Using the extended Melnikov method to study the multi-pulse global bifurcations and chaos of a cantilever beam

被引：62
|
作者：
Zhang, W. [1 ]
Yao, M. H. [1 ]
Zhang, J. H. [1 ]
机构：
[1] Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China
来源：
JOURNAL OF SOUND AND VIBRATION | 2009年 / 319卷 / 1-2期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
PARAMETRICALLY EXCITED CANTILEVER; NONLINEAR NONPLANAR OSCILLATIONS; HOMOCLINIC ORBITS; THIN-PLATE; QUALITATIVE RESONANCE; HAMILTONIAN-SYSTEMS; INTERNAL RESONANCE; STRANGE ATTRACTORS; NORMAL FORMS; DYNAMICS;
D O I：
10.1016/j.jsv.2008.06.015
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
The aim of this paper is to investigate the multi-pulse global bifurcations and chaotic dynamics for the nonlinear non-planar oscillations of a cantilever beam subjected to a harmonic axial excitation and two transverse excitations at the free end by using an extended Melnikov method in the resonant case. First, the extended Melnikov method for studying the Shilnikov-type multi-pulse homoclinic orbits and chaos in high-dimensional nonlinear systems is briefly introduced in the theoretical frame. Then, this method is utilized to investigate the Shilnikov-type multi-pulse homoclinic bifurcations and chaotic dynamics for the nonlinear non-planar oscillations of the cantilever beam. How to employ this method to analyze the Shilnikov-type multi-pulse homoclinic bifurcations and chaotic dynamics of high-dimensional nonlinear systems in engineering applications is demonstrated through this example. Finally, the results of numerical simulation are given and also show that the Shilnikov-type multi-pulse chaotic motions can occur for the nonlinear non-planar oscillations of the cantilever beam, which verifies the analytical prediction. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：541 / 569
页数：29
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