摘要
本文给出了参数激励作用下两自由度非线性振动系统，在１∶２内共振条件下主参数激励低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，采用Ｍｅｌｎｉｋｏｖ方法研究全局分岔行为。
The non_linear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first_order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steady_state solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.
出处
《应用数学和力学》
EI
CSCD
北大核心
1999年第4期337-345,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金
