Green’s function for SH-waves in inhomogeneous anisotropic elastic solid with power-function velocity variation

The present paper is aimed at the study of wave phenomena in inhomogeneous, anisotropic media such as functionally graded materials. We derive a Green’s function which can be used to model transient SH-waves in inhomogeneous and anisotropic media, with a power function velocity variation in one direction of the Cartesian coordinate system. The Green’s function is subjected to the restriction that one of the elastic modulus has a quadratic variation, whilst the other elastic modulus and the density have the same power function profile. The results open possibilities for obtaining fundamental solutions and Green’s functions for various (scalar) inhomogeneous equations. We were able to analyze vertical velocities ranging from the limiting linear velocity profile to beyond. We have additionally identified a secondary diffracted wave, originated at a material singular point of the medium.

► We model SH waves in a special type of inhomogeneous anisotropic media.
► We derive a Green’s function for a power-function velocity variation.
► We identify a secondary diffracted wave originated at a singular mate- rial point of the medium.
► We present wave fronts for the direct and secondary waves.