李万祥, 张永燕. 一类四自由度系统碰撞问题[J]. 工程力学, 2013, 30(9): 259-263. DOI: 10.6052/j.issn.1000-4750.2011.12.0847
引用本文: 李万祥, 张永燕. 一类四自由度系统碰撞问题[J]. 工程力学, 2013, 30(9): 259-263. DOI: 10.6052/j.issn.1000-4750.2011.12.0847
LI Wan-xiang, ZHANG Yong-yan. COLLISION PROBLEM OF A FOUT-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM[J]. Engineering Mechanics, 2013, 30(9): 259-263. DOI: 10.6052/j.issn.1000-4750.2011.12.0847
Citation: LI Wan-xiang, ZHANG Yong-yan. COLLISION PROBLEM OF A FOUT-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM[J]. Engineering Mechanics, 2013, 30(9): 259-263. DOI: 10.6052/j.issn.1000-4750.2011.12.0847

一类四自由度系统碰撞问题

COLLISION PROBLEM OF A FOUT-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

  • 摘要: 该文建立了一类四自由度碰撞系统的数学模型,推导出系统周期运动的八维Poincaré映射,计算了中心流行,给出了降维过程和简化方程。研究了周期运动的稳定性,并选取适当的参数,分析了系统周期运动的Hopf分岔和倍化分岔现象,并验证了四自由度碰撞系统Hopf分岔的存在性。编程仿真出系统通向混沌的演化过程,数值模拟了系统的不变环面,揭示了碰撞振动系统不变环面失稳与混沌的形成过程。

     

    Abstract: A mathematical model of a four-degree-of-freedom vibro-impact system is established,deriving the eight-dimensional Poincar?maps of periodic motion in the system,calculating the centre manifold and showing the steps for the reduction of high-dimensional maps to a two-dimensional one. The stability of periodic motion is studied,the Hopf bifurcation and period-doubling bifurcation phenomena of periodic motion in the system are analyzed based on the suitable parameter combination,and the existence of the Hopf bifurcation is verified in a four-degree-of-freedom vibro-impact system. The evolution process of the system to chaos and the system invariant torus are simulated numerically. Consequently,the formation process of instability and chaos of invariant torus in the vibro-impact system are revealed.

     

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