Modal exchange between an elastic mode and an acoustic mode of a fluid‐filled spherical shell resonator at an avoided crossing.

Abstract

High pressure liquid‐filled spherical resonators are promising devices for increasing the energy density of a cavitating liquid. Since increasing the static pressure in the liquid also increases the sound speed, it is important to investigate the dependence of the resonances on the sound speed. In this paper, we report on an avoided crossing or repulsion between an elastic mode and an acoustic mode of a fluid‐filled spherical shell resonator as the sound speed is varied. Such an avoided crossing is attributed to the fluid‐shell interaction and leads to a modal exchange between the acoustic and the elastic modes. Furthermore, the eigenfrequency curves of both the acoustic and elastic modes are discontinuous in the frequency‐sound speed phase space in the neighborhood of the avoided crossing. Additional analysis reveals that the elastic mode also forms an avoided crossing with other acoustic mode orders and that this result can be extended to other pairs of modes with different symmetry. The acoustic pressure field in the fluid and the stress field in the shell are shown to take extreme values at this region. [Work supported and funded by Impulse Devices, Inc. ACPT Contract No. W9113M‐07‐C‐0178.]