两自由度单侧碰撞振动系统的分岔与混沌
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摘要
建立了一类两自由度单侧碰撞振动系统的力学模型和Poincaré映射。通过计算机编程仿真,得到了以Poincaré截面上的不变圈表示的拟周期运动,证明了系统在一定条件下存在Neimark-Sacker分岔和周期倍化分岔,并分析了其向混沌演化的不同道路,可为工程实际中该类系统的优化设计提供依据。
A two-degree-of-freedom unilateral impact vibration system and Poincare mapping are established. The quasi periodic motion of the invariant ring on the Poincaré section is obtained by using computer simulation. It is proved that the Neimark-Sacker bifurcation and periodic doubling bifurcation exist under certain conditions,and the routes to chaos are different. It is possible to provide the basis for the optimal design of the system in engineering practice.
A two-degree-of-freedom unilateral impact vibration system and Poincare mapping are established. The quasi periodic motion of the invariant ring on the Poincaré section is obtained by using computer simulation. It is proved that the Neimark-Sacker bifurcation and periodic doubling bifurcation exist under certain conditions,and the routes to chaos are different. It is possible to provide the basis for the optimal design of the system in engineering practice.
引文
[1]Luo Guanwei.Xie Jianhua.Bifurcation and chaos in a system with impacts[J].Physica D,2001(148):183-200.
[2]李万祥,牛卫中.一类含间隙系统的分岔与混沌的形成过程[J].振动与冲击,2005,24(3):47-49.
[3]潘利平.一类两自由度碰撞振动系统的分岔与混沌演化[J].机械研究与应用,2010,23(6):42-45.
[4]Zhou Liangqiang,CHEN Faqi,CHEN Yushu.Bifurcations and chaotic motions of a class of mechanical system with parametric excitations[J].Journal of Computational and Nonlinear Dynamics,2015(10):502-510.
[5]Natsiavas S.Stability and bifurcation analysis for oscillator with limiting constraints[J].Journal of Sound and Vibration,1994,141(1):91-102.
[6]罗冠炜,谢建华.一类两自由度碰撞振动系统的周期运动与稳定性[J].兰州铁道学院学报,1999,18(2):47-54.
[7]丁旺才,谢建华.碰撞振动系统强共振下的两参数动力学分析[J].计算力学学报,2004,21(6):658-663.
[8]罗冠炜,褚衍东.多自由度含间隙振动系统周期运动的Hopfpitchfork余维二分岔[J].工程力学,2006,23(1):99-106.
[2]李万祥,牛卫中.一类含间隙系统的分岔与混沌的形成过程[J].振动与冲击,2005,24(3):47-49.
[3]潘利平.一类两自由度碰撞振动系统的分岔与混沌演化[J].机械研究与应用,2010,23(6):42-45.
[4]Zhou Liangqiang,CHEN Faqi,CHEN Yushu.Bifurcations and chaotic motions of a class of mechanical system with parametric excitations[J].Journal of Computational and Nonlinear Dynamics,2015(10):502-510.
[5]Natsiavas S.Stability and bifurcation analysis for oscillator with limiting constraints[J].Journal of Sound and Vibration,1994,141(1):91-102.
[6]罗冠炜,谢建华.一类两自由度碰撞振动系统的周期运动与稳定性[J].兰州铁道学院学报,1999,18(2):47-54.
[7]丁旺才,谢建华.碰撞振动系统强共振下的两参数动力学分析[J].计算力学学报,2004,21(6):658-663.
[8]罗冠炜,褚衍东.多自由度含间隙振动系统周期运动的Hopfpitchfork余维二分岔[J].工程力学,2006,23(1):99-106.