| 窄带随机噪声作用下非线性系统的响应 |
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| 引用本文： | 戎海武,王向东,孟光,徐伟,方同. 窄带随机噪声作用下非线性系统的响应[J]. 应用数学和力学, 2003, 24(7): 723-729 |
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| 作者姓名： | 戎海武 王向东 孟光 徐伟 方同 |
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| 作者单位： | 1.佛山科学技术学院数学系, 广东佛山 528000; |
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| 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(000017)，上海交通大学振动、冲击、噪声国家重点实验室开放基金(VSN＿2002＿04) |
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| 摘 要： | 研究了Duffing振子在窄带随机噪声激励下的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,讨论了系统的阻尼项、随机项等对系统响应的影响.在一定条件下,系统具有两个均方响应值.数值模拟表明方法是有效的.
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| 关 键 词： | Duffing振子 主共振 多尺度法 |
| 文章编号： | 1000-0887(2003)07-0723-07 |
| 收稿时间： | 2000-08-30 |
| 修稿时间： | 2000-08-30 |
Response of Nonlinear Oscillator Under Narrow-Band Random Excitation |
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| Affiliation: | 1.Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P. R. China;2.The State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, Shanghai 200030, P. R. China;3.Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China |
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| Abstract: | The principal resonance of Duffing oscillator to narrow_band random parametric excitation was 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 by means of qualitative analyses. The effects of damping, detuning, bandwidth and magnitudes of deterministic and random excitations were analyzed. The theoretical analyses were verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions. |
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| Keywords: | principal resonance Duffing oscillator multiple scale method |
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