Volume 44 Issue 1
Jan.  2023
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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

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

doi: 10.21656/1000-0887.430116
  • Received Date: 2022-04-04
  • Accepted Date: 2022-06-01
  • Rev Recd Date: 2022-05-04
  • Available Online: 2022-12-27
  • Publish Date: 2023-01-15
  • Porous material structures have been widely used in civil engineering, mechanical engineering, aerospace engineering and other fields due to their high specific strength and specific stiffness. The stochastic response analysis of porous material structures under random excitations deserves more attention. The multiscale governing differential equations for porous material structures were derived based on the multiscale asymptotic-homogenization method (AHM), and the macroscale and microscale explicit time-domain expressions of structural responses were further established. On this basis, the statistical moments of dynamic responses of porous material structures under non-stationary random excitations were achieved with the explicit time-domain method (ETDM). The proposed method combines the advantages of the AHM for high-efficiency explicit formulation of macroscale and microscale dynamic responses of porous material structures and the benefits of the ETDM for fast analysis of non-stationary random vibration problems. A numerical example shows the computation accuracy and efficiency of the presented approach for non-stationary random vibration analysis of porous material structures.

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  • [1]
    刘培生. 多孔材料引论[M]. 北京: 清华大学出版社, 2012.

    LIU Peisheng. Introduction to Porous Materials[M]. Beijing: Tsinghua University Press, 2012. (in Chinese)
    卢天健, 何德坪, 陈常青, 等. 超轻多孔金属材料的多功能特性及应用[J]. 力学进展, 2006, 36(4): 517-535 doi: 10.3321/j.issn:1000-0992.2006.04.004

    LU Tianjian, HE Deping, CHEN Changqing, et al. The multi-functionality of ultra-light porous metals and their applications[J]. Advances in Mechanics, 2006, 36(4): 517-535.(in Chinese) doi: 10.3321/j.issn:1000-0992.2006.04.004
    SMITH B H, SZYNISZEWSKI S, HAJJAR J F, et al. Steel foam for structures: a review of applications, manufacturing and material properties[J]. Journal of Constructional Steel Research, 2012, 71: 1-10. doi: 10.1016/j.jcsr.2011.10.028
    任石磊, 韩飞鹏, 谢斌, 等. 基于三维CFD-DEM的多孔介质流场数值模拟[J]. 应用数学和力学, 2017, 38(10): 1093-1102

    REN Shilei, HAN Feipeng, XIE Bin, et al. Numerical simulation of flow fields in porous media based on the 3D CDF-DEM[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1093-1102.(in Chinese)
    SUN Y, LI Q M. Dynamic compressive behaviour of cellular materials: a review of phenomenon, mechanism and modelling[J]. International Journal of Impact Engineering, 2018, 112: 74-115. doi: 10.1016/j.ijimpeng.2017.10.006
    PIÑEIRO L T, PARRY T, HAUGHEY F, et al. Architected cellular particles to mitigate asphalt stone loss[J]. Construction and Building Materials, 2022, 328: 127056. doi: 10.1016/j.conbuildmat.2022.127056
    郑晓霞, 郑锡涛, 缑林虎. 多尺度方法在复合材料力学分析中的研究进展[J]. 力学进展, 2010, 40(1): 41-56 doi: 10.6052/1000-0992-2010-1-J2008-104

    ZHENG Xiaoxia, ZHENG Xitao, GOU Linhu. The research progress on multiscale method for the mechanical analysis of composites[J]. Advances in Mechanics, 2010, 40(1): 41-56.(in Chinese) doi: 10.6052/1000-0992-2010-1-J2008-104
    陈玉丽, 马勇, 潘飞, 等. 多尺度复合材料力学研究进展[J]. 固体力学学报, 2018, 39(1): 1-68 doi: 10.19636/j.cnki.cjsm42-1250/o3.2017.030

    CHEN Yuli, MA Yong, PAN Fei, et al. Research progress in multi-scale mechanics of composite materials[J]. Chinese Journal of Solid Mechanics, 2018, 39(1): 1-68.(in Chinese) doi: 10.19636/j.cnki.cjsm42-1250/o3.2017.030
    HASSANI B, HINTON E. A review of homogenization and topology optimization Ⅰ: homogenization theory for media with periodic structure[J]. Computers & Structures, 1998, 69(6): 707-717.
    HASSANI B, HINTON E. A review of homogenization and topology optimization Ⅱ: analytical and numerical solution of homogenization equations[J]. Computers & Structures, 1998, 69(6): 719-738.
    李鸿鹏, 凌松, 戚振彪, 等. 热力耦合问题数学均匀化方法的计算精度[J]. 应用数学和力学, 2020, 41(1): 54-69

