Bifurcation in a Parametrically Excited Two-Degree-of-Freedom Nonlinear Oscillating System with 1:2 Internal Resonance
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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,确定了产生Smale马蹄型混沌的参数值.
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关键词:
- 参数激励 /
- 内共振 /
- Melnikov方法
Abstract: The nonlinear 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.-
Key words:
- parametric excitation /
- internal resonance /
- Melnikov method
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