The propagation of inhomogeneous waves in an orthotropic viscoelastic medium.

This article focuses on the propagation, reflection, and transmission of inhomogeneous plane waves in orthotropic viscoelastic media, specifically analyzing quasi-longitudinal (qP) and quasi-transverse (qSV) waves at the interface between two orthotropic viscoelastic half-spaces. Using a complex slowness vector that incorporates both propagation and attenuation directions, the study derives closed-form expressions for reflection and transmission coefficients based on boundary conditions ensuring continuity of stresses and displacements. Numerical examples illustrate how the inhomogeneity parameter of the incident wave and the angle of incidence affect wave velocities, attenuation angles, propagation directions, and energy reflection/transmission coefficients. The work also investigates the existence conditions for homogeneous and inhomogeneous incident waves, highlighting differences from purely elastic media and providing insights relevant for theoretical and observational studies of wave behavior in anisotropic, dissipative solids.