Propagation of Lamb waves in an elastic layer with irregular surfaces

In this article, we investigate the problem of Lamb wave propagation in a layer composed of homogeneous, isotropic material with irregular free surfaces. It is assumed that the irregular free surfaces vary slowly in the direction of wave propagation. By employing an asymptotic perturbation method, a unique asymptotic solution for the amplitude function of Lamb waves is obtained. The dispersion relation is expressed as a function of phase velocity of waves, wave number and the direction of wave propagation. We examine the effect of irregularities of the boundary surfaces on the propagation of waves under the assumption that free surfaces have periodic properties.