Dynamic response of in vacuo prolate spheroidal shells excited by surface force fields

Abstract

The equations of motion for nonaxisymmetric vibration of prolate spheroidal shells of constant thickness were derived using Hamilton’s principle. The thin shell theory used in this derivation includes three displacements and two changes of curvature. The effects of membrane, bending, shear deformations, and rotatory inertias are included in this theory. The resulting five partial differential equations are self-adjoint and positive definite. The shells are excited by axisymmetric line forces. The axisymmetric modal solutions are expanded in an infinite series of comparison functions. These include associated Legendre functions in terms of the prolate spheroidal angular coordinate. Numerical results for the frequency response were obtained 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. Sample mode shapes were obtained at selected resonant frequencies. [Work supported by ONR and the Navy/ASEE Summer Faculty Program.]