Vibration of submerged prolate spheroidal shells with internal fluid loading

Abstract

The equations of motion for nonaxisymmetric vibration of submerged prolate spheroidal shells of constant thickness with internal fluid loading were derived using Hamiltons principle. The shell theory used in this derivation includes shear deformations and rotatory inertias. The shell displacements and rotations were expanded in infinite series of comparison functions. These include associated Legendre functions in terms of the prolate spheroidal angular coordinate and circular functions in the azimuthal angle coordinate. The external and internal fluid loading impedances were computed using expansions of prolate spheroidal wave functions in each domain. The shell was excited by axisymmetric normal surface forces, including a point load at the shell apex and ring load at other locations. Numerical results were obtained for the driving and transfer mobilities for several shell thickness-to-half-length ratios ranging from 0.005 to 0.1, and for various shape parameters, a, ranging from an elongated spheroid shell (a=1.01) to a spherical shell (a=100). Results are presented for various combinations of external and internal fluid loading, and comparisons are made to the in vacuo shell vibration. [Work supported by ONR and the Navy/ASEE Summer Faculty Program.]