Propagation of shear horizontal surface acoustic waves parallel to the grooves of a random grating

Abstract

An elastic medium that occupies the region x3≳ζ(x1), where the surface-profile function ζ(x1) is assumed to be a stationary, stochastic process, is studied. The displacement field u(x;t) in this region is assumed to satisfy stress-free boundary conditions on the surface x3=ζ(x1). First the boundary conditions satisfied by the mean displacement field 〈u(x;t)〉 on the plane x3=0 are obtained, where the angle brackets 〈 〉 denote an average over the ensemble of realizations of ζ(x1). The results are then used to obtain the dispersion relation for surface acoustic waves of shear horizontal polarization propagating in the x2 direction, i.e., parallel to the grooves of the random grating defined by the surface-profile function ζ(x1). It is found that the surface acoustic waves of this polarization, which cannot exist on a planar, stress-free surface of an elastic medium, are trapped by the random roughness, but are bound to the surface for only a finite range of values of the wave number k2 characterizing their propagation in the x2 direction. The attenuation of these roughness-trapped surface acoustic waves is also determined.