Relationship between the homotopy analysis method and harmonic balance method

被引：10

作者：

Chen, Y. M. ^{[1
]}

Liu, J. K. ^{[2
]}

Meng, G. ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, State Key Lab Mech Syst & Vibrat, Shanghai 200240, Peoples R China

[2] Sun Yat Sen Univ, Dept Mech, Guangzhou 510275, Guangdong, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2010年 / 15卷 / 08期

关键词：

Homotopy analysis method; Harmonic balance method; Relationship; APPROXIMATE SOLUTION TECHNIQUE; SMALL PARAMETERS; LIMIT-CYCLE; EQUATION;

D O I：

10.1016/j.cnsns.2009.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a study of the relationship between the homotopy analysis method (HAM) and harmonic balance (HB) method. The HAM is employed to obtain periodic solutions of conservative oscillators and limit cycles of self-excited systems, respectively. Different from the usual procedures in the existing literature, the HAM is modified by retaining a given number of harmonics in higher-order approximations. It is proved that as long as the solution given by the modified HAM is convergent, it converges to one HB solution. The Duffing equation, the van der Pol equation and the flutter equation of a two-dimensional airfoil are taken as illustrations to validate the attained results. (C) 2009 Elsevier B.V. All rights reserved.

引用

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页码：2017 / 2025

页数：9

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