Rayleigh Waves on Curved Surfaces

Rayleigh waves, which are elastic surface waves occurring at the interface between a solid elastic body and vacuum, are investigated. The exact solution of some canonical elastodynamic problems in a circular cylindrical geometry is given, from which the Rayleigh wave contribution is isolated. The dispersion—i.e., the dependence of the velocity of propagation of these waves on the local radius of curvature (of the interface)—is investigated. The propagation velocity diminishes as the ratio between wavelength and radius of curvature diminishes, reaching an asymptotic value at “zero wavelength.” A comparison is made with the small‐wavelength asymptotic approach of Keller and Karal, which does not take dispersion into account. It is found that the effects of dispersion should not be ignored down to rather small wavelengths. Moreover, it is found that there occurs a “critical” or “cutoff” wavelength, above which no proper Rayleigh wave can exist. Thus, a Rayleigh wave that propagates on an interface of variabl...