Transient analytic and numerical results for the fluid endash solid interaction of prolate spheroidal shells

A transient solution is presented which models the fluid endash solid interaction of a thin elastic prolate spheroidal shell loaded end-on by a nonconservative acoustic shock wave. Solutions to the Lagrangian equations of motion are provided for the normal and tangential shell displacement fields, as well as for the incident, scattered, and radiated fluid pressure fields. The explicit analytic solutions converge uniformly and absolutely to the exact solution of the actual coupled differential equations over the entire temporal and spatial domains both in the structure and in the fluid. Numerical results for the free vibrations and for the transient fluid endash solid interactions of a fluid-loaded prolate spheroidal shell are presented. As in the case for the spherical geometry, the fluid loading is shown to down shift the frequencies and to introduce additional proliferant structural frequencies. Long time history plots of the shell displacements are presented for the submerged shock-loaded low aspect ratio case. Insights into the qualitative and quantitative effects of the fluid on the structural response are revealed. DOE-MACSYMA was used extensively to develop and verify the solutions. copyright 1996 Acoustical Society of America