Interfacial viscoelastic SH waves

Shear horizontal waves, in the form of transient perturbations, are considered at the interface between two different viscoelastic solids. The admissibility of these interfacial waves is studied via the asymptotic expansion of the Laplace transform of the viscoelastic kernel. The compatibility condition is reduced to a set of algebraic systems which can be solved iteratively to the desired order in the asymptotic expansion. Two classes of solutions are found which correspond to transient waves decaying away from the interface and attenuated along the propagation direction. Numerical examples are given to illustrate the results.