| 一类参数激励与强迫激励并存的非线性振动系统的分叉 |
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| 引用本文： | 王德石,陈予恕,王良桂.一类参数激励与强迫激励并存的非线性振动系统的分叉[J].海军工程大学学报,1994(2). |
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| 作者姓名： | 王德石 陈予恕 王良桂 |
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| 作者单位： | 华中理工大学，天津大学 |
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| 基金项目： | 国家自然科学基金,博士点基金 |
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| 摘 要： | 本文用Ｌｉａｐｕｎｏｖ—Ｓｃｈｍｉｄｔ方法研究了同时受参数激励与强迫激励作用的非线性振动系统的亚谐分叉问题，用奇异性理论确定了等价意义下的分叉方程的形式，导出了必需的分叉系数，求出并且分析了１／２—１／２亚谐共振分叉方程的普适开折，画出了各个结构稳定域及分叉集上的响应图。
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| 关 键 词： | 非线性振动，参数激励，强迫激励，1／2－1／2亚谐共振 奇异性理论 分叉 |
Bifurcation of a Class of Nonlinear Vibration System with Both Parametric Excitation and Forced Excitation |
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| Wang Deshi,Chen Yushu,Wang Lianggui.Bifurcation of a Class of Nonlinear Vibration System with Both Parametric Excitation and Forced Excitation[J].Journal of Naval University of Engineering,1994(2). |
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| Authors: | Wang Deshi Chen Yushu Wang Lianggui |
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| Institution: | Wang Deshi;Chen Yushu;Wang Lianggui |
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| Abstract: | In this paper,bifurcation of a class of nonlinear vibration system with both parametric excitation and forced excitation has been studied by Liapunov-Schmidt method.The theory of singularity is applied to determine the forms of the equivalent bifurcation equations,and the coefficients of the equations are solved. Moreover,the universal unfoldings of the bifurcation equations in 1/2-1/2 subharmonic resonance are analysed,and the bifurcation set as well as the response diagrams are drawm. |
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| Keywords: | Bifurcation Nonlinear vibration Parametric excitation Forced excitation 1/2-1/2 subharmonic resonance Sigularity theory |
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