| 一类两自由度碰撞振动系统的Hopf分岔和混沌 |
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| 引用本文： | 乐源,谢建华,丁旺才.一类两自由度碰撞振动系统的Hopf分岔和混沌[J].动力学与控制学报,2004,2(3):36-41. |
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| 作者姓名： | 乐源 谢建华 丁旺才 |
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| 作者单位： | 西南交通大学应用力学与工程系,成都,610031;西南交通大学应用力学与工程系,成都,610031;兰州交通大学机电工程学院,兰州,730070 |
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| 基金项目： | 国家自然科学基金资助项目(10072051)
教育部高等学校博士点专项科研基金资助项目(20010613001)~~ |
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| 摘 要： | 分析了一类两自由度碰撞振动系统的周期运动,并通过计算Poincare映射的线性化矩阵,确定周期运动的稳定性.分析表明,在一定的参数条件下系统存在周期倍化分岔和Hopf分岔,并通过数值模拟方法得到了以Poincare截面上的不变圈表示的拟周期响应.简明地讨论了系统通向混沌的道路.
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| 关 键 词： | 碰撞振动 周期运动 Poincaré映射 Hopf分岔 混沌 |
| 收稿时间： | 5/9/2004 12:00:00 AM |
| 修稿时间： | 2004年5月9日 |
Hopf bifurcation and chaos of a two-degree-of-freedom vibro-impact systems |
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| Le Yuan,Xie Jianhua and Ding Wangcai.Hopf bifurcation and chaos of a two-degree-of-freedom vibro-impact systems[J].Journal of Dynamics and Control,2004,2(3):36-41. |
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| Authors: | Le Yuan Xie Jianhua and Ding Wangcai |
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| Abstract: | The periodic motion and the Poincare maps of a two-degree-of-freedom vibro-impact system were studied,and the stability of the periodic motion was determined by the eigenvalues of the Jacobian matrix. The analysis showed that there existed Hopf bifurcations and period-doubling bifurcations in the vibro-impact system under suitable system parameters. The quasi-periodic responses of the system represented by invariant circles in the projected Poincare section were obtained by numerical simulations, and the routes to chaos were described . |
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