Optimum design of tuned liquid column dampers under stochastic earthquake load considering uncertain bounded system parameters

The Tuned Liquid Column Damper (TLCD) is an effective alternative to the Tuned Mass Damper (TMD) to reduce the response of structures due to dynamic loads. The optimum TLCD parameters are normally obtained based on the implicit assumption that the system parameters involved are deterministic. But, the efficiency of dampers may reduce if the TLCD parameters are not tuned to the vibrating mode it is designed to suppress due to the unavoidable presence of system parameter uncertainty. The study of TMD parameters’ optimization considering random system parameters is noteworthy. But, the same is not the case for liquid dampers. Moreover, though the damper parameters optimization under uncertain parameters in probabilistic framework is powerful; the approach cannot be applied in many real situations when the required detailed information to describe the parameters in probabilistic format is limited. In present work, the TLCD parameters optimization to control vibration of structures subjected to stochastic earthquake load under uncertain system parameters modeled as uncertain but bounded (UBB) type is studied. With the aid of matrix perturbation theory using first-order Taylor series expansion and interval extension of the dynamic response function, the vibration control problem is transformed to appropriate deterministic optimization problems yielding the lower and upper bound solution. Numerical study is performed to elucidate the effect of parameters’ uncertainties on the optimization of damper parameters and the performance of TLCD.