Design principle of a nonlinear robust dynamic vibration absorber

Abstract

This study aims to develop a design principle of a nonlinear dynamic vibration absorber focusing on its robustness against the alteration of the natural frequency of the primary system. To this end, a 2-DOF coupled system consisting of the primary and absorber systems is analytically solved to evaluate the maximally possible level of the displacement response of the primary system by means of averaging method. In this approach, the equation of motion of the vibration absorber is first solved in the steady-state by the averaging method for a given amplitude of the primary system assuming that the whole responses of the coupled system have the same frequency as the excitation force. Then, the equivalent dynamic stiffness of the dynamic absorber is derived which represents how the absorber acts on the primary system in reaction of the displacement of the primary system. Because the maximally possible displacement amplitude of the primary system is enveloped by the reciprocal of the imaginary part of the equivalent dynamic stiffness, the benefit of introducing a softening effect into the design of the dynamic absorber is theoretically suggested, and validated through numerical simulations.