Guided acoustic waves at the intersection of interfaces and surfaces

In numerical calculations, guided acoustic waves, localized in two spatial dimensions, have been shown to exist and their properties have been investigated in three different geometries, (i) a half-space consisting of two elastic media with a planar interface inclined to the common surface, (ii) a wedge made of two elastic media with a planar interface, and (iii) the free edge of an elastic layer between two quarter-spaces or two wedge-shaped pieces of a material with elastic properties and density differing from those of the intermediate layer. For the special case of Poisson media forming systems (i) and (ii), the existence ranges of these 1D guided waves in parameter space have been determined and found to strongly depend on the inclination angle between surface and interface in case (i) and the wedge angle in case (ii). In a system of type (ii) made of two materials with strong acoustic mismatch and in systems of type (iii), leaky waves have been found with a high degree of spatial localization of the associated displacements, although the two materials constituting these structures are isotropic. Both the fully guided and the leaky waves analyzed in this work could find applications in non-destructive evaluation of composite structures and should be accounted for in geophysical prospecting, for example. A critical comparison is presented of the two computational approaches employed, namely a semi-analytical finite element scheme and a method based on an expansion of the displacement field in a double series of special functions.