Guided modes in a layered elastic half-space with doubly corrugated surfaces

Abstract

Time-harmonic Rayleigh, Love, and Rayleigh–Lamb-like waves in a layer on a half-space with both the free surface and the interface doubly periodically corrugated are considered. The dispersion relation for the full problem is derived using the null-field approach. The stopband and passband structure of the physical modes are investigated numerically for doubly sinusoidally corrugated geometries with equal periods and equal corrugation heights. First the Rayleigh-like surface waves that exist when there is no layer are investigated. The passbands, stopbands, and damped parts are presented as a function of frequency and angle of propagation for two different corrugations heights. Some dispersion curves of wave number versus frequency are also given. With the layer present similar dispersion curves are given for some of the lowest Love and Rayleigh–Lamb-like waves. In general, the modes have a considerable angular dependence. Their resonance structure with respect to the position as well as the number of resonances and the stopband widths are affected. The passband, stopband, and the damped part for a mode as well as the possibility of an appearance of new physical solutions are also dependent on the corrugation height. More surprising is that some inhomogeneous modes become involved in the interaction pattern for the layered half-space, thus changing the characteristic behavior of the homogeneous modes and generating new passbands, stopbands, and damped parts.