Analytical approach of Lamb waves coupling in rough isotropic plates

The present work aims at contributing to the investigation of an analytical method to describe Lamb waves which undergoes Lamb waves coupling when propagating along the rough surfaces of finite extent of isotropic, solid, and infinite plates. The motions considered are assumed to be independent of one of the coordinates for which the component of the displacement is equal to zero (two-dimensional problem). In some respect, the analytical approach is an extension of an analytical model describing the coupling of SH waves due to ridges (on the surface of a plate) parallel to the polarization of the waves, but it is treated in a somewhat different manner because the acoustic field involves here both the longitudinal and the transversal displacements of the Lamb waves. The formalism relies on an integral formulation, using Green’s functions which permit to express Lamb waves perturbations, to describe the coupling process between the longitudinal and the transversal components of the forward and the backward propagating Lamb waves, due to the roughness (including the effects of both its depth and its slope). A methodology is given to solve the problem, and results on specific examples (periodic and random rough surfaces) are discussed in order to support the method.