| 谐和随机噪声联合作用下Van der PolDuffing振子的参数主共振 |
| |
| 引用本文： | 戎海武,徐伟,等.谐和随机噪声联合作用下Van der PolDuffing振子的参数主共振[J].应用数学和力学,2002,23(3):273-282. |
| |
| 作者姓名： | 戎海武 徐伟 等 |
| |
| 作者单位： | [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 |
| |
| 基金项目： | 国家自然科学基金资助项目 (10 0 72 0 4 9，19972 0 5 4 )，广东省自然科学基金资助项目 (974 4 )，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_2 0 0 2_0 4 )，教育部骨干教师计划资助项目 |
| |
| 摘 要： | 研究了Van der 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。
|
| 关 键 词： | 参数主共振 Van－der－Pol－Duffing振子 多尺度法 谐和噪声 激励 随机噪声 |
| 文章编号： | 1000-0887(2002)03-0273-10 |
| 修稿时间： | 2000年9月6日 |
Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation |
| |
| RONG Hai-wu ,XU Wei ,WANG Xiang-dang ,MENG Guang ,FANG TONG.Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation[J].Applied Mathematics and Mechanics,2002,23(3):273-282. |
| |
| Authors: | RONG Hai-wu XU Wei WANG Xiang-dang MENG Guang FANG TONG |
| |
| Institution: | RONG Hai-wu 1,2,XU Wei 3,WANG Xiang-dang 1,MENG Guang 2,FANG TONG 3 |
| |
| 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. |
| |
| Keywords: | principal resonance Van der Pol-Duffing oscillator multiple scate method largest Liapunov exponent steady state probebility density function |
| 本文献已被 CNKI 维普 等数据库收录！ |
