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 such mode will resonate at all those “eigenfrequencies” where the mode velocity coincides with the speed of one of the creeping waves. For an elastic cylinder, the 180° sound-scattering amplitude is shown to possess marked minima at many of the eigenfrequencies, whose spacing over a sequence of modes thus determines the group velocities of circumferential pulsed signals. [Work supported by ONR.]