Modified Lindstedt-Poincare methods for some strongly non-linear oscillations Part I: expansion of a constant

被引：281

作者：

He, JH ^{[1
]}

机构：

[1] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2002年 / 37卷 / 02期

基金：

中国国家自然科学基金;

关键词：

perturbation method; non-linear equations; duffing equation; Lindstedt-Poincare method;

D O I：

10.1016/S0020-7462(00)00116-5

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In this paper, a modified Lindstedt-Poincare method is proposed. In this technique. a constant. rather than the non-linear frequency, is expanded in powers of the expanding parameter to avoid the occurrence of secular terms in the perturbation series solution. Some examples are given here to illustrate its effectiveness and convenience. The results show that the obtained approximate solutions are uniformly valid on the whole solution domain, and they are suitable not only for weakly non-linear systems, but also for strongly non-linear systems. (C) 2001 Elsevier Science Ltd. All rights reserved.

引用

页码：309 / 314

页数：6

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