渐近法在一类强非线性系统中的应用
The Application of the Asymptotic Method to a Class of Strongly Nonlinear Systems
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摘要: 本文采用文[1、2]的渐近解形式,将渐近法推广到如下较为广泛一类的强非线性振动系统式中g和f为x,的非线性解析函数,ε>0为小参数,并假设对应于ε=0的派生系统有周期解.本文推得系统(0.1)的渐近解递推方法,并应用于实例.Abstract: In this paper, according to the form of the asymptotic solution of papers [1,2], the asymptotic method is extended to the following a class of more general strong nonlinear vibration systems where g and f are the nonlinear analytical-functions of x and , and ε>0 is a small parameter. We assume that the derivative system corresponding to ε=0 has periodic solution. The recurrence equations of the asymptotic solution for the system(0.1) are deduced in this paper, and they are applied to practical examples.
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