Stochastic earthquake response control of structures by liquid column vibration absorber with uncertain bounded system parameters

The present work deals with optimum design of liquid column vibration absorber (LCVA) for seismic vibration control of structures characterized by uncertain system parameters. This involves optimization of the frequency and damping properties of LCVA considering uncertain properties of the structure and ground motion parameters. The study on optimum design of tuned mass damper system considering random system parameters is noteworthy. But, the same is not the case for liquid dampers. Moreover, though the probabilistic methods are powerful, the approach cannot be applied in many real situations when the required detailed information about uncertain parameters is limited. In such cases, the interval method is a viable alternative. With the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem under bounded uncertainty is transformed to appropriate deterministic optimization problems. This requires optimizing two separate objective functions correspond to a lower bound and an upper bound optimum solutions. A numerical study is performed to study the effect of system parameter uncertainty on the optimization of LCVA parameters and its response reduction efficiency. Though the efficiency is not completely eliminated, the advantage of the LCVA tends to reduce as the level of uncertainty increases. It is also seen that neglecting the effect of system parameter uncertainty may overestimate the damper performance.