双重内共振系统非线性模态分岔的奇异性分析  

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

作　　者：李欣业[1] 陈予恕[1] 吴志强[1] 

机构地区：[1]天津大学力学系,天津300072

出　　处：《应用数学和力学》2002年第10期997-1007,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目 (重大 19990 5 10 ) ;国家重点基础研究专项经费资助项目(G19980 2 0 316 ) ;教育部博士点基金资助项目 (D0 990 1)

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 。The nonlinear normal modes(NNMs) associated with integrnal 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.

关 键 词：双重内共振 非线性模态 耦合模态 模态分析 奇异性理论 

分 类 号：O322[理学—一般力学与力学基础]