Study of SH-wave in a pre-stressed anisotropic magnetoelastic layer sandwich by heterogeneous semi-infinite media

A brief study of SH-wave has been encountered in a pre-stressed anisotropic magnetoelastic layer loaded by heterogeneous half-spaces. The semi-infinite media are heterogeneous with different heterogeneity parameters and the upper half-space is taken exponentially varying with depth while the lower medium varying linearly. The solutions are more apparent with analytical methods clubbed with Mathematica-7 to get the numerical results for a particular model with available data. The study involves obtaining the closed-form expression for reflection and transmission coefficients with the continuous boundary conditions at interfaces. The terms for reflection and transmission coefficients manifest the notable dependencies of material coefficients with inhomogeneity parameters, layer thickness, and the known components of wave propagation, i.e., phase velocity, wave number, and incidence angle. The two special cases have been considered, i.e., one when the layer vanishes means only two heterogeneous half-spaces and the other two isotropic half-spaces that lead to validation of results with well-known reference. The numerical results are shown by graphs which make the result transpicuous to interpret physically.