Exact Algebraic Optimization of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Response (1st Report, Viscous Damped Absorber)

摘要

Recently, Nishihara and Matsuhisa have proposed a new theory for attaining the H_∞ optimiza- tion of a dynamic vibration absorber (DVA) in the linear vibratory systems. This is a classical optimization problem, and already solved more than 50 years ago using the so-called fixed-points theory. However, this solution is only an approximate one for the H_∞ optimization of DVA. The new theory proposed them gives us the exact solution. Using this theory, they found the closed-form exact solution for a typical performance index, namely, compliance transfer function of the 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 responces to acceleration, velocity or displacement input to foundation for motion excitation system. As a result, we found the closed-form exact solutions for all performance indexes described above when the primary system has no damping. The results obtained here are compared with the approximate ones derived by the fixed-points theory.