Transient fluid–solid interaction of submerged spherical shells revisited: Proliferation of frequencies and acoustic radiation effects

Abstract

The exact series solutions for the transient shell displacement and fluid pressure fields resulting from the axisymmetric acoustic loading of a submerged, thin elastic, spherical shell are well known. Plots of the shell displacements, velocities, accelerations, strains, and strain rates have been published previously. Further investigation for the more general prolate spheroidal geometry has elucidated a complex exchange of energy between the structure and the fluid through the kinematic boundary conditions, which is presented herein for the simpler spherical geometry. The importance of the time evolution of the acoustic radiation coupling to the structure is discussed, including phase information. A comparison of the unloaded versus fluid-loaded frequencies for an example problem demonstrates the ‘‘softening’’ effect of the fluid on the structural response and reveals it to be more complex than simple damping. The reloading of the shell due to radiation in the fluid introduces a proliferation of frequencies in the structural response which is characteristic of fluid–solid interaction problems. The computer algebra system PARAMACS is used to perform the analytical and numerical calculations.