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黏弹性多层介质中SH波动的一种吸收边界条件

吴利华, 赵密, 杜修力

吴利华, 赵密, 杜修力. 黏弹性多层介质中SH波动的一种吸收边界条件[J]. 力学学报, 2020, 52(2): 480-490. DOI: 10.6052/0459-1879-19-315
引用本文: 吴利华, 赵密, 杜修力. 黏弹性多层介质中SH波动的一种吸收边界条件[J]. 力学学报, 2020, 52(2): 480-490. DOI: 10.6052/0459-1879-19-315
shu
Wu Lihua, Zhao Mi, Du Xiuli. AN ABSORBING BOUNDARY CONDITION FOR SH WAVE PROPAGATION IN VISCOELASTIC MULTILAYERED MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 480-490. DOI: 10.6052/0459-1879-19-315
Citation: Wu Lihua, Zhao Mi, Du Xiuli. AN ABSORBING BOUNDARY CONDITION FOR SH WAVE PROPAGATION IN VISCOELASTIC MULTILAYERED MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 480-490. DOI: 10.6052/0459-1879-19-315
shu
吴利华, 赵密, 杜修力. 黏弹性多层介质中SH波动的一种吸收边界条件[J]. 力学学报, 2020, 52(2): 480-490. CSTR: 32045.14.0459-1879-19-315
引用本文: 吴利华, 赵密, 杜修力. 黏弹性多层介质中SH波动的一种吸收边界条件[J]. 力学学报, 2020, 52(2): 480-490. CSTR: 32045.14.0459-1879-19-315
shu
Wu Lihua, Zhao Mi, Du Xiuli. AN ABSORBING BOUNDARY CONDITION FOR SH WAVE PROPAGATION IN VISCOELASTIC MULTILAYERED MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 480-490. CSTR: 32045.14.0459-1879-19-315
Citation: Wu Lihua, Zhao Mi, Du Xiuli. AN ABSORBING BOUNDARY CONDITION FOR SH WAVE PROPAGATION IN VISCOELASTIC MULTILAYERED MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 480-490. CSTR: 32045.14.0459-1879-19-315
shu

黏弹性多层介质中SH波动的一种吸收边界条件

  • 北京工业大学城市与工程安全减灾教育部重点实验室, 北京 100124

基金项目: 1)国家重点研发项目(2018YFC1504305);国家自然科学基金项目(51678015);中国教育部创新团队(IRT_17R03)
详细信息
    通讯作者:

    赵密

  • 中图分类号: O241

AN ABSORBING BOUNDARY CONDITION FOR SH WAVE PROPAGATION IN VISCOELASTIC MULTILAYERED MEDIA

  • Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China

摘要

    摘要
  • 摘要: 提出一种高精度时域吸收边界条件,与有限元法结合用于模拟瞬态标量SH波在达朗贝尔黏弹性多层介质中传播问题.建立时域吸收边界条件的过程是:首先将半无限域沿着竖向半离散得到半离散的位移方程以及人工边界处的力-位移关系,再通过引入模态分解, 将物理空间下的量转化到模态空间,从而获得半无限域模态空间下的频域动力刚度;其次采用一种在全频范围内收敛的连分式精确逼近单层介质模态空间下标量形式的频域动力刚度,将标量连分式扩展为矩阵形式用来表示多层介质的频域动力刚度;最后通过引入辅助变量技术,将模态空间下基于连分式的频域动力刚度关系转化为时域吸收边界条件,进一步转换到物理空间后得到物理空间下的时域吸收边界条件.单层介质和五层介质的数值算例表明,建立的高精度时域吸收边界条件对于达朗贝尔黏弹性单层介质是精确且稳定的;对于达朗贝尔黏弹性多层介质, 为了保证其高精度特性,需要将人工边界放置在距离感兴趣区域约为0.5倍无限域高度的位置处.
    Abstract: A high-accuracy absorbing boundary condition in the time domain is proposed, which can be coupled with the finite element method seamlessly to simulate the propagation of the transient scalar wave in the D'Alembert viscoelastic multilayered media. First, a semi-discrete displacement equation of the semi-infinite domain and the force-displacement relationship in the artificial boundary are obtained by semi-discretizing the semi-infinite domain along the vertical depth. Modal decomposition is utilized to convert the field of the semi-infinite domain in the physical space into the modal space. Then the dynamic stiffness of the semi-infinite domain in the frequency domain in the modal space is obtained according to both the displacement equation and the force-displacement relationship in the modal space. Second, a scalar continued fraction, which is convergent over the whole frequency domain, is proposed to describe the scalar dynamic stiffness in the modal space of the D'Alembert viscoelastic single-layered medium. The scalar continued fraction is extended to the matrix form to represent the dynamic stiffness in the modal space of the D'Alembert viscoelastic multilayered media. Last, by introducing auxiliary variables, a time-domain absorbing boundary condition in the modal space is constructed based on the proposed continued fraction. Subsequently, considering the relationship of the field in the modal space and in the physical space, a time-domain absorbing boundary condition in the physical space is obtained by converting the absorbing boundary condition in the modal space into the physical space. Two numerical examples of a single-layered medium and a five-layered media verify that the proposed method is accurate and stable for the D'Alembert viscoelastic single-layered medium, and for the D'Alembert viscoelastic multilayered media, in order to ensure the proposed method's property of high-accuracy, the distance from artificial boundary to the region of interest needs to be about 0.5 times of the total layer height of the infinite domain.
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  • [1] Kennett B. Seismic Wave Propagation in Stratified Media. ANU E Press, 2009
    [2] 杜修力 . 工程波动理论与方法. 北京: 科学出版社, 2009
    [2] ( Du Xiuli. Theories and Methods of Wave Motion for Engineering. Beijing: Science Press, 2009 (in Chinese))
    [3] Lysmer J, Kuhlemeyer RL . Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, 1969,95(4):859-878
    [4] Higdon RL . Absorbing boundary conditions for acoustic and elastic waves in stratified media. Journal of Computational Physics, 1992,101(2):386-418
    [5] 杜修力, 赵密, 王进廷 . 近场波动模拟的人工应力边界条件. 力学学报, 2006,38(1):49-56
    [5] ( Du Xiuli, Zhao Mi, Wang Jintin . A stress artificial boundary in FEA for near-field wave problem. Chinese Journal of Theoretical and Applied Mechanics, 2006,38(1):49-56 (in Chinese))
    [6] Skelton EA, Adams SDM, Craster RV . Guided elastic waves and perfectly matched layers. Wave Motion, 2007,44(7-8):573-592
    [7] Hagstrom T, Mar-Or A, Givoli D . High-order local absorbing conditions for the wave equation: Extensions and improvements. Journal of Computational Physics, 2008,227(6):3322-3357
    [8] Du X, Zhao M . A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media. Soil Dynamics & Earthquake Engineering, 2010,30(10):937-946
    [9] 章旭斌, 谢志南, 廖振鹏 . SH波动模拟中透射边界反射放大失稳研究. 哈尔滨工程大学学报, 2019(6):1-6
    [9] ( Zhang Xubin, Xie Zhinan, Liao Zhenpeng . Study on reflection amplification instability of transmitting boundary in SH wave simulation. Journal of Harbin Engineering University, 2019(6):1-6 (in Chinese))
    [10] Hagstrom T, Kim S . Complete radiation boundary conditions for the Helmholtz equation I: Waveguides. Numerische Mathematik, 2019,141(4):917-966
    [11] Medvinsky M, Tsynkov S, Turkel E . Direct implementation of high order BGT artificial boundary conditions. Journal of Computational Physics, 2019,376:98-128
    [12] Liu T, Xu Q . Discrete artificial boundary conditions for transient scalar wave propagation in a 2D unbounded layered media. Computer Methods in Applied Mechanics and Engineering, 2002,191(27-28):3055-3071
    [13] Prempramote S, Song C, Tin-Loi F , et al. High-order doubly asymptotic open boundaries for scalar wave equation. International Journal for Numerical Methods in Engineering, 2009,79(3):340-374
    [14] Liu T, Zhao C . Finite element modeling of wave propagation problems in multilayered soils resting on a rigid base. Computers and Geotechnics, 2010,37(3):248-257
    [15] Du X, Zhao M . Stability and identification for rational approximation of frequency response function of unbounded soil. Earthquake Engineering & Structural Dynamics}, 2010,39(2):165-186
    [16] Zhao M, Du X, Liu J , et al. Explicit finite element artificial boundary scheme for transient scalar waves in two-dimensional unbounded waveguide. International Journal for Numerical Methods in Engineering, 2011,87(11):1074-1104
    [17] 陈灯红, 杜成斌 . 结构-地基动力相互作用的时域模型. 岩土力学, 2014(4):1164-1172
    [17] ( Chen Denghong, Du Chengbin . A computational model for structure-foundation dynamic interaction in time domain. Rock and Soil Mechanics, 2014(4):1164-1172 (in Chinese))
    [18] Zhao M, Li H, Du X , et al. Time-domain stability of artificial boundary condition coupled with finite element for dynamic and wave problems in unbounded media. International Journal of Computational Methods, 2019,16(4):1850099
    [19] Zhao M, Wu L, Du X , et al. Stable high-order absorbing boundary condition based on new continued fraction for scalar wave propagation in unbounded multilayer media. Computer Methods in Applied Mechanics and Engineering, 2018,334:111-137
    [20] Li H, Zhao M, Wu L , et al. High-order absorbing boundary condition based on new continued fraction for transient scalar wave propagation in 2D and 3D unbounded layers. Engineering Computation, 2019,36(7):2445-2479
    [21] 牛滨华, 孙春岩 . 半无限空间各向同性黏弹性介质与地震波传播. 北京: 地质出版社, 2007
    [21] ( Niu Binhua, Sun Chunyan. Viscoelastic Medium and Seismic Wave Propagation. Beijing: Geological Publishing House, 2007 (in Chinese))
    [22] Abu-Alshaikh I, Turhan D, Mengi Y . Two-dimensional transient wave propagation in viscoelastic layered media. Journal of Sound and Vibration, 2001,244(5):837-858
    [23] Sun L, Luo F . Transient wave propagation in multilayered viscoelastic media: theory, numerical computation, and validation. Journal of Applied Mechanics, 2008,75(3):031007
    [24] Sun L, Pan Y, Gu W . High-order thin layer method for viscoelastic wave propagation in stratified media. Computer Methods in Applied Mechanics and Engineering, 2013,257:65-76
    [25] Basu U, Chopra AK . Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation. Computer Methods in Applied Mechanics and Engineering, 2003,192(11-12):1337-1375
    [26] 单启铜, 乐友喜 . PML 边界条件下二维粘弹性介质波场模拟. 石油物探, 2007,46(2):126-130
    [26] ( Shan Qitong, Yue Youxi . Wavefield simulation of 2-D viscoelastic medium in perfectly matched layer boundary. Geophysical Prospecting for Petroleum, 2007,46(2):126-130 (in Chinese))
    [27] Martin R, Komatitsch D . An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation. Geophysical Journal International, 2009,179(1):333-344
    [28] Josifovski J . Analysis of wave propagation and soil-structure interaction using a perfectly matched layer model. Soil Dynamics and Earthquake Engineering, 2016,81:1-13
    [29] Farzanian M, Arbabi F, Pak R . PML solution of longitudinal wave propagation in heterogeneous media. Earthquake Engineering and Engineering Vibration, 2016,15(2):357-368
    [30] 韩泽军, 林皋, 周小文 等. 横观各向同性层状地基动应力响应的求解与分析. 岩土力学, 2018(6):2287-2294
    [30] ( Han Zejun, Lin Gao, Zhou Xiaowen , et al. Solution and analysis of dynamic stress response for transversely isotropic multilayered soil. Rock and Soil Mechanics, 2018(6):2287-2294 (in Chinese))
    [31] 王振宇, 刘晶波 . 成层地基非线性波动问题人工边界与波动输入研究. 岩石力学与工程学报, 2004,23(7):1169-1169
    [31] ( Wang Zhenyu, Liu Jingbo . Study on wave motion input and artificial boundary for problem of nonlinear wave motion in layered soil. Chinese Journal of Rock Mechanics and Engineering, 2004,23(7):1169-1169 (in Chinese))
    [32] Badry RS, Ramancharla PK . Local absorbing boundary conditions to simulate wave propagation in unbounded viscoelastic domains. Computers & Structures, 2018,208:1-16
    [33] 谢志南, 郑永路, 章旭斌 等. 弱形式时域完美匹配层——滞弹性近场波动数值模拟. 地球物理学报, 2019,62(8):3140-3154
    [33] ( Xie Zhinan, Zheng Yonglu, Zhang Xubin , et al. Weak-form time-domain perfectly matched layer for numerical simulation of viscoelastic wave propagation in infinite-domain. Chinese Journal of Geophysics, 2019,62(8):3140-3154 (in Chinese))
    [34] Ping P, Zhang Y, Xu Y , et al. Efficiency of perfectly matched layers for seismic wave modeling in second-order viscoelastic equations. Geophysical Journal International, 2016,207(3):1367-1386
    [35] Poul MK, Zerva A . Time-domain PML formulation for modeling viscoelastic waves with Rayleigh-type damping in an unbounded domain: Theory and application in ABAQUS. Finite Elements in Analysis and Design, 2018,152:1-16
    [36] Sembalt JF, Lenti L, Ali G . A simple multi directional Absorbing Layer method to simulate elastic wave propagation in unbounded domains, International Journal for Numerical methods in engineering, 2010,1:1-22
    [37] Rajagopal P, Drozdz M, Skelton EA , et al. On the use of absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available finite element packages, NDT & E Int, 2012,51:30-40
    [38] 尹训强, 李建波, 林皋 . 无限地基相互作用力时域求解的阻尼溶剂逐步抽取法. 工程力学, 2015,32(9):20-26
    [38] ( Yin Xunqiang, Li Jianbo, Lin Gao . Damping solvent stepwise extraction method for evalution of interaction forces of unbounded soil in time domain, Engineering Mechanics, 2015,32(9):20-26 (in Chinese))
    [39] Liu T, Li Q . The control-theory-based artificial boundary conditions for time-dependent wave guide problems in unbounded domain. Communications in Numerical Methods in Engineering, 2005,21(12):691-700
    [40] Kausel E . Thin-layer method: Formulation in the time domain. International Journal for Numerical Methods in Engineering, 1994,37(6):927-941
    [41] Chen X, Birk C, Song C . Transient analysis of wave propagation in layered soil by using the scaled boundary finite element method. Computers and Geotechnics, 2015,63:1-12
    [42] 张金波, 杨顶辉, 贺茜君 等. 求解双相和黏弹性介质波传播方程的间断有限元方法及其波场模拟. 地球物理学报, 2018,61(3):926-937
    [42] ( Zhang Jinbo, Yang Dinghui, He Qianjun , et al. Discontinuous Galerkin method for solving wave equations in two-phase and viscoelastic media. Chinese Journal of Geophysics-Chinese Edition, 2018,61(3):926-937 (in Chinese))
    [43] Chen X, Duan J, Li Y. Mass proportional damping in nonlinear time-history analysis//3rd International Conference on Material, Mechanical and Manufacturing Engineering (IC3ME 2015), Atlantis Press, 2015
    [44] 王笃国, 赵成刚 . 地震波斜入射下考虑场地非线性、地形效应和土结动力相互作用的大跨连续刚构桥地震响应分析. 工程力学, 2017,34(4):37-46
    [44] ( Wang Duguo, Zhao Chenggang . Seismic analysis of long-span continuous rigid frame bridge considering site nonlinearity, topography effect and soil-structure dynamic interaction under oblique incidence. Engineering Mechanics, 2017,34(4):37-46 (in Chinese))
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  • 收稿日期:  2019-11-13
  • 刊出日期:  2020-04-09

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