Stochastic Structural Optimization of Multiple Tuned Mass Damper (MTMD) System with Uncertain Bounded Parameters

Abstract

This study deals with the optimization of parameters of multiple tuned mass damper (MTMD) system for seismic vibration control considering uncertain bounded structural parameters. An approach based on Taylor expansion of objective function along with subsequent interval extension is taken into account in this study. The objective function involving the uncertain bounded parameters is transformed into two independent deterministic sub-problems leading to the lower and upper bound solutions with the help of interval extension. The optimization strategy investigated in this optimization framework is the stochastic structural optimization (SSO) where the root mean square displacement of the primary–secondary coupled system is minimized. A numerical study is performed to observe the effect of uncertainties on the optimization of MTMD parameters where the primary system is coupled with MTMD system with two, three, five and ten mass units. The performance of these MTMD systems is also compared under various levels of uncertainties. Fundamental mode of the system is considered for vibration control, where natural frequency and damping ratio associated with the fundamental mode are found to be nearly 10 rad/s and 0.03, respectively. In this study, natural frequency and damping ratio of the primary system, natural frequency and damping ratio of elastic filter, intensity of the power spectral density of white noise excitation at the bed rock are taken as the uncertain parameters. It is observed that SSO is suitable for higher levels of uncertainties associated with structural parameters. It may be mentioned that such observations are found for various numbers of mass-units of MTMD system.