<title>Closed-form exact solution to H<formula><inf><roman>(infinity)</roman></inf></formula> optimization of dynamic vibration absorbers: II. Application to different performance indexes for vibration isolation</title>

Abstract

Recently, Nishihara and Matsuhisa have proposed a new theory for attaining the H_(infinity) optimization of a dynamic vibration absorber (DVA) in the linear vibratory systems. The H_(infinity) optimization of DVA is a classical optimization problem, and already solved more than 50 years ago. All of us know the solution through the textbook written by Den Hartog. The new theory proposed them gives us the exact algebraic solution of the problem. In the first report, we have expounded the theory and showed the procedure of finding the algebraic solution to a typical performance index (compliance transfer function) of the viscous damped system. In this paper, we will apply this theory to another performance indexes: mobility and accelerance transfer functions for force excitation system, and the absolute and relative displacement responses to acceleration, velocity or displacement input to foundation for motion excitation system. We apply this theory not only the viscous damped system but also the hysteretic damped system. As a result, we found the closed-form exact solutions in every performance indexes when the primary system has no damping. The solutions obtained here are compared with the classical ones solved by the fixed-points theory. We further apply this theory to design of DVAs attached to damped primary systems, and found the closed-form exact solutions to some performance indexes of the hysteretic damped system.