谐和与随机噪声联合作用下Vander Pol-Duffing振子的参数主共振

戎海武; 徐伟; 王向东; 孟光; 方同

谐和与随机噪声联合作用下Vander Pol-Duffing振子的参数主共振

戎海武^1,2,
徐伟³,
王向东¹,
孟光^1,2,
方同³

1.
佛山科学技术学院, 广东佛山, 528000;
2.
上海交通大学振动、冲击、噪声国家重点实验室, 上海, 200030;
3.
西北工业大学, 应用数学系, 西安, 710072

基金项目: 国家自然科学基金资助项目(10072049;19972054);广东省自然科学基金资助项目(9744);上海交通大学振动、冲击、噪声国家重点实验室开放基金资助项目(VSN-2002-04);教育部骨干教师计划资助项目

详细信息

作者简介:
戎海武(1965- ),男,浙江宁波人,副教授,博士.

中图分类号: O324
计量
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- 被引次数: 0
出版历程
- 收稿日期: 2000-09-06
- 修回日期: 2001-08-20
- 刊出日期: 2002-03-15

Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation

1.
Foshan Institute of Science and Technology, Foshan, Guangdong 528000, P R China;
2.
State Key Laboratry of Vibration, Shoch and Noise, Shanghai Jiaotong University, Shanghai 200030, P R China;
3.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P R China

摘要

摘要: 研究了Vander Pol-Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题。用多尺度法分离了系统的快变项,并求出了系统的最大Liapunov指数和稳态概率密度函数,还分析了失稳、分叉和跳跃现象,讨论了系统的阻尼项、非线性项、随机项和确定性参激强度等参数对系统响应的影响。数值模拟表明所提出的方法是有效的。
- 参数主共振 /
- Vander Pol-Duffing振子 /
- 多尺度法 /
- 最大Liapunov指数 /
- 稳态概率密度
Abstract: The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated.The method of multiple scales was used to determine the equations of modulation of amplitude and phase.The behavior,stability and bifurcation of steady state response were studied.Jumps were shown to occur under some conditions.The effects of damping,detuning,bandwidth,and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.
- principal resonance /
- Van der Pol-Duffing oscillator /
- multiple scate method /
- largest Liapunov exponent /
- steady state probebility density function

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参考文献(13)

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