Reliability based optimum design of Tuned Mass Damper in seismic vibration control of structures with bounded uncertain parameters

A reliability based optimization of Tuned Mass Damper (TMD) parameters in seismic vibration control under bounded uncertain system parameters is presented. The study on TMD with random parameters in a probabilistic framework is noteworthy. But, it cannot be applied when the necessary information about parameters uncertainties is limited. In such cases, the interval method is a viable alternative. Applying matrix perturbation theory through a first order Taylor series expansion about the mean values of the uncertain parameters’ conservative dynamic response bounds are obtained assuming a small degree of parameter uncertainty. The first-passage probability of failure of the system is taken as the performance objective. Using the interval extension of the performance objective, the vibration control problem under bounded uncertainties is transformed to the appropriate deterministic optimization problems yielding the lower and upper bound solutions. A numerical study is performed to elucidate the effect of parameters’ uncertainties on the TMD parameters’ optimization and the safety of the structure.