Gauss白噪声激励下分数阶导数系统的非平稳响应

李伟; 赵俊锋; 李瑞红; N·特里索维奇

doi:10.3879/j.issn.1000-0887.2014.01.007

Gauss白噪声激励下分数阶导数系统的非平稳响应

doi: 10.3879/j.issn.1000-0887.2014.01.007

¹西安电子科技大学数学与统计学院, 西安 710071;²西北工业大学理学院应用数学系, 西安 710072;³贝尔格莱德大学机械工程学院力学系, 贝尔格莱德 11000, 塞尔维亚

基金项目: 国家自然科学基金（11302157；11202155）；中央高校基本科研业务费专项资金（K5051370008）；中国与塞尔维亚科技合作项目（2-14）

详细信息

作者简介:
李伟（1977—），女，辽宁葫芦岛人，副教授，博士（通讯作者. E-mail: liweilw@mail.xidian.edu.cn）；

中图分类号: O324
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出版历程
- 收稿日期: 2013-06-03
- 修回日期: 2013-10-27
- 刊出日期: 2014-01-15

Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation

¹School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China;²Department of Applied Mathematics, School of Natural and Applied Sciences,Northwestern Polytechnical University, Xi’an 710072, P.R.China;³Department of Mechanics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade 11000, Serbia

Funds: The National Natural Science Foundation of China（11302157；11202155）

摘要

摘要: 研究了Gauss（高斯）白噪声激励下具有分数阶导数阻尼的非线性随机动力系统的非平稳响应．应用等价线性化方法将非线性系统转化为等价的线性系统，之后采用随机平均法获得系统响应满足的FPK（Fokker-Planck-Kolmogorov）方程，其中分数阶导数近似为一个周期函数．使用Galerkin方法求解FPK方程进而得到系统的近似非平稳响应．数值结果验证了方法的正确性和有效性.
- 非平稳响应 /
- 分数阶导数 /
- 随机平均法 /
- Galerkin方法
Abstract: Non-stationary response of a nonlinear stochastically dynamical system with fractional derivative damping under Gaussian white-noise excitation was investigated. Based on the equivalent linearization method, the original nonlinear system was converted to a linear system with respect to the vibration amplitude and phase, then the stochastic averaging method was applied to obtain the FPK equation, in which the fractional derivative was approximated by a periodic function. The approximate non-stationary response of the FPK equation was derived with Galerkin method. Numerical results verify the efficiency and correction of the proposed method.
- non-stationary response /
- fractional derivative /
- stochastic averaging method /
- Galerkin method

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参考文献(14)

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