Numerical simulation of anti-plane wave propagation in heterogeneous media

This paper formulates a semi-analytical boundary meshless method, the singular boundary method (SBM), to simulate the anti-plane wave motion in the heterogeneous media. Two different continuous inhomogeneity variations are studied, and the corresponding fundamental solutions are derived by means of a simple variable transformation. The derivation reveals that the fundamental solutions are determined by the wavenumbers of the resulted governing equations after the variable transformation. The source singularities of these fundamental solutions are overcome by the novel origin intensity factors (OIFs). The fundamental solutions and OIFs make the SBM applicable for the simulation of the anti-plane wave scattering and diffraction in nonhomogeneous media. Numerical experiments, including the finite and semi-infinite cases with different variations and boundary conditions, are presented to illustrate the convergence, accuracy and effectiveness of the proposed SBM.