Robust Design of Tuned Mass Damper Systems for Seismic Protection of Multistory Buildings
Publication: Journal of Structural Engineering
Volume 140, Issue 8
Abstract
In this paper, a method is proposed for the robust design of tuned mass damper (TMD) systems for seismic protection of multistory buildings. The seismic excitation is a random ground motion acceleration modeled by a stationary filtered white noise process. The protected building consists of a generic multi-degree-of-freedom (MDOF) structure, represented by its modes of vibration and linear mass dampers. The design properties of the TMD system are mass, frequency and damping ratio of the TMD units, along with their location within the structure, considered as fixed at its base. Uncertainties in the properties of both the building and the input seismic excitation are explicitly accounted for in the robust design of the TMD system. In particular, the uncertain parameters considered are stiffness and damping of the structure, and frequency and damping properties of the Kanai-Tajimi model used for representing the surface ground filter of the white noise process acting at the bedrock. The response quantity chosen to be representative of the seismic demand in the building is the interstory drift ratio. Its variation to the uncertainties is treated with the direct perturbation method, by applying a mixed-order approach. Robustness in the design of the TMD properties is formulated as a multiobjective optimization problem, in which both mean and standard deviation of the building response, produced by the considered uncertain parameters, are minimized. The weighted sum method is applied for transforming the multiple objective into an aggregated scalar objective function and then solving the minimization problem. The proposed design procedure is implemented on an illustrative example, consisting of a multistory building protected with a TMD system made from two units that have to be tuned with the first- and second-mode period of the structure, respectively. Parametric analyses on protected systems characterized by different properties are carried out, and the significance of the effects produced by the variation of such properties on the optimum design of the TMD system is shown. Differences between a robust design with the proposed procedure and a more conventional one that does not account for uncertainties in the system properties are finally evaluated.
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References
Bartels, R. H., and Stewart, G. W. (1972). “Solution of the matrix equation .” Commun. ACM, 15(9), 820–826.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics and decision for civil engineers, McGraw-Hill, New York.
Chakraborty, S., and Roy, B. K. (2011). “Reliability based optimum design of tuned mass damper in seismic vibration control of structures with bounded uncertain parameters.” Probab. Eng. Mech., 26(2), 215–221.
Chen, G., and Wu, J. (2001). “Optimal placement of multiple tuned mass dampers for seismic structures.” J. Struct. Eng., 1054–1062.
Clark, A. J. (1988). “Multiple passive tuned mass dampers for reducing earthquake induced building motion.” Proc., 9th World Conf. on Earthquake Engineering, Vol. 5, International Association for Earthquake Engineering, Tokyo-Kyoto, Japan, 779–784.
Coleman, T. F., Branch, M. A., and Grace, A. (1999). Optimization toolbox for use with MATLAB, User’s Guide Version 2, The MathWorks, Natick, MA.
Dehghan-Niri, E., Zahrai, S. M., and Mohtat, A. (2010). “Effectiveness-robustness objectives in MTMD system design: An evolutionary optimal design methodology.” Struct. Contr. Health Monit., 17(2), 218–236.
Fu, T., and Johnson, E. (2011). “Distributed mass damper system for integrating structural and environmental control in buildings.” J. Eng. Mech., 205–213.
Giovenale, P., Ciampoli, M., and Jalayer, F. (2003). “Comparison of ground motion intensity measures using the incremental dynamic analysis.” 9th Int. Conf. on Applications of Statistics and Probability in Civil Engineering, A. Der Kiureghian, S. Madanat, and J. M. Pestana, eds., IOS Press Incorporated, Amsterdam.
Goicoechea, A., Hansen, D. R., and Duckstein, L. (1982). Multiobjective decision analysis with engineering and business applications, John Wiley & Sons, New York.
Guo, Y. Q., and Chen, W. Q. (2007). “Dynamic analysis of space structures with multiple tuned mass dampers.” Eng. Struct., 29(12), 3390–3403.
Hadi, M., and Arfiadi, Y. (1998). “Optimum design absorber for MDOF structures.” J. Struct. Eng., 1272–1280.
Hoang, N., and Warnitchai, P. (2005). “Design of multiple tuned mass dampers by using a numerical optimizer.” Earthquake Eng. Struct. Dyn., 34(2), 125–144.
Joshi, A. S., and Jangid, R. S. (1997). “Optimum parameters of multiple tuned mass dampers for base-excited damped systems.” J. Sound Vib., 202(5), 657–667.
Li, C. (2002). “Optimum multiple tuned mass dampers for structures under the ground acceleration based on DDMF and ADMF.” Earthquake Eng. Struct. Dyn., 31(4), 897–919.
Lin, C. C., Ueng, J. M., and Huang, T. C. (2000). “Seismic response reduction of irregular buildings using passive tuned mass dampers.” Eng. Struct., 22(5), 513–524.
Luco, N. (2002). “Probabilistic seismic demand analysis, SMRF connection fractures, and near-source effects.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Stanford Univ., Stanford, CA.
Lutes, L. D., and Sarkani, S. (2001). Random vibrations, Butterworth-Heinemann, Oxford, U.K.
Marano, G. C., Sgobba, S., Greco, R., and Mezzina, M. (2008). “Robust optimum design of tuned mass dampers devices in random vibrations mitigation.” J. Sound Vib., 313(3–5), 472–492.
Matta, E., and De Stefano, E. (2009a). “Robust design of mass-uncertain rolling-pendulum TMDs for the seismic protection of buildings.” Mech. Syst. Sig. Process., 23(1), 127–147.
Matta, E., and De Stefano, E. (2009b). “Seismic performance of pendulum and translational roof-garden TMDs.” Mech. Syst. Sig. Process., 23(3), 908–921.
Mohtat, A., and Dehghan-Niri, E. (2011). “Generalized framework for robust design of tuned mass damper systems.” J. Sound Vib., 330(5), 902–922.
Ok, S. Y., Song, J., and Park, K. S. (2009). “Development of optimal design formula for bi-tuned mass dampers using multi-objective optimization.” J. Sound Vib., 322(1–2), 60–77.
Papadimitriou, C., Beck, J. L., and Katafygiotis, L. S. (1997). “Asymptotic expansions for reliability and moments of uncertain systems.” J. Eng. Mech., 1219–1229.
Sadek, F., Mohraz, B., Taylor, A. W., and Chung, R. M. (1997). “A method for estimating the parameters of tuned mass dampers for seismic applications.” Earthquake Eng. Struct. Dyn., 26(6), 617–635.
Singh, M. P., Singh, S., and Moreschi, L. M. (2002). “Tuned mass dampers for response control of torsional buildings.” Earthquake Eng. Struct. Dyn., 31(4), 749–769.
Wang, J. F., and Lin, C. C. (2005). “Seismic performance of multiple tuned mass dampers for soil–irregular building interaction systems.” Int. J. Solids Struct., 42(20), 5536–5554.
Xu, H., and Rahman, S. (2004). “A generalized dimension-reduction method for multidimensional integration in stochastic mechanics.” Int. J. Numer. Methods Eng., 61(12), 1992–2019.
Zadeh, L. A. (1963). “Optimality and non-scalar-valued performance criteria.” IEEE Trans. Autom. Control, 8(1), 59–60.
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Published In
Journal of Structural Engineering
Volume 140 • Issue 8 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 25, 2012
Accepted: Jul 23, 2013
Published online: Jul 25, 2013
Published in print: Aug 1, 2014
Discussion open until: Aug 11, 2014
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