| 高维映射的Hopf分叉分析及其在冲击振动系统中的应用 |
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| 引用本文： | 罗冠炜 谢建华. 高维映射的Hopf分叉分析及其在冲击振动系统中的应用[J]. 振动工程学报, 1999, 12(3): 360-366 |
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| 作者姓名： | 罗冠炜 谢建华 |
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| 作者单位： | 兰州铁道学院机械系!兰州730070(罗冠炜)，西南交通大学应用力学与工程系!成都610031(谢建华，孙训方) |
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| 基金项目： | 国家自然科学基金，甘肃省自然科学基金 |
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| 摘 要： | 应用中心流形范式方法研究了高维映射方程在非共振和弱共振情况下的 Ｈｏｐｆ 分叉问题，计算了中心流形，给出了映射的降维过程和简化方程，将 Ｒ２ 映射的 Ｈｏｐｆ分叉理论推广到了高维映射。应用该方法分析了一类两自由度冲击振动系统周期运动 Ｈｏｐｆ 分叉的存在性，并用数值方法得到了该冲击系统的拟周期响应及其向混沌的演化过程
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| 关 键 词： | 非线性振动 混沌 高维映射 Hopf分叉 冲击振动 |
Analysis of Hopf Bifurcation of Map and Its Applications in Impact System |
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| Luo Guanwei. Analysis of Hopf Bifurcation of Map and Its Applications in Impact System[J]. Journal of Vibration Engineering, 1999, 12(3): 360-366 |
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| Authors: | Luo Guanwei |
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| Abstract: | The Hopf bifurcation of high dimensional maps in non resonance and weak resonance cases are investigated by using the center manifold normal from method. The centre manifold is calculated and the steps for reduction of a high dimensional map to a two dimensional one are given. Then the theory of Hopf bifurcation of maps in R 2 is applied to high dimensional map. The Hopf bifurcations of a two degree freedom vibro impact system in non resonance and weak resonance cases are analyzed by means of the method. The theoretical analyses are well supported by numerical results, and the routes of quasi periodic impacts to chaos are obtained. |
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| Keywords: | nonlinear vibration chaos map Hopf bifurcation vibro impact |
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