Periodic-impact motions and bifurcations of vibro-impact systems near 1:4 strong resonance point

被引：18

作者：

Luo, Guanwei ^{[1
]}

Zhang, Yanlong ^{[2
]}

Xie, Jianhua ^{[3
]}

Zhang, Hangang ^{[1
]}

机构：

[1] Lanzhou Jiaotong Univ, Sch Math Phys & Software Engn, Lanzhou 730070, Peoples R China

[2] Lanzhou Jiaotong Univ, Sch Mech Engn, Lanzhou 730070, Peoples R China

[3] SW Jiatong Univ, Dept Engn Mech, Chengdu 610031, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2008年 / 13卷 / 05期

基金：

中国国家自然科学基金;

关键词：

vibration; impact; resonance; periodic motion; bifurcation;

D O I：

10.1016/j.cnsns.2006.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two typical vibro-impact systems are considered. The periodic-impact motions and Poincare maps of the vibro-impact systems are derived analytically. A center manifold theorem technique is applied to reduce the Poincare map to a two-dimensional one, and the normal form map associated with 1:4 strong resonance is obtained. Two-parameter bifurcations of fixed points in the vibro-impact systems, associated with 1:4 strong resonance, arc analyzed. The results from simulation illustrate some interesting features of dynamics of the vibro-impact systems. Some complicated bifurcations, e.g., tangent, fold and Neimark-Sacker bifurcations of period-4 orbits are found to exist near the 1:4 strong resonance points of the vibro-impact systems. (C) 2006 Elsevier B.V. All rights reserved.

引用

页码：1002 / 1014

页数：13

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