Vibration of fluid-loaded hemi-prolate spheroidal shells

Abstract

The equations of motion for nonaxisymmetric vibration of hemi-prolate spheroidal shells of constant thickness were derived using Hamilton’s principle. The shell is clamped at the equator and is excited by mechanical surface force fields. The shell theory used in this derivation includes shear deformations and rotatory inertias. The displacements and rotations were expanded in an infinite series of comparison functions. The shell is fluid-filled and is submerged in an infinite fluid medium. The external and internal fluid loading impedances were computed using expansions of prolate spheroidal wavefunctions in each domain. The dynamic response of the fluid-loaded shell was determined using an axisymmetric normal surface force as the excitation input. Numerical results were obtained for the driving and transfer mobilities for several shell thickness-to-length ratios ranging from 0.005 to 0.1, and for various shape parameters, ‘‘a,’’ ranging from an elongated hemi-spheroidal shell (a=1.01) to a hemispherical 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.]