Buckling and vibrations of polar orthotropic annular plates of variable thickness

Abstract

The effect of an hydrostatic in-plane force, together with the orthotropy, on the axisymmetric vibrations of an annular plate of linearly varying thickness in the radial direction has been analyzed on the basis of classical theory of plates. The numerical solution of the governing differential equation for two boundary conditions (inner and outer both clamped; inner clamped and outer simply supported at the periphery) has been obtained by a spline technique. Transverse displacements, moments in normalized form for a particular set of plate parameters and buckling loads in compression with thickness variation and various values of rigidity ratios have been computed for first two modes of vibrations. A comparison of present results with those available in the literature shows a very good agreement.