Frictional slip of an elastic layer on a half-space caused by an anti-plane wave of an arbitrary form

The slip between an elastic layer and a half-space caused by an anti-plane wave of arbitrary form is examined. The incident wave is assumed to be sufficiently strong so that friction may be broken, and the local slip may take place at the interface. The analysis is restricted to the sub-critical angle of incidence. Fourier analysis is employed to cast the mixed boundary value problem to a recurrence relation. The calculation of the local slip velocities and the interface traction, together with the determination of the extent and location of slip zones, which are unknown before the solution of the problem, are discussed. As an example, a parabolic pulse incident wave is considered. The distribution of the slip zones, the interface shearing traction and slip velocities are calculated in detail. The results show that the problem involves a lot of features different from those for an infinite medium due to the existence of the free surface of the elastic layer. For instance, multiple slip zones may appear due to the reflection of waves at the free surface, and the slip zones become closer and closer when the thickness of the layer decreases. On the other hand, when the thickness of the layer is infinity, the distances between the slip zones become infinitely large, and the results reduce to those obtained for the infinite medium.