Dynamic response of SH wave scattering in a two-dimensional inhomogeneous medium with an embedded elliptical inclusion

Abstract

This study investigated the dynamic stress distribution of an elliptical inclusion embedded in a two-dimensional inhomogeneous medium under shear horizontal wave incidence. The inhomogeneity of the medium was characterized by a continuous density variation expressed as a polynomial function. The governing equation, developed based on this inhomogeneity, was solved analytically using the complex function method. By solving the governing equation, an incident wave at an arbitrary angle was constructed, and complete expressions for the displacement and stress fields in the inhomogeneous medium were obtained. The conformal mapping method was then applied to transform the elliptical inclusion into a unit circle, and the boundary conditions were formulated accordingly. Finally, the undetermined coefficients in the scattering and standing waves were obtained using the orthogonal Fourier series expansion method, and the dynamic stress concentration factor (DSCF) at the inclusion was calculated. Comprehensive dimensionless parameters were considered to analyze the dynamic stress distribution around the inclusion. The effect of various parameters on the DSCF was examined. Overall, this research provides theoretical references for wave propagation problems in solid mechanics and materials science.