Dispersion computation of guided waves in a layered transversely isotropic elastic medium sandwiched between two half‐spaces

Abstract

AbstractA transversely isotropic elastic medium with a vertical axis of symmetry is considered. We obtain dispersion equations in real terms for guided Love and Rayleigh waves in a such a medium consisting of horizontal layers sandwiched between two half‐spaces by brief modifications of the available literatures on dispersion equations in elastic layered media through transfer matrix. To illustrate the applicability, dispersion curves of guided waves are computed for three‐ and five‐layered symmetric models with transversely isotropic coal seam in the middle. The Airy phase is marked by a minimum or maximum of group velocity in a dispersion curve, and this phase is important to get seam structure for mining safety. For the first three modes, the effect of Thomsen anisotropy parameters γ, ε and δ of a coal seam on frequency (fA) and group velocity (UA) of the Airy phase is similar in three‐ and five‐layered models. For guided Love waves, fA and UA have nearly a uniform increase with the increase of γ. For guided Rayleigh waves, the increase of ε causes fA and UA to increase; however, the increase of δ causes fA and UA to decrease.