The propagation of time harmonic Rayleigh–Lamb waves in a bimaterial plate

The time harmonic elastodynamic response of two semi-infinite elastic plates of dissimilar material properties perfectly bonded along their lateral faces is studied. The wave field in either half-plate can be written as a superposition of the so-called Rayleigh–Lamb eigenmodes of an infinite plate. The interaction of a time harmonic incident wave with the interface results in reflected and transmitted fields that contain contributions from all of the real, imaginary, and complex eigenmodes of an infinite plate. Attention is focused on the distribution of energy among the various reflected and transmitted eigenmodes over a range of frequencies. The fundamental symmetric and the fundamental antisymmetric Lamb modes are each used as input excitations. Such excitations can be approximately realized in experiments. It is assumed that the solution of such a canonical problem will facilitate the solution of problems with complicated time-dependent sources.