Sub-harmonic resonances of nonlinear oscillations with parametric excitation by means of the homotopy analysis method

被引：24

作者：

Jianmin, Wen ^{[1
]}

Zhengcai, Cao ^{[2
]}

机构：

[1] Harbin Inst Technol, Sch Automobile Engn, Weihai 264209, Peoples R China

[2] Tongji Univ, CIMS Res Ctr, Shanghai 200092, Peoples R China

来源：

PHYSICS LETTERS A | 2007年 / 371卷 / 5-6期

关键词：

sub-harmonic resonances; nonlinear oscillation; series solutions; homotopy analysis method (HAM);

D O I：

10.1016/j.physleta.2007.09.057

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

An analytical technique, namely the homotopy analysis method (HAM), is applied to solve periodic solutions for sub-harmonic resonances of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniques, the HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter h. In this Letter, periodic analytic approximations for sub-harmonic resonances of nonlinear oscillations with parametric excitation are obtained by using the HAM for the first time, which agree well with numerical results. This Letter shows that the HAM is a powerful and effective technique for nonlinear dynamical systems. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：427 / 431

页数：5

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