Green’s function technique to study the influence of heterogeneity on horizontally polarised shear-wave propagation due to a line source in composite layered structure

Abstract

The present paper investigates Green’s function technique to study the impact of the non-linear heterogeneity on the propagation of the horizontally polarised shear (SH) wave in a composite layered structure due to the line source. The composite structure is comprised of two distinct isotropic homogeneous elastic layers of finite width lying over an isotropic heterogeneous semi-infinite elastic medium. A general quadratic heterogeneity (including the linear heterogeneity term) in the rigidity of the semi-infinite medium has been taken into account. An efficient analytical treatment involving Green’s function technique along with the application of Fourier transformation has been employed to establish the closed form of the dispersion equation for the propagating wave. As a special case of the problem, the closed form of the dispersion equation has been found in well agreement with the pre-established and classical results. The influence of linear and non-linear heterogeneities on the phase velocity of the horizontally polarised shear-wave has been analysed comparatively for numerous cases associated with the considered model and the corresponding single layer half-space model. It is reported that the phase velocity of the horizontally polarised shear-wave is more pronounced in the case of the corresponding single layer half-space structure as compared to the considered structure. Also, the impact of the general quadratic heterogeneity (supported by the linear heterogeneity) enhances the phase velocity most favourably as compared to the case of the simple quadratic heterogeneity, linear heterogeneity and homogeneity in the semi-infinite medium.