A modified Mickens iteration procedure for nonlinear oscillators

被引：20

作者：

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

Liu, J. K. ^{[1
]}

机构：

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

来源：

JOURNAL OF SOUND AND VIBRATION | 2008年 / 314卷 / 3-5期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1016/j.jsv.2008.03.007

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

Based on the Mickens procedure, it new iteration scheme is proposed for nonlinear oscillators. Different from the existing Mickens procedures, in the proposed procedure, the algebraic equation governing the frequency of oscillation deduced at each iteration stage is always linear. Taking the Duffing equation its an illustrative example, excellent approximations can be easily obtained. Furthermore, the proposed procedure is extended to obtain the limit cycle of the van der Pol equation. Additionally, a computational disadvantage of the Mickens procedure is eliminated. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：465 / 473

页数：9

共 16 条

[1] A new method based on the harmonic balance method for nonlinear oscillators [J].

Chen, Y. M. ;

Liu, J. K. .

PHYSICS LETTERS A, 2007, 368 (05) :371-378

[2] Modified Lindstedt-Poincare methods for some strongly non-linear oscillations Part I: expansion of a constant [J].

He, JH .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2002, 37 (02) :309-314

[3] A classical iteration procedure valid for certain strongly nonlinear oscillators [J].

Hu, H. ;

Tang, J. H. .

JOURNAL OF SOUND AND VIBRATION, 2007, 299 (1-2) :397-402

[4] Solutions of a quadratic nonlinear oscillator: Iteration procedure [J].

Hu, H. .

JOURNAL OF SOUND AND VIBRATION, 2006, 298 (4-5) :1159-1165

[5] Solutions of the Duffing-harmonic oscillator by an iteration procedure [J].

Hu, H. .

JOURNAL OF SOUND AND VIBRATION, 2006, 298 (1-2) :446-452

[6] Solutions of nonlinear oscillators with fractional powers by an iteration procedure [J].

Hu, H. .

JOURNAL OF SOUND AND VIBRATION, 2006, 294 (03) :608-614

[7] An iteration approach to nonlinear oscillations of conservative single-degree-of-freedom systems [J].

Li, PS ;

Wu, BS .

ACTA MECHANICA, 2004, 170 (1-2) :69-75

[8] A modified Mickens procedure for certain non-linear oscillators [J].

Lim, CW ;

Wu, BS .

JOURNAL OF SOUND AND VIBRATION, 2002, 257 (01) :202-206

[9] A modified iteration perturbation method for some nonlinear oscillation problems [J].

Marinca, V ;

Herisanu, N .

ACTA MECHANICA, 2006, 184 (1-4) :231-242

[10] Iteration method solutions for conservative and limit-cycle x1/3 force oscillators [J].

Mickens, RE .

JOURNAL OF SOUND AND VIBRATION, 2006, 292 (3-5) :964-968

← 1 2 →