| 带有粘性阻尼摆的自参数振动系统混沌研究 |
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| 引用本文： | 张文娟,俞建宁,安新磊,杨留猛.带有粘性阻尼摆的自参数振动系统混沌研究[J].温州大学学报(自然科学版),2012,33(6):19-24. |
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| 作者姓名： | 张文娟 俞建宁 安新磊 杨留猛 |
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| 作者单位： | 兰州交通大学数理与软件工程学院,甘肃兰州,730070 |
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| 摘 要： | 对一类带有粘性阻尼摆的自参数振动系统的复杂动力学行为进行研究．根据系统运动的拉格朗日方程和牛顿第二定律，建立了系统的动力学方程，借助Poincaré截面和分岔图研究了系统的混沌行为，通过数值仿真得到其相图、Poincaré映射图、分岔图和Lyapunov指数谱，进而证明了该模型是混沌数学模型；对该系统弹簧振子刚度的增加，可导致该系统产生新的混沌区域．
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| 关 键 词： | 自参数振动系统 混沌 Poincaré映射图 分岔图 Lyapunov指数谱 |
Chaos of the Autoparametric Vibration System with a Viscous Damping Pendulum |
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| ZHANG Wenjuan
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YU Jianning
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AN Xinlei
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YANG Liumeng.Chaos of the Autoparametric Vibration System with a Viscous Damping Pendulum[J].Journal of Wenzhou University Natural Science,2012,33(6):19-24. |
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| Authors: | ZHANG Wenjuan YU Jianning AN Xinlei YANG Liumeng |
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| Institution: | (School of Mathematics and Software Engineering, Lanzhou Jiaotong University, Lanzhou, China 730070) |
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| Abstract: | According to Lagrange equation of the dynamic motion and Newton＇s second law, the paper makes a study on the complex dynamic behavior of a kind of autoparametric vibration system with a viscous damping pendulum and thus establishes the kinetic equation of the system. With the help of the Poincaré sections and the bifurcation diagram, the paper has studied the chaotic behavior of the system, and then obtained its phase diagram, Poincaré map, bifurcation diagram and Lyapunov exponent spectrum by numerical simulation, and thus proved that the model is a chaotic mathematical one. And the increase of the spring oscillator stiffness of the system will cause the system to produce a new chaotic region |
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| Keywords: | Autoparametric Vibration System Chaos Poincaré Map Bifurcation Diagram Lyapunov Exponent Spectrum |
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