Bifurcations in a Mathieu equation with cubic nonlinearities

被引：52

作者：

Ng, L ^{[1
]}

Rand, R ^{[1
]}

机构：

[1] Cornell Univ, Dept Theoret & Appl Mech, Ithaca, NY 14853 USA

来源：

CHAOS SOLITONS & FRACTALS | 2002年 / 14卷 / 02期

关键词：

The authors thank Professor Paul Steen of Cornell University for his help in the use of the AUTO software. Partial funding was provided by the Office of Naval Research; Program Officer Dr. Roy C. Elswick; ONR; 321; and by NUWC; Code; 10; Dr. Richard Nadolink. A version of this paper was presented at the ASME IMECE 2000 Conference in Orlando; FL; November; 5–10; 2000;

D O I：

10.1016/S0960-0779(01)00226-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the nonlinear dynamics of the classical Mathieu equation to which is added a nonlinearity which is a general cubic in x, x(over dot). We use a perturbation method (averaging) which is valid in the neighborhood of 2:1 resonance, and in the limit of small forcing and small nonlinearity. By comparing the predictions of first-order averaging with the results of numerical integration, we show that it is necessary to go to second-order averaging in order to obtain the correct qualitative behavior. Analysis of the resulting slow-flow equations is accomplished both analytically as well as by use of the software AUTO. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：173 / 181

页数：9