Transmission of SH waves through an elastic layer between two solids with frictional contact interfaces

The propagation of SH waves in a three-layered medium containing an interlayer between two semi-infinite solids with frictional contact interfaces is studied. The incident wave, which propagates through the layer from one half-space to another with subcritical angle, is assumed to be strong enough so that friction may be broken, and the local slip may take place at the interfaces. The mixed boundary conditions involving inequalities and unknown intervals lend to a set of recurrence relations. Special examples are given for the case of identical materials to illustrate the mathematical procedure to obtain final results. The interface tractions and relative slip velocities are presented. The interaction between the two interfaces is discussed. It is shown that the slip of the interface near the incident wave may restrain the slip of the interface far from the incident wave, while that the latter may facilitate the former We also find the instability of the system for similar values of the two interface friction coefficients. Finally, the energy transmitted through the interlayer and dissipated by the friction of the two interfaces are examined.