高维含间隙振动系统的分岔与混沌研究

通过用解析法和变步长四阶Runge-Kutta数值法相结合，对一类三自由度含间隙弹性约束系统进行分析与仿真，证明三自由度含间隙系统通向混沌的道路不仅有倍周期道路和拟周期道路，而且还有包含Neimark-sacke，分岔的倍周期道路、包含叉式分岔的倍周期道路等复杂的混沌演化过程。对该系统分岔与混沌行为的研究，为工业实际中含间隙机械系统和冲击振动系统的优化设计提供理论依据。

BIFURCATION AND CHAOS OF MULTI-DEGREE-OF-FREEDOM SYSTEM WITH CLEARANCE

An important field in vibration engineering is the dynamics of mechanical systems with piecewise smooth features, such as clearance, constraint, friction and hysteresis Bifurcation and chaos of a three degree of freedom system with a pair of symmetric set up elastic stops is investigated by numerical simulations and analytical method The results of system responses show that routes to chaos from period doubling, or quasi periodic, period doubling with Neimark Sarker bifurcation, period doubling with pitchfork bifurcation are rather complicated It is helpful to optimize system parameter of a practical system by investigation of bifurcation and chaos