Dynamic response 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. Damping is introduced into the shell via a complex Young’s modulus. Numerical results for the drive and transfer mobilities due to surface force excitations 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). Sample mode shapes were obtained at selected resonant frequencies. [Work supported by ONR and the Navy/ASEE Summer Faculty Program.]