Vibration of in vacuo hemiprolate spheroidal shells

Abstract

The equations of motion for nonaxisymmetric vibration of hemiprolate spheroidal shells of constant thickness were derived using Hamilton’s principle. The thin shell theory used in this derivation includes shear deformations and rotatory inertias. The shell is clamped at the equator and is excited by mechanical surface force fields. The 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. Five-branched frequency spectra were computed for several shell thickness-to-length ratios ranging from 0.005 to 0.1, and for various diameter-to-length ratios, including the limiting case of a spherical shell. Numerical results were obtained for the frequency spectra of the driving and transfer mobilities of these shells due to surface force excitations. Some comparisons of the dynamic response of hemiprolate and full prolate spheroidal shells are presented. [Work supported by ONR and the Navy/ASEE Summer Faculty Program.]