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加性非平稳激励下结构速度响应的FPK方程降维

芮珍梅 陈建兵

芮珍梅, 陈建兵. 加性非平稳激励下结构速度响应的FPK方程降维[J]. 力学学报, 2019, 51(3): 922-931. doi: 10.6052/0459-1879-18-411
引用本文: 芮珍梅, 陈建兵. 加性非平稳激励下结构速度响应的FPK方程降维[J]. 力学学报, 2019, 51(3): 922-931. doi: 10.6052/0459-1879-18-411
Zhenmei Rui, Jianbing Chen. DIMENSION REDUCTION OF FPK EQUATION FOR VELOCITY RESPONSE ANALYSIS OF STRUCTURES SUBJECTED TO ADDITIVE NONSTATIONARY EXCITATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 922-931. doi: 10.6052/0459-1879-18-411
Citation: Zhenmei Rui, Jianbing Chen. DIMENSION REDUCTION OF FPK EQUATION FOR VELOCITY RESPONSE ANALYSIS OF STRUCTURES SUBJECTED TO ADDITIVE NONSTATIONARY EXCITATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 922-931. doi: 10.6052/0459-1879-18-411

加性非平稳激励下结构速度响应的FPK方程降维

doi: 10.6052/0459-1879-18-411
基金项目: 1) 国家杰出青年科学基金(51725804),国家自然科学基金(11672209,11761131014)和上海市国际科技合作基金 (18160712800)资助项目.
详细信息
    通讯作者:

    陈建兵

  • 中图分类号: U260.17;

DIMENSION REDUCTION OF FPK EQUATION FOR VELOCITY RESPONSE ANALYSIS OF STRUCTURES SUBJECTED TO ADDITIVE NONSTATIONARY EXCITATIONS

  • 摘要: 结构在随机激励下的非线性响应分析是具有高度挑战性的困难问题. 对于白噪声或过滤白噪声激励,求解FPK方程将获得结构响应 的精确解. 遗憾的是,对于非线性多自由度系统,FPK方程难以直接求解. 事实上,其数值解法严重受限于方程维度,而解析求解 则仅适用于少数特定的系统,且多是稳态解. 因此,将FPK方程进行降维,是求解高维随机动力响应分析问题的重要途径. 本文针 对幅值调制的加性白噪声激励下多自由度非线性结构的非平稳随机响应分析问题,将联合概率密度函数满足的高维FPK方程进行降 维. 针对结构速度响应概率密度函数求解,通过引入等价漂移系数,原FPK方程可转化为一维FPK型方程. 建议了构造等价漂移系数 的条件均值函数方法. 进而,采用路径积分方法求解降维FPK型方程,得到速度概率密度函数的数值解答. 结合单自由度Rayleigh 振子、十层线性剪切型框架和非线性剪切型框架结构在幅值调制的加性白噪声激励下的非平稳速度响应求解,讨论了本文方法的精 度和效率,验证了其有效性.

     

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出版历程
  • 收稿日期:  2018-12-05
  • 刊出日期:  2019-05-18

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