Propagation of elastic surface waves along a cylindrical cavity and their excitation by a point force

Abstract

The existence of surface wave modes, propagating along an infinite cylindrical cavity in an elastic medium, is established for every integer m, where m is the azimuthal mode number. These waves are analogous to the Rayleigh wave on a half-space, being confined to the immediate vicinity of the cavity. The modes exhibit dispersion and have a cutoff frequency which increases with m, except for the flexural (m = 1) mode which exists at all frequencies. At cutoff the phase velocity is equal to that of the shear waves and decreases, with increasing frequency, to that of the Rayleigh wave. We present results for the group velocities and displacement and stress fields of the modes and also exhibit the effect of various point forces acting near the cavity. In the vicinity of the cavity, not too near the point force, the surface wave contribution dominates the total displacement field.