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一种求解非线性振动系统渐近解的新方法——计算向量场Normal Form系数的简单方法

A NEW METHOD OF CALCULATING THE ASYMPTOTIC SOLUTION OF NONLINEAR VIBRATION SYSTEMS——A SIMPLE METHOD OF CALCULATING THECOEFFICIENTS OF NORMAL FORM

  • 摘要: 利用非线整变换,本文推导出了一种只需通过简单代数运算即可算出Hopf分叉Normal Form系数的简单方法,用这种方法求解非线性振动问题,只需把原方程变换成本文讨论的典则形式的一阶微分方程组,然后进行简单的代数运算即可得到原非线性振动方程的解,这种方法简单方便容易掌握。

     

    Abstract: Applying nonlinear transformation, the simple method for calculating the coef-ficients of Normal Form by simple algebra has been derived. This method can also be used to solve nonlinear vibration problems. The process are as follows: first, to transform the original (equations to the standard first order differential equations discussed in this paper, then to find the solution of nonlinear vibration equation by simple algebra calculation. This method is easy to learn, and to use.

     

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