Circumferential-wave phase velocities for empty, fluid-immersed spherical metal shells

Abstract

Our earlier studies regarding acoustic scattering resonances and the dispersive phase velocities of the surface waves that generate them, have demonstrated the effectiveness of obtaining phase velocity dispersion curves from the known acoustic resonance frequencies, and their accuracy. This possibility is offered by the picture of phase matching after each complete circumnavigation of these waves, which leads to close agreement of resonance results with those calculated from 3-D-elasticity theory whenever the latter are available. The present investigation is based on the mentioned resonance frequency/elasticity-theory connection, and we obtain comparative dispersion-curve results for water-loaded, evacuated spherical shells of various metals. In particular, the characteristic upturn of the dispersion curves of low-order shell-borne circumferential waves (A or A0 waves) which takes place on spherical shells when the frequency tends towards low values, is demonstrated here for all the metals under consideration