Design Optimization of Conventional Dynamic Vibration Absorber for Damped Primary System Subjected to White Noise Excitation

(On precise approximate solution)

Abstract

In the present paper, the evaluation of the time average output of the time-invariant linear system is explained in the context of the covariance matrix as the solution to the Lyapunov equation. This problem reduces to simultaneous linear equations with respect to the elements of the covariance matrix. These general relations are applied to two cases, in which the primary system is subjected to the Gaussian white noise excitation, and the dynamic vibration absorber is optimized to minimize the time average of the squared displacement or the squared velocity. The optimum tuning ratios and the damping ratios for the compliance and mobility functions are given as exact solutions. The effects of the primary system damping of the optimal solution proven to be almost negligible.