High frequency approximations for elastic surface waves propagating along cylinders of general cross section

Abstract

The propagation of high frequency elastic surface waves along the generators of a homogeneous isotropic cylinder of general cross section is considered. The boundary surface is stress-free and the surface waves, or Rayleigh waves, are disturbances whose amplitudes decay rapidly with depth into the cylinder. An approximate equation, and a refined one, are derived which describe the high frequency behavior of the surface wave modes. These approximate equations lead to the asymptotic results derived earlier by Wilson and the author for the case of an open boundary curve for which the curvature attains its algebraic maximum at a single point, and in fact they permit a more complete analysis of the higher order modes. Moreover, the refined approximate equation describes the behavior of the surface wave modes in the transition region, at high frequencies, between the case of cross-sectional boundary curves of nonconstant (and not ’’almost’’ constant) curvature, for which the modes are localized, and the case of constant curvature, for which they are not localized. Some particular examples are considered.