1305 任意周期関数励振を受けるばね-質量系の衝突振動 : 調和および分数調波振動の解析

Abstract

This paper deals with impact vibration in spring-mass system excited by periodic force with arbitrary function. The analytical model is steady impact vibration of a mass with spring and damping in the case where the system is subjected to excitation by displacement. The restoring force, which has an unsymmetric piecewise-linear characteristics, is elastic collision to unsymmetric faces. In order to analyze the main and the 1/2nd order subharmonic resonances, the Fourier series method is applied to this system. Following the theoretical analysis, numerical calculation is performed and the resonance curves are made from the wave of resulting vibration. Effects of the excitation wave form and the excitation amplitude ratio on the resonance curves are shown by numerical results. Also, the stability problems of these vibrations are discussed utilizing Hill's infinite determinant which is obtained from a variational equation of motion. As a result, the stable branches of resonance curves are distinguished from unstable ones. For verification of the numerical method, the experiments are performed. The analytical results are in a fairly good agreement with the experimental ones.