Leaky surface-elastic waves on both flat and strongly corrugated surfaces for isotropic, nondissipative media

Abstract

The dispersion relation for Rayleigh waves propagating across a grating, on the surface of a semi-infinite, nondissipative, isotropic elastic medium was recently calculated by Rayleigh’s method and equivalently by a formally exact method based on Green’s theorem. Now, using a complex wave-vector k or complex frequency ω in the present work, we continue the solutions of the dispersion relation into the radiative region of the kω-plane (i.e., above the bulk transverse sound line) and into the first frequency-gap on the boundary of the Brillouin zone caused by the grating periodicity. Here the solutions for the surface waves have components that radiate outwardly into the bulk. The acoustic attenuation for the Rayleigh waves, calculated from the imaginary part of complex k, agrees very well with experiment: all the observed peaks, including those missed by previous perturbation scattering theories, are found. Moreover, a branch is found in the dispersion relation, to which a corresponding complex solution is also found for the flat surface, between the bulk transverse and longitudinal sound lines, that represents an intrinsically leaky flat-surface wave or surface resonance. The principal peak in the Rayleigh wave attenuation can be associated with an interaction between the Rayleigh wave and this new intrinsically leaky wave.