Closed-form optimum liquid column vibration absorber parameters for base-excited damped structures

There have been significant development of techniques for determining optimum parameters of passive dampers and vibration absorbers, but most of the existing studies are limited to the case of an undamped primary structure. This paper aims to develop a first order approximation of the optimal liquid column vibration absorber (LCVA) parameters for suppressing the displacement response of a damped structure under white noise induced ground acceleration. The optimum parameters of a LCVA for the case of an undamped primary structure subjected to white noise induced ground acceleration are first derived and the results are then extended to the case where some damping exists in the primary structure by using a perturbation technique. The accuracy of the derived formulas is then verified through a comparison with the results obtained from numerical methods as well as the results of other studies found in the literature. Finally, a direct approach for determining the optimal head loss coefficient is presented in this study. It is demonstrated that the closed-form approach is capable of predicting the optimal liquid column vibration absorber parameters with reasonable accuracy for damped primary structure.