| 一类两自由度含间隙系统的Hopf分岔 |
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| 引用本文： | 周伟,褚衍东,俞建宁,李志苹.一类两自由度含间隙系统的Hopf分岔[J].动力学与控制学报,2008,6(3):235-238. |
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| 作者姓名： | 周伟 褚衍东 俞建宁 李志苹 |
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| 作者单位： | 兰州交通大学数理与软件工程学院,兰州,730070 |
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| 基金项目： | 国家自然科学基金，教育部高等学校博士学科点专项科研基金 |
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| 摘 要： | 建立了一类两自由度含间隙系统的力学模型，并研究了该系统的周期运动及运动的受扰运动．通过选取适当的Poincare截面及系统碰撞的周期性条件，建立了系统的Poincare映射．利用Poincare映射数值证明了Hopf圈的存在性，揭示了并讨论了随着参数的变化系统通过Hopf分岔及周期倍化分岔向混沌演化的过程．最后讨论了系统参数对系统动力学行为的影响，为系统的动力学优化设计找到了理论依据．
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| 关 键 词： | 含间隙系统 Poincare映射 周期运动 Hopf分岔 |
| 收稿时间： | 2008/4/22 0:00:00 |
| 修稿时间： | 2008/5/16 0:00:00 |
The Hopf bifurcation of a two-degree-of-freedom system with clearance |
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| Zhou Wei,Chu Yandong,Yu Jianning and Li Zhiping.The Hopf bifurcation of a two-degree-of-freedom system with clearance[J].Journal of Dynamics and Control,2008,6(3):235-238. |
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| Authors: | Zhou Wei Chu Yandong Yu Jianning and Li Zhiping |
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| Affiliation: | School of Mathematics;Physics and Software Engines Lanzhou Jiaotong University;Lanzhou 730070;China |
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| Abstract: | A mechanical model of two degree of freedom system with clearance was established,whose periodic motion and disturbed motion were studied. The Poincaré mapping of the system was established by selecting the appropriate Poincaré section and the periodic conditions of vibro impact. The existence of Hopf circle was proved by Poincaré mapping numerically. The route to chaos through Hopf bifurcation and period doubling bifurcation of this system was revealed. Finally, the impact of the system parameters on the dynamical behaviors of this system was analyzed,and the theoretical criterion for the optimal design of dynamical systems was found. |
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| Keywords: | system with clearance Poincare mapping periodic motion Hopf bifurcation |
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