| 一类两自由度碰撞振动系统的周期运动稳定性与分岔 |
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| 引用本文： | 杨小刚,赵利颇.一类两自由度碰撞振动系统的周期运动稳定性与分岔[J].邢台职业技术学院学报,2008,25(3):38-40. |
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| 作者姓名： | 杨小刚 赵利颇 |
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| 作者单位： | 邢台职业技术学院汽车工程系,河北邢台054035 |
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| 摘 要： | 本文建立了一类两自由度变碰撞面的碰撞振动系统动力学模型，获得了系统的周期响应，推导出系统n-1周期运动的四维Poincaré映射。利用Poincaré映射方法，对系统单碰撞周期运动的稳定性与分岔进行分析，分析了系统n-1周期运动的Hopf分岔、周期倍化分岔及强共振情况下的亚谐分岔，研究了当分岔参数变化时碰撞振动系统由概周期碰撞运动向混沌运动的演化过程，为冲击振动系统的优化设计提供了理论依据。
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| 关 键 词： | 碰撞振动 Poincaré映射 稳定性 Hopf分岔 混沌 |
Stabilty and Bifurcatuons of Periodic Moton in a Two-degree-of-freedom Vibro-Impact System |
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| YANG Xiao-gang,ZHAO Li-po.Stabilty and Bifurcatuons of Periodic Moton in a Two-degree-of-freedom Vibro-Impact System[J].Xingtai Vocational and Technical College,2008,25(3):38-40. |
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| Authors: | YANG Xiao-gang ZHAO Li-po |
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| Institution: | (Xingtai Polytechnic College, Xingtai Hebei054035, China) |
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| Abstract: | A two-degree-of-freedom vibro-impact system is discussed in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the four-dimension Poincaré maps of n-1 periodic motion are established. The stability of the periodic motions is investigated by the Poincaré map and numerical simulation. Hopf bifurcation, subharmonic in strong resonance case and multi-impact periodic motion are analyzed by local bifurcation criterion and numerical simulation. As controlling parameter varies further, the routes of quasi-periodic impact motions to chaos are studied. It is possible to optimize practical system parameters by investigation of bifurcation and chaos. |
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| Keywords: | vibro-impact Poincaré map stability hopfbifurcation chaos |
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