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Scattering of SH waves by orthotropic lining groups in half space

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Abstract

As an important underground structure, reinforced concrete lining tunnel is widely used in transportation and urban underground drainage. Reinforced concrete has orthogonal anisotropy. Therefore, the wave equation of SH wave in orthotropic lining in cylindrical coordinate system is studied. In this paper, the expression of standing wave in lining is given based on the separated variable method, and the expression of the scattering wave of the lining in the homogeneous half space is given by using the mirror image method. The unknown coefficients in the wave field expression are determined according to the boundary conditions. Finally, a numerical example is given to analyze the scattering of SH waves by a pair of identical orthotropic subsurface lining, the influence of incident angle and wave number of SH waves, lining thickness, spacing between two lining and two shear modulus ratio parameters on dynamic stress concentration factor and surface displacement amplitude of lining and its adjacent surface are studied.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 12072085); the Opening Fund of Acoustics Science and Technology Laboratory (Grant No. SSKF2020011); the Fundamental Research Funds for the Central Universities (No. 3072021CF0206); the “Young Talents” Project of Northeast Agricultural University (17QC12) and the Research Team Project of Heilongjiang Natural Science Foundation (Grant No.TD2020A001).

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Authors and Affiliations

  1. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China

    Yong Xiao, Zai-lin Yang, Yong Yang & Meng-han Sun

  2. Key Laboratory of Advanced Material of Ship and Mechanics, Ministry of Industry and Information Technology, Harbin Engineering University, Harbin, 150001, China

    Zai-lin Yang, Yong Yang & Meng-han Sun

  3. School of Water Conservancy and Civil Engineering, Northeast Agricultural University, Harbin, 150030, Heilongjiang, China

    Hong-yu Deng

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  1. Yong Xiao
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Correspondence to Yong Yang or Hong-yu Deng.

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Xiao, Y., Yang, Zl., Yang, Y. et al. Scattering of SH waves by orthotropic lining groups in half space. Arch Appl Mech 92, 691–712 (2022). https://doi.org/10.1007/s00419-021-02067-0

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