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多孔结构多尺度随机振动分析的渐近均匀化-时域显式法

苏成 罗俊哲 许秩

苏成,罗俊哲,许秩. 多孔结构多尺度随机振动分析的渐近均匀化-时域显式法 [J]. 应用数学和力学,2023,44(1):1-11 doi: 10.21656/1000-0887.430116
引用本文: 苏成,罗俊哲,许秩. 多孔结构多尺度随机振动分析的渐近均匀化-时域显式法 [J]. 应用数学和力学,2023,44(1):1-11 doi: 10.21656/1000-0887.430116
SU Cheng, LUO Junzhe, XU Zhi. An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures[J]. Applied Mathematics and Mechanics, 2023, 44(1): 1-11. doi: 10.21656/1000-0887.430116
Citation: SU Cheng, LUO Junzhe, XU Zhi. An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures[J]. Applied Mathematics and Mechanics, 2023, 44(1): 1-11. doi: 10.21656/1000-0887.430116

多孔结构多尺度随机振动分析的渐近均匀化-时域显式法

doi: 10.21656/1000-0887.430116
基金项目: 国家自然科学基金(51678252;52178479);广东省现代土木工程技术重点实验室项目(2021B1212040003)
详细信息
    作者简介:

    苏成(1968—),男,教授,博士,博士生导师(通讯作者. E-mail:cvchsu@scut.edu.cn

  • 中图分类号: O324

An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures

  • 摘要:

    由于具有高比强、高比刚度等优点,多孔结构在土木工程、机械工程和航天航空工程等领域得到了广泛应用。在随机动力荷载作用下多孔结构的随机响应分析是值得关注的研究方向之一。采用多尺度渐近均匀化法,推导了周期性多孔结构动力问题的多尺度控制微分方程,并建立了多孔结构宏观和细观动力响应的时域显式表达式。在此基础上,结合结构随机振动时域显式法,实现了非平稳随机激励下多孔结构动力响应统计矩的计算。所提出的渐近均匀化-时域显式法,一方面可以发挥多尺度动力分析渐近均匀化法的计算优势,高效建立多孔结构宏观和细观动力响应的时域显式表达式;另一方面也可以利用随机振动时域显式法的计算特点,快速精确地求解非平稳随机激励下多孔结构的随机振动问题。通过数值算例,验证了所提方法在多孔结构非平稳随机振动问题求解中的计算精度和计算效率。

  • 图  1  周期性多孔结构和宏观等效结构

    Figure  1.  The periodic porous structure and the macroscopic equivalent structure

    图  2  随机激励$f(t)$的一个样本

    Figure  2.  A sample of random excitation $f(t)$

    图  3  A水平位移时程

    Figure  3.  Time histories of the horizontal displacement at point A

    图  4  A竖向位移时程

    Figure  4.  Time histories of the vertical displacement at point A

    图  5  A竖向正应力时程

    Figure  5.  Time histories of the vertical normal stress at point A

    图  6  A水平位移方差时程

    Figure  6.  Time histories of variance of the horizontal displacement at point A

    图  7  A竖向位移方差时程

    Figure  7.  Time histories of variance of the vertical displacement at point A

    图  8  A竖向正应力方差时程

    Figure  8.  Time histories of variance of the vertical normal stress at point A

    表  1  各时刻显式表达式的系数矩阵

    Table  1.   Coefficient matrices for explicit formulation at different instants

    instantcoefficient matrix
    ${{\boldsymbol{F}}_0}$${{\boldsymbol{F}}_1}$${{\boldsymbol{F}}_2}$${{\boldsymbol{F}}_3}$$ {{\boldsymbol{F}}_{n - 2}} $${{\boldsymbol{F}}_{n - 1}}$${{\boldsymbol{F}}_n}$
    ${t_1}$${{\boldsymbol{A}}_{1,0}}$$ {{\boldsymbol{A}}_{1,1}} $
    ${t_2}$$ {{\boldsymbol{A}}_{2,0}} $${{\boldsymbol{A}}_{2,1}}$${{\boldsymbol{A}}_{1,1}}$
    ${t_3}$$ {{\boldsymbol{A}}_{3,0}} $${{\boldsymbol{A}}_{3,1}}$$ {{\boldsymbol{A}}_{2,1}} $${{\boldsymbol{A}}_{1,1}}$
    $ \vdots $$ \vdots $$ \vdots $$ \vdots $$ \vdots $$ \ddots $
    ${t_{n - 2}}$$ {{\boldsymbol{A}}_{n - 2,0}} $$ {{\boldsymbol{A}}_{n - 2,1}} $$ {{\boldsymbol{A}}_{n - 3,1}} $$ {{\boldsymbol{A}}_{n - 4,1}} $${{\boldsymbol{A}}_{1,1}}$
    ${t_{n - 1}}$${{\boldsymbol{A}}_{n - 1,0}}$${{\boldsymbol{A}}_{n - 1,1}}$$ {{\boldsymbol{A}}_{n - 2,1}} $$ {{\boldsymbol{A}}_{n - 3,1}} $${{\boldsymbol{A}}_{2,1}}$${{\boldsymbol{A}}_{1,1}}$
    ${t_n}$${{\boldsymbol{A}}_{n,0}}$$ {{\boldsymbol{A}}_{n,1}} $${{\boldsymbol{A}}_{n - 1,1}}$$ {{\boldsymbol{A}}_{n - 2,1}} $${{\boldsymbol{A}}_{3,1}}$${{\boldsymbol{A}}_{2,1}}$${{\boldsymbol{A}}_{1,1}}$
    下载: 导出CSV

    表  2  两种方法的计算时间(单位:s)

    Table  2.   Time costs of the 2 methods(unit: s)

    methodconstruction of explicit time-domain
    expressions of dynamic responses
    calculation of statistical moments
    of dynamic responses
    total computation
    time
    multi-scale explicit time-domain method42.002.4644.46
    single-scale explicit time-domain method4482.002.464484.46
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-04-04
  • 录用日期:  2022-06-01
  • 修回日期:  2022-05-04
  • 网络出版日期:  2022-12-27
  • 刊出日期:  2023-01-15

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