三自由度复杂冲击振动系统的分岔与混沌

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The mechanical model of a three-degree-of-freedom vibration system is considered in this paper. The analytical solution of the periodic motion in the system is derived, and through the Poincar6 map of the system, Neimark-Sacker bifurcations, period-doubling bifurcations and the routes to chaos of the system are investigated by analytical method. Study on bifurcation and chaos behavior of the system provides a basis for optimal design of the mechanical system with clearance and vibro-impact system in practical engineer- ing.建立了一类三自由度冲击振动系统的力学模型,推出了系统周期运动的解析解,并通过建立系统的Poincaré映射,研究了系统的内依马克-沙克分岔、倍化分岔及其通向混沌的演化过程.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.