Tuned Liquid Column Damper in Seismic Vibration Control Considering Random Parameters: A Reliability Based Approach

Abstract

The present study deals with reliability based optimization of tuned liquid column damper (TLCD) parameters in seismic vibration control considering uncertainties in the properties of primary structure and ground motion parameters. In doing so, the conditional second order information of the response quantities is obtained in random vibration framework using state space formulation. Subsequently, the total probability theorem is used to evaluate the unconditional response of the primary structures considering random system parameters. The unconditional root mean square displacement (RMSD) of the primary structures is considered as the performance index to define the failure of the primary system which is used as the objective function to obtain the optimum TLCD parameters. Numerical study is performed to elucidate the effect of parameters uncertainties on the optimization of TLCD parameters and system performance. As expected, the RMSD of the primary system is quite significantly reduced with increasing mass ratio and damping ratio of the structure. However, when the system parameters uncertainties are considered, there is a definite change in the optimal tuning ratio and head loss coefficient of the TLCD yielding a reduced efficiency of the system. It is observed that though the randomness in the seismic events dominates, the random variations of the system parameters have a definite and important role to play in affecting the design. In general, the advantage of the TLCD system tends to reduce with increasing level of uncertainty. However, the efficiency is not completely eliminated as it is seen that the probability of failure of the primary structure is still remains much lower than that of the unprotected system.