Asymmetric Vibrations of Shells of Revolution Having Meridionally Varying Curvature and Thickness

Abstract

An exact method using power series expansions is presented for solving asymmetric free vibration problems for shells of revolution having meridionally varying curvature and thickness. The governing equations of motion and the boundary conditions are derived from the stationary conditions of the Lagrangian of the shells of revolution. The method is demonstrated for shells of revolution having elliptical, cycloidal, parabolical, catenary and hyperbolical meridional curvature. The natural frequencies are numerically calculated for these shells having second degree thickness variation.