| 谐和与有界噪声联合参激作用下的Visco-Elastic系统 |
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| 引用本文： | 徐伟,戎海武,方同.谐和与有界噪声联合参激作用下的Visco-Elastic系统[J].应用数学和力学,2003,24(9):963-972. |
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| 作者姓名： | 徐伟 戎海武 方同 |
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| 作者单位： | 1.西北工业大学应用数学系, 西安 710072; |
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| 基金项目： | 国家自然科学基金资助项目(10072049) |
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| 摘 要： | 研究了带visco-elastic项的非线性系统,在谐和与有界噪声联合参激作用下的响应和稳定性问题。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,根据最大Liapunov指数可得系统解稳定的充分必要条件。讨论了系统的visco-elastic项对系统阻尼项和刚度项的贡献,给出了随机项和确定性参激强度等参数对系统响应影响的讨论。数值模拟表明该方法是有效的。
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| 关 键 词： | 参数主共振 visco-elastic项 多尺度法 最大Liapunov指数 分岔 |
| 文章编号： | 1000-0887(2003)09-0963-10 |
| 收稿时间： | 2001-12-12 |
| 修稿时间： | 2001年12月12 |
Visco-Elastic Systems Under Both Deterministic and Bound Random Parametric Excitation |
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| Institution: | 1.Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P.R.China;2.Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P.R.China;3.Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, P.R.China |
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| Abstract: | The principal resonance of a visco-elastic systems under both deterministic and 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 contributions from the visco-elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, band-width, and magnitudes of deterministic and random excitations were analyzed. The theoretical analyses are verified by numerical results. |
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| Keywords: | principal resonance visco-elastic system multiple scale method largest Liapunov exponent bifurcation |
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