Equivalent boundary conditions for thin orthotropic layer between two solids: reflection, refraction, and interface waves.

Abstract

Boundary conditions for an interface between two solids are introduced to model a thin orthotropic interface layer. The plane of symmetry of the layer material coincides with the incidence plane. Boundary conditions relating stresses and displacements on both sides of the interface are obtained from an asymptotic representation of the three-dimensional solutions for an interface layer whose thickness is small compared to the wavelength. The results for anisotropic boundary conditions are a generalization of our previous results [S. I. Rokhlin and Y. J. Wang, J. Acoust. Soc. Am. 89, 505-515 (1991)] for an isotropic viscoelastic layer. The interface boundary conditions obtained contain interface stiffness and inertia and terms involving coupling between normal and tangential stresses and displacements. The applicability of such boundary conditions is analyzed by comparison with exact solutions for reflection. As in the isotropic case, fundamental boundary-layer conditions are introduced containing only one transverse or normal mass or stiffness. It is shown that the solution for more accurate interface boundary conditions, which include two inertia elements and two stiffness elements, can be decomposed into a sum of fundamental solutions. Interface waves along such an interface are considered. Characteristic equations for these waves are obtained in closed form for different types of approximate boundary conditions and the velocities calculated from them are compared to the exact solution. It is shown that retention of the terms describing coupling between normal and transverse stresses and displacements is essential for calculating the velocity of an antisymmetric interface wave.