Frequency spectra of bilaminar prolate spheroidal shells.

Abstract

The kinetic and strain energy densities were derived for the vibration of a bilaminar prolate spheroidal shell of constant thickness. The bilaminar shell is composed of two bonded concentric prolate spheroidal layers of different material properties and thicknesses. The elastic strain energy density has seven independent kinematic variables: three displacements, two thickness shears, and two thickness stretches. Continuity of displacements is enforced at the interfacial reference surface. The shell has constant thickness h=h1+h2, where h1 and h2 denote the thicknesses of the respective layers. The reference surface eccentricity is defined by 1/a, where a is its shape parameter. Using appropriate comparison functions in terms of Legendre polynomials that satisfy the boundary conditions for a closed spheroidal shell, the system is solved using the Galerkin method. Numerical results of the frequency spectra are presented for various ratios of h1/h2 and various material properties for the two layers. Initial results are presented for a=100 (a nearly spherical shape). [Work supported by the ONR/ASEE Summer Faculty Research Program.]