    LI Hongpeng, LING Song, QI Zhenbiao, et al. Accuracy of the mathematical homogenization method for thermomechanical problems[J]. Applied Mathematics and Mechanics, 2020, 41(1): 54-69.(in Chinese)
    周凤玺, 李丹, 曹小林. 含液饱和不可压多孔弹性板的随机振动[J]. 振动与冲击, 2017, 36(10): 168-174 doi: 10.13465/j.cnki.jvs.2017.10.027

    ZHOU Fengxi, LI Dan, CAO Xiaolin. Random vibration of fluid-saturated porous elastic plates[J]. Journal of Vibration and Shock, 2017, 36(10): 168-174.(in Chinese) doi: 10.13465/j.cnki.jvs.2017.10.027
    苏成, 徐瑞. 非平稳随机激励下结构体系动力可靠度时域解法[J]. 力学学报, 2010, 42(3): 512-520 doi: 10.6052/0459-1879-2010-3-2009-042

    SU Cheng, XU Rui. Time-domain method for dynamic reliability of structural systems subjected to non-stationary random excitations[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 512-520.(in Chinese) doi: 10.6052/0459-1879-2010-3-2009-042
    SU C, XU R. Random vibration analysis of structures by a time-domain explicit formulation method[J]. Structural Engineering and Mechanics, 2014, 52(2): 239-260. doi: 10.12989/sem.2014.52.2.239
    苏成, 黄志坚, 刘小璐. 高层建筑地震作用计算的时域显式随机模拟法[J]. 建筑结构学报, 2015, 36(1): 13-22 doi: 10.14006/j.jzjgxb.2015.01.002

    SU Cheng, HUANG Zhijian, LIU Xiaolu. Time-domain explicit random simulation method for seismic analysis of tall buildings[J]. Journal of Building Structures, 2015, 36(1): 13-22.(in Chinese) doi: 10.14006/j.jzjgxb.2015.01.002
    SU C, HUANG H, MA H T. Fast equivalent linearization method for nonlinear structures under nonstationary random excitations[J]. Journal of Engineering Mechanics, 2016, 142(8): 04016049. doi: 10.1061/(ASCE)EM.1943-7889.0001094
    陈玉震, 张盛, 陈飙松, 等. 非均质结构非平稳随机响应的快速算法[J]. 振动与冲击, 2015, 34(19): 24-30 doi: 10.13465/j.cnki.jvs.2015.19.004

    CHEN Yuzhen, ZHANG Sheng, CHEN Biaosong, et al. A fast algorithm for non-stationary random responses of heterogeneous material structures[J]. Journal of Vibration and Shock, 2015, 34(19): 24-30.(in Chinese) doi: 10.13465/j.cnki.jvs.2015.19.004
    李家春, 周显初. 数学物理中的渐近方法[M]. 北京: 科学出版社, 1998.

    LI Jiachun, ZHOU Xianchu. Asymptotic Methods in Mathematical Physics[M]. Beijing: Science Press, 1998. (in Chinese)
    HASSANI B. A direct method to derive the boundary conditions of the homogenization equation for symmetric cells[J]. Communications in Numerical Methods in Engineering, 1996, 12(3): 185-196. doi: 10.1002/(SICI)1099-0887(199603)12:3<185::AID-CNM970>3.0.CO;2-2
    PAVLIOTIS G A, STUARTA M. Multiscale Methods[M]. New York: Springer, 2008.
    宣立新, 马明. 周期函数初论[M]. 合肥: 安徽教育出版社, 1990.

    XUAN Lixin, MA Ming. Introduction to Periodic Functions[M]. Hefei: Anhui Education Press, 1990. (in Chinese)
    HU Z Q, SU C, CHEN T C, et al. An explicit time-domain approach for sensitivity analysis of non-stationary random vibration problems[J]. Journal of Sound and Vibration, 2016, 382: 122-139. doi: 10.1016/j.jsv.2016.06.034
    范金娟, 张卫方, 陈新文. 定向有机玻璃的拉伸断裂行为研究[J]. 航空材料学报, 2006, 26(5): 106-108 doi: 10.3969/j.issn.1005-5053.2006.05.024

    FAN Jinjuan, ZHANG Weifang, CHEN Xinwen. Investigation of tensile fracture behavior of directional PMMA[J]. Journal of Aeronautical Materials, 2006, 26(5): 106-108.(in Chinese) doi: 10.3969/j.issn.1005-5053.2006.05.024
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