Tuned vibration absorbers with nonlinear viscous damping for damped structures under random load

Abstract

The classical problem for the application of a tuned vibration absorber is to minimize the response of a structural system, such as displacement, velocity, acceleration or to maximize the energy dissipated by tuned vibration absorber. The development of explicit optimal absorber parameters is challenging for a damped structural system since the fixed points no longer exist in the frequency response curve. This paper aims at deriving a set of simple design formula of tuned vibration absorber with nonlinear viscous damping based on the frequency tuning for harmonic load for a damped structural system under white noise excitation. The vibration absorbers being considered include tuned mass damper (TMD) and liquid column vibration absorber (LCVA). Simple approximate expression for the standard deviation velocity response of tuned vibration absorber for damped primary structure is also derived in this study to facilitate the estimation of the damping coefficient of TMD with nonlinear viscous damping and the head loss coefficient of LCVA. The derived results indicate that the higher the structural inherent damping the smaller the supplementary damping provided by a tuned vibration absorber. Furthermore, the optimal damping of tuned vibration absorber is shown to be independent of structural damping when it is tuned using the frequency tuning for harmonic load. Finally, the derived closed-form expressions are demonstrated to be capable of predicting the optimal parameters of tuned vibration absorbers with sufficient accuracy for preliminary design of tuned vibration absorbers with nonlinear viscous damping for a damped primary structure.