Stochastic design of multiple tuned mass damper system under seismic excitation

Design/optimization of the tuned mass damper (TMD) system may not always lead toward robust performance if uncertainties exist. In view of this, a stochastic design of multiple TMD (MTMD) systems has been proposed in the present study taking into account various uncertainties. Taylor-expansion is used to perturb the objective function facilitating stochastic design/optimization. An interval-extension is used to observe the effect of uncertainties of different levels. The Lyapunov equation is used in the design of TMD systems by minimizing the dispersion of displacement of the primary system. The present work takes into account a model of generalized MTMD system. Seismic excitation is considered as a random process in the form of both: (a) stationary Kanai–Tajimi (KT) filter and (b) stationary Gaussian white noise directly applied to the base of structure. A numerical investigation is carried out to observe the consequences of uncertainties on the optimum design of MTMD parameters for both the excitation models (with and without incorporating Kanai–Tajimi filter). Efficiency of the MTMD systems (with variation of number of MTMD mass-units) is compared under various levels of uncertainties. Finally, some significant earthquake records are utilized toward more realistic understanding on the performance of stochastic design of TMD/MTMD systems under seismic excitation with various levels of uncertainties.