Exact Solution for Scattering of SH-Waves by a Locally Asymmetric Bump in an Elastic Half-Space

Geometric features, particularly bump, on elastic media surfaces greatly impact wave propagation, affecting material mechanical properties and structural response. In this study, a novel analytical method is proposed to solve the interaction between trapezoidal and triangular surface bump of a half-space medium and SH waves using the wave function expansion and complex variable methods. This approach is applicable to both the symmetric and asymmetric cases. First, based on the multipole partition technique, two semicircular auxiliary boundaries were introduced to divide the model into three simpler enclosed regions. Second, a new approach for constructing displacement functions is proposed, which allows the translation of polar coordinates in both the vertical and horizontal directions while ensuring the convergence of the solution. Finally, the differences brought about by the asymmetric assumptions in the trapezoidal and triangular protrusion problems under various incident angles are analyzed.