Relation between creeping waves and normal modes of vibration of a curved body

Abstract

The natural way for a disturbance to propagate over the surface of a smoothly curved, fluid-loaded elastic body is in the form of a series of damped circumferential (creeping) waves. Mathematically, the process is most conveniently described by a sum of normal modes, each characterized by a wavelength that fits the body’s circumference an integer number of times. We demonstrate that any given mode will resonate at a multiplicity of ’’eigenfrequencies,’’ determined by the speed of any one of the creeping waves matching the mode velocity. For an elastic cylinder, the 180° sound-scattering amplitude is seen to possess marked minima at many of the eigenfrequencies, which are shown to be generated successively by a single circumferential wave, and whose spacing in this sequence determines the group velocities of circumferential pulsed signals.