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调制白噪声激励下的单自由度强非线性系统的近似瞬态响应概率密度

金肖玲 黄志龙 梁以德

金肖玲, 黄志龙, 梁以德. 调制白噪声激励下的单自由度强非线性系统的近似瞬态响应概率密度[J]. 应用数学和力学, 2011, 32(11): 1294-1305. doi: 10.3879/j.issn.1000-0887.2011.11.004
引用本文: 金肖玲, 黄志龙, 梁以德. 调制白噪声激励下的单自由度强非线性系统的近似瞬态响应概率密度[J]. 应用数学和力学, 2011, 32(11): 1294-1305. doi: 10.3879/j.issn.1000-0887.2011.11.004
JIN Xiao-ling, HUANG Zhi-long, LEUNG Andrew Y T. Nonstationary Probability Densities of System Response of Strongly Nonlinear Single-Degree-of-Freedom System Subject to Modulated White Noise Excitation[J]. Applied Mathematics and Mechanics, 2011, 32(11): 1294-1305. doi: 10.3879/j.issn.1000-0887.2011.11.004
Citation: JIN Xiao-ling, HUANG Zhi-long, LEUNG Andrew Y T. Nonstationary Probability Densities of System Response of Strongly Nonlinear Single-Degree-of-Freedom System Subject to Modulated White Noise Excitation[J]. Applied Mathematics and Mechanics, 2011, 32(11): 1294-1305. doi: 10.3879/j.issn.1000-0887.2011.11.004

调制白噪声激励下的单自由度强非线性系统的近似瞬态响应概率密度

doi: 10.3879/j.issn.1000-0887.2011.11.004
基金项目: 国家杰出青年基金资助项目(11025211);浙江省自然科学基金资助项目(Z6090125);全国百篇优秀博士论文专项基金及香港研资局资助项目(CityU115807)
详细信息
    作者简介:

    金肖玲(1983- ),女,浙江浦江人,讲师(E-mail:jinling113@gmail.com);黄志龙(联系人.E-mail:zlhuang@zju.edu.cn).

  • 中图分类号: O324; O322

Nonstationary Probability Densities of System Response of Strongly Nonlinear Single-Degree-of-Freedom System Subject to Modulated White Noise Excitation

  • 摘要: 研究调制白噪声激励下,包含弱非线性阻尼及强非线性刚度的单自由度系统的近似瞬态响应概率密度.应用基于广义谐和函数的随机平均法,导出关于幅值瞬态概率密度的平均Fokker-Planck-Kolmogorov 方程.该方程的解可近似表示为适当的正交基函数的级数和,其中系数是随时间变化的.应用Galerkin方法,这些系数可由一阶线性微分方程组解得,从而可得幅值响应的瞬态概率密度的半解析表达式及系统状态响应的瞬态概率密度和幅值的统计矩.以受调制白噪声激励的van der Pol-Duffing振子为例验证其求解过程,并讨论了线性阻尼系数及非线性刚度系数等系统参数对系统响应的影响.
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出版历程
  • 收稿日期:  2010-09-10
  • 修回日期:  2011-09-05
  • 刊出日期:  2011-11-15

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