Vibrations of prolate spheroidal shells of constant thickness

Abstract

The general displacement‐equilibrium equations, which include the effects of transverse shear and rotary inertia, have been derived for a prolate spheroidal shell of constant thickness. The solution is formulated for a shell that is immersed in an inviscid fluid of infinite extent and subjected to an harmonically time‐varying, arbitrarily spatially distributed force normal to the shell surface. The approximate formal solutions for the three displacements of the shell surface and the two rotations of the shell cross section are obtained using an extension of Galerkin's variational method developed by Chi and Magrab [Proceedings of the International Conference on Variational Methods in Engineering (University of Southampton, 1974)]. Numerical results are presented for the lowest seven axisymmetric natural frequencies of the shell in vacuo. Using 15‐term solutions for both thick and thin shells, which have eccentricities that vary from 0.46 to 0.99, the approximate natural frequencies are found to converge t...