An analytical technique to find approximate solutions of nonlinear damped oscillatory systems

被引：3

作者：

Alam, M. Shamsul ^{[1
]}

Roy, Kamalesh Chandra ^{[1
]}

Rahman, M. Saifur ^{[1
]}

Hossain, Md Mossaraf ^{[2
]}

机构：

[1] RUET, Dept Math, Rajshahi 6204, Bangladesh

[2] RUET, Dept Ind & Prod Engn, Rajshahi 6204, Bangladesh

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2011年 / 348卷 / 05期

关键词：

HARMONIC-BALANCE; PERIODIC-SOLUTIONS;

D O I：

10.1016/j.jfranklin.2011.03.001

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Combining Krylov-Bogoliubov-Mitropolskii (KBM) and harmonic balance methods, an analytical technique is presented to determine approximate solutions of nonlinear oscillatory systems with damping. The first approximate perturbation solutions in which the unperturbed solutions contain two harmonic terms agree with numerical solutions nicely even if the damping force is significant. With suitable examples it has been shown that the combination of classical KBM and harmonic balance methods sometimes fails to measure satisfactory results; but the combination of extended KBM method (by Popov) and harmonic balance method always give the desired results. The method is illustrated by several examples and the solutions are compared to some existing solutions. (C) 2011 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

引用

页码：899 / 916

页数：18

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