Effect of initial stress on the reflection and transmission of shear horizontal waves at the interface between two transversely isotropic elastic half-spaces

The phenomenon of reflection and transmission of shear wave (horizontally polarized) at an imperfect interface between two different transversely isotropic elastic half-spaces is investigated in this paper. First, the characteristic equation in the transversely isotropic half-space is derived. The forms of the incident, reflected, and transmitted waves are derived. Then, from the interface conditions for two cases (perfect and imperfect interfaces), the displacement and stress are required to be satisfied. The reflection and transmission coefficients in terms of the amplitude ratio of various waves are calculated using interface continuous conditions. The energy ratios of reflected and transmitted waves of the structures have been computed and shown to observe the law of conservation of energy. Numerical examples are shown graphically to exhibit the effects of initial stress as well as the imperfect interface on the phase velocity, phase angles, and reflection and transmission coefficients.