Resonance spectra of elongated elastic objects

Abstract

It is well known [H. Überall, L. R. Dragonette, and L. Flax, J. Acoust. Soc. Am. 61, 711 (1977)] that the complex eigenfrequencies at which smooth convex objects resonate under the incidence of an acoustic wave are those at which circumferential waves generated by the incident signal phase match over a closed orbit. This principle was verified by us, by analytically obtaining the resonance frequencies of elastic cylinders and spheres [E. D. Breitenbach et al., J. Acoust. Soc. Am. 74, 1267 (1983)] and deriving phase and group velocities of the surface waves from this. In the present study, this approach is inverted, and applied to elastic prolate spheroids and to cylinders with hemispherical endcaps. From the known phase velocities and trajectories (geodesics) of the surface waves, we were able to predict the elastic resonance frequencies of these bodies. [Work supported by the David W. Taylor Naval Ship R & D Center, the Naval Research Laboratory, and the Office of Naval Research.]