Rayleigh wave propagation in curved waveguides

A JWKB asymptotic expansion describing inplane elastic waves is used to approximate a Rayleigh-like wave guided within an elastic waveguide whose curvature is small and changes slowly over a wavelength. The two lowest eigenmodes in a curved guide, taken together, constitute the Rayleigh-like wave. It is shown that this wave lies in the shadows of four, closely spaced, virtual caustics, two caustics per constituent eigenmode. If the curvature becomes too large one or more of the caustics ceases to be virtual and enters the guide after which it is not possible for a Rayleigh-like wave to propagate. The Rayleigh-like wave is dispersive. The dispersion is caused by the constraint that it be confined within the guide, but may also be caused by the curvature alone. For propagation in a thin curved guide, the dispersion caused by the confinement is calculated. The possibility that dispersion may also caused by the curvature alone is not resolved. For a thick guide the effect of confinement is eliminated. In this case it is shown that dispersion caused by a linear dependence of the wavenumber on the curvature is present. Propagation into an environment of increasing curvature is studied, for both waveguides, to exhibit the influence of the nearby caustics.Air Force Office of Scientific Research; National Science Foundatio