Vibration of elliptic cylindrical shells: Higher order shell theory

Abstract

The equations for the free vibration of an elliptic cylindrical shell of constant thickness were derived using a Ritz approach. A higher order shell theory is employed that includes the effects of shear deformation, rotary inertia, and symmetric and antisymmetric thickness stretch deformations. The frequency-wavenumber spectrum has seven branches: flexural, extensional, torsional, 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. Numerical results for the natural frequencies were obtained for two values of h/l and L/l, and various shape parameters, including the limiting case of a simply supported cylindrical shell (a approximately 100).