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非线性模态的分类和新的求解方法

CLASSIFICATION OF NONLINEAR NORMAL MODES AND THEIR NEW CONSTRUCTIVE METHOD

  • 摘要: 引入不可分偶数维不变流形的概念来定义非线性模态.在此基础上,揭示出了一种新的模态——耦合非线性模态,并对实际系统中各种可能的模态进行了分类.这种分类可能是新的构筑非线性模态理论的框架.用此方法构造非线性模态,得到的模态振子具有范式的形式,形式最简、却能反映原系统在平衡点附近的主要动力学行为,且易于得到非线性频率及非线性稳定性等方面的信息.不仅适用于分析一般的多自由度系统,还可用于分析奇数维系统;不仅可构造内共振系统的非耦合模态,还可用于构造内共振耦合模态.从掌握的资料看,以前的方法还不能解决上述所有问题

     

    Abstract: The definition of the nonlinear normal modes is given by introducing the undivided even dimensional invariant manifold, and a new kind of normal modes (i.e. coupled nonlinear mode) are proposed which may classify all the normal modes expected in physical systems. This idea of classification may form a new base of constructing the nonlinear normal mode theory. Modal oscillators obtained by the method presented here are of Normal Form type,which are simplest in expression and can represent the main dynamical...

     

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