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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

李伟, 赵俊锋, 李瑞红, N·特里索维奇. Gauss白噪声激励下分数阶导数系统的非平稳响应[J]. 应用数学和力学, 2014, 35(1): 63-70. doi: 10.3879/j.issn.1000-0887.2014.01.007
引用本文: 李伟, 赵俊锋, 李瑞红, N·特里索维奇. Gauss白噪声激励下分数阶导数系统的非平稳响应[J]. 应用数学和力学, 2014, 35(1): 63-70. doi: 10.3879/j.issn.1000-0887.2014.01.007
LI Wei, ZHAO Jun-feng, LI Rui-hong, Natasa Trisovic. Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation[J]. Applied Mathematics and Mechanics, 2014, 35(1): 63-70. doi: 10.3879/j.issn.1000-0887.2014.01.007
Citation: LI Wei, ZHAO Jun-feng, LI Rui-hong, Natasa Trisovic. Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation[J]. Applied Mathematics and Mechanics, 2014, 35(1): 63-70. 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
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

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

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

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