Vibration of in-vacuo elliptic cylindrical shells

Abstract

The equations of motion for the vibration of elliptic cylindrical shells of constant thickness were derived using a Galerkin approach. The elastic strain energy density used in this derivation has seven independent kinematic variables: three displacements, two thickness-shear, and two thickness-stretch. The resulting seven coupled algebraic equations are symmetric and positive definite. The shell has a constant thickness, h, finite length, L, and is simply supported at its ends, (z=0,L), where z is the axial coordinate. The elliptic cross-section is defined by the shape parameter, a, and the half-length of the major axis, l. The modal solutions are expanded in a doubly infinite series of comparison functions in terms of circular functions in the angular and axial coordinates. The natural frequencies and the mode shapes were obtained by the Galerkin method. Numerical results were obtained for several h/l and L/l ratios, and various shape parameters, including the limiting case of a simply supported cylindrical shell (a=100). [Work supported by ONR and the Navy/ASEE Summer Faculty Program.]