三自由度复杂非线性系统的混沌与分岔

Chaos and Bifurcation of the Three-degree-of-freedom Non-linear System

建立了三自由度碰撞振动系统的动力学模型,推导出系统n-1周期运动的六维Poincaré映射,运用数值法演示了系统由Hopf分岔,周期倍化分岔通向混沌过程.对该系统分岔与混沌行为的研究,为工程实际中含间隙机械系统和冲击振动系统的优化设计提供了依据.

The dynamic model of three-degree-of-freedom vibro-impact system is established, and six-dimensional poincar6 map of n-1 periodic motion of the system is derived,then the process of Hopf bifurcation and period doubling bifurcation to chaos is demonstrated by using numerical method. The study of the bifurcation and chaos of the system provides the basis for the optimal design of mechanical system with clearance and vibro-impact system in tbe actual project.