参数激励两自由度非线性振动系统的分岔分析

Bifurcation of a Two Degree of Freedom Nonlinear Vibrating System Subject to Parametric Excitation

文章给出了在参数激励作用下及在固有频率为２∶１的内共振条件下，两自由度非线性振动系统主参数激励高阶模态的非线性响应．采用多尺度法得到其振幅和相位的调制方程，分析发现平凡解通过树枝分岔产生耦合模态解；并采用Ｍｅｌｎｉｋｏｖ方法研究全局分岔行为，确定了产生Ｓｍａｌｅ马蹄型混沌的参数值．

The non linear response of a two degree of freedom nonlinear vibrating system subject to parametric excitation is examined for a two to one internal resonance and one half subharmonic parametric resonance. The method of multiple scales is used to determine the amplitude and phase modulation equations to the first order. The coupled mode steady state solutions are obtained from the trivial solution through pitchfork bifurcation. The Melnikov method is used to study the global bifurcation behavior while the critical parameter is determined for which the dynamical system possesses a Smale horseshoe type of chaos.