AN ABSORBING BOUNDARY CONDITION FOR SH WAVE PROPAGATION IN VISCOELASTIC MULTILAYERED MEDIA 1)
Wu Lihua, Zhao Mi,2), Du XiuliKey Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China
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. Keywords:high-accuracy absorbing boundary condition;continued fraction;D'Alembert viscoelastic multilayered media;scalar wave;finite element method
PDF (1580KB)元数据多维度评价相关文章导出EndNote|Ris|Bibtex收藏本文 本文引用格式 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 1). 力学学报[J], 2020, 52(2): 480-490 DOI:10.6052/0459-1879-19-315 Wu Lihua, Zhao Mi, Du Xiuli. AN ABSORBING BOUNDARY CONDITION FOR SH WAVE PROPAGATION IN VISCOELASTIC MULTILAYERED MEDIA 1). Chinese Journal of Theoretical and Applied Mechanics[J], 2020, 52(2): 480-490 DOI:10.6052/0459-1879-19-315
如图4(a)所示, 总高为40 m的刚性基岩上卧达朗贝尔黏弹性单层介质的场地内嵌一个矩形孔洞,其位于地表以下8 m, 尺寸为6 m $\times $ 8 m. 均匀场地的材料参数如图4(a)中所示.$A$点施加如图5所示的狄拉克脉冲点载荷, 载荷的频谱范围约为0$\sim $55 rad/s,其表达式为
分析方法与5.1节单层介质算例类似. 因为表示多层介质动力刚度的连分式是通过简单扩展单层介质的连分式获得的,必然会有误差引进. 为了使吸收边界条件对于多层介质具有高精度的特性,人工边界的位置到感兴趣区域的距离$L$需要被讨论, 分别取$L=0.5$ $H$和$L=0.75$ $H$.从上到下每层竖向网格的尺寸为2 m, 2 m, 3 m, 3 m和4 m, 横向网格尺寸为2.5 m,如图8(b)所示. 时步为0.004 s.
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