The extended Melnikov method for non-autonomous nonlinear dynamical systems and application to multi-pulse chaotic dynamics of a buckled thin plate

被引：51

作者：

Zhang, W. ^{[1
]}

Zhang, J. H. ^{[1
]}

Yao, M. H. ^{[1
]}

机构：

[1] Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 03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：

Multi-pulse chaotic dynamics; Extended Melnikov method; Non-autonomous nonlinear system; Buckled rectangular thin plate; VISCOELASTIC MOVING BELT; HOMOCLINIC ORBITS; GLOBAL BIFURCATIONS; HAMILTONIAN-SYSTEMS; CANTILEVER BEAM; MOTION; PERTURBATIONS; SINGULARITIES; OSCILLATIONS; RESONANCES;

D O I：

10.1016/j.nonrwa.2009.03.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The extended Melnikov method, which was used to solve autonomous perturbed Hamiltonian systems, is improved to deal with high-dimensional non-autonomous nonlinear dynamical systems. The multi-pulse Shilnikov type chaotic dynamics of a parametrically and externally excited, simply supported rectangular thin plate is studied by using the extended Melnikov method. A two-degree-of-freedom non-autonomous nonlinear system of the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. The case of buckling is considered for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of motion to investigate multi-pulse Shilnikov type chaotic motions of the buckled rectangular thin plate for the first time. The results obtained here indicate that multi-pulse chaotic motions can occur in the parametrically and externally excited, simply supported buckled rectangular thin plate. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1442 / 1457

页数：16

共 35 条

[11] Finite element analysis of post-buckling dynamics in plates. Part II: A non-stationary analysis [J].