H_∞ Optimisation of Viscoelastic Dynamic Vibration Absorber described by Fractional Differential Voigt Model for Damped Linear Systems

Abstract

In this paper, an approximate solution of the optimal parameters by H_∞ optimization of the viscoelastic dynamic vibration absorber (DVA) attached to a damped primary system is proposed. The viscoelastic DVA is described by the fractional differential Voigt model. The approximate solution is derived combining a method in which the viscoelastic DVA is regarded as a equivalent viscous DVA and the fixed point theory for a damped system. The effectiveness of the present method is demonstrated by comparing the approximate solution with the numerical results. Finally, the damping performance of the viscoelastic DVA is evaluated using approximate solution. And it is shown that the damping performance is slightly improved compared to the conventional viscous DVA if the optimum parameters are given.