Abstract
Diffraction of a two-dimensional (2D) semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique. This so-called “improved cosine halfrange expansion” algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern. The governing equations are developed in a manner that minimizes the residues of the boundary conditions. Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented. The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.
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Luo, H., Lee, V.W. & Liang, J. Anti-plane (SH) waves diffraction by an underground semi-circular cavity: analytical solution. Earthq. Eng. Eng. Vib. 9, 385–396 (2010). https://doi.org/10.1007/s11803-010-0023-3
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DOI: https://doi.org/10.1007/s11803-010-0023-3