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