非线性碰撞两自由度系统的混沌运动

A two-degree-of-freedom system with one-side amplitude constraint subjected to periodic excitation is considered. Dynamics of the system are studied with special attention to Hopf bifurcations of period motions in two kinds of strong resonance cases. The PoincareH map of the vibro-impact system with proportional damping property is established. The stability of a class of periodic motions with one impact is investigated by analytical methods. Hopf bifurcation values and intersecting conditions of the period motions with one impa ct, in two kinds of strong resonance cases, are determined. A center manifoldtheorem technique is applied to reduce the PoincareH map to a two-dimensional one, which is put into normal form by theory of normal forms. By theory of Hopf bifurcations of "xedpoints in R-strong resonance, local dynamic behavior of the vibro-impact system, near points of resonance, is analyzed. The theoretical analyses are veri"ed by numerical solutions. Routes of periodic impacts to chaos, in two kinds of strong resonance cases, are obtained by numerical simulations. 2001 Elsevier Science Ltd. All rights reserved. ct, in two kinds of strong resonance cases, are determined. A center manifoldtheorem technique is applied to reduce the PoincareH map to a two-dimensional one, which is put into normal form by theory of normal forms. By theory of Hopf bifurcations of "xedpoints in R-strong resonance, local dynamic behavior of the vibro-impact system, near points of resonance, is analyzed. The theoretical analyses are veri"ed by numerical solutions. Routes of periodic impacts to chaos, in two kinds of strong resonance cases, are obtained by numerical simulations. 2001 Elsevier Science Ltd. All rights reserved.