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

✍ Scribed by Guanwei Luo; Yanlong Zhang; Jianhua Xie; Jiangang Zhang

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 942 KB
• Volume: 13
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2006.08.004

✦ Synopsis

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 twodimensional 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, are 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.