural and
artificial systems, Ann Arbor: The University of
Michigan Press, 1975-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Mühlenbein, H. and Schlierkamp-Voosen, D.,
"Predictive models for the breeder genetic
algorithm: I. Continuous parameter
optimization”, Evolutionary Computation, 1(1),
1993, 25-49-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Baker, J.E., "Reducing bias and inefficiency in
the selection algorithm”, Proc. ICGA 2, 1987,
14-21-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Jenkins, W.M., "A decimal-coded evolutionary
algorithm for constrained optimization",
Computer and Structure, 80, 2002, 471-480-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Arfiadi, Y. and Hadi, M.N.S., "Optimal direct
(static) output feedback controller using real
coded genetic algorithms", Computer and
Structure, 79, 2001, 1625-1634-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Fan, F.G. and Ahmadi, G., "Nonstationary
Kanai-Tajimi models for El-Centro 1940 and
Mexico-City 1985 earthquakes”, Probabilistic
Engineering Mechanics, 5, 1990, 171-181-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Li, C. and Liu, Y., "Further characteristics for
multiple tuned mass dampers," ASCE Journal
of Structural Engineering 128(10), 2002, 1362-
1365-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Li, C, "Performance of multiple tuned mass
dampers for attenuating undesirable oscillations
of structures under the ground acceleration,"
Earthquake Engineering & Structural
Dynamics, 29, 2000, 1405-1421.-محتشم محبی1*، کاظم شاکری2، حسین مجذوب3
Modares Civil Engineering journal
Volume 12, Issue 1
March and April 2012