Buckling and vibrations of polar orthotropic annular plates on elastic foundation subjected to hydrostatic peripheral loading

Abstract

An analysis is presented of the effect of hydrostatic peripheral loading and that of an elastic foundation on the natural frequencies of free axisymmetric vibