Optimal design of a new vibration absorber setup for randomly forced systems

In this work, vibration reduction in randomly forced systems is considered using a new vibration absorber setup. In the new setup, the absorber consists of a mass spring and damper, and is attached such that it separates the primary system from the fixed support. White noise excitation is assumed and the objective function is the mean square value of the primary system response function. For given damping and mass ratios of the system, the optimal stiffness and damping ratios of the absorber are determined. The optimal parameters are obtained in an analytical closed form when the primary system is undamped, and calculated numerically for damped primary systems. It is shown that an optimal mass ratio exists, unlike the case of classical absorbers where performance increases with increasing absorber mass. The optimal parameters associated with the optimal mass ratio are calculated and tabulated for a range of primary system damping ratios. The efficiency of the proposed absorber is discussed and compared to that of the classical absorber.