摘要
通过对工程中一种三自由度弹簧摇床的建模,选择一个碰撞界面作为Poincaré映射的截面,解析法和数值法相结合,证明三自由度含间隙系统通向混沌的道路不仅有典型的倍周期道路、拟周期道路和阵发性混沌,而且还存在包含Neimark-Sacker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。
An important field in vibration engineering is the dynamics of mechanical systems with clearance and constraint. A three degrees-of-freedom system with a pair of symmetric set-up elastic stops is considered in this paper. The differential equation of the system motion is derived and the Poincaré map is established numerically. Bifurcations and chaos of the system are investigated by numerical simulations and analytical method. The routes from quasi-periodic, period-doubling with Neimark-Sarker bifurcation, period-doubling with pitchfork bifurcation, to chaos, are discussed, respectively. It is shown that some routes to chaos in the three degrees-of-freedom system are non-typical. It is possible to optimize the parameters of the practical system by investigation of bifurcation and chaos.
出处
《工程力学》
EI
CSCD
北大核心
2005年第5期111-114,53,共5页
Engineering Mechanics
基金
国家自然科学基金资助项目(50475109)
