双重内共振系统非线性模态分岔的奇异性分析

李欣业; 陈予恕; 吴志强

双重内共振系统非线性模态分岔的奇异性分析

天津大学力学系, 天津 300072

基金项目: 国家自然科学基金资助项目(重大19990510);国家重点基础研究专项经费资助项目(G1998020316);教育部博士点基金资助项目(D09901)

详细信息

作者简介:
李欣业(1966- ),男,唐山人,副教授,博士,已发表论文30余篇(E-mail:xinyeli@eyou.com).

中图分类号: O322
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- 文章访问数: 2382
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- 被引次数: 0
出版历程
- 收稿日期: 2001-05-08
- 修回日期: 2002-05-10
- 刊出日期: 2002-10-15

Singular Analysis of Bifurcation of Nonlinear Normal Modes for a Class of Systems With Dual Internal Resonances

Department of Mechanics, Tianjin University, Tianjin 300072, P R China

摘要

摘要: 利用多尺度法构造的一类1:2:5双重内共振系统的耦合非线性模态的分岔是一个两变量的分岔问题.利用Maple计算机代数可以通过消元将耦合的模态分岔方程分离为两个单变量的分岔方程.对分离后的单变量分岔方程进行奇异性分析,发现随着系统参数的变化,非线性模态的分岔既可以是一种模态向另一种模态的转化,也可以是一种模态的突然出现与消失.最后给出了两变量分岔问题可以利用消元后得到的单变量分岔方程和耦合方程进行处理的一种方法.
- 双重内共振 /
- 非线性模态 /
- 耦合模态 /
- 模态分岔 /
- 奇异性理论
Abstract: The nonlinear normal modes(NNMs) associated with internal resonance can be classified into two kinds:uncoupled and coupled. The bifurcation problem of the coupled NNM of systems with 1:2:5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra,and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance,the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last,it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.
- dual internal resonance /
- nonlinear normal mode /
- mode coupling /
- mode bifurcation /
- the singularity theory

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参考文献(17)

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