Vibration and stability of stiffened annular plates

Abstract

The vibration and stability of radially stiffened annular plates subjected to an in‐plane force uniformly distributed at the edges are analyzed by the energy method. For this purpose, the transverse deflection of a stiffened annular plate is written in a series of the products of the deflection function of a sectorial beam with a small angle and the trigonometric function of angular coordinate. The deflection function of the sectorial beam is approximately expressed by a quintic spline function satisfying the boundary conditions at the edges, and the frequency equation of the plate is derived by the Ritz method. The method is applied to annular plates with several stiffeners of uniform rectangular cross section located at equal angular intervals; the natural frequencies and the critical buckling loads are calculated numerically and the effects of stiffeners on them are studied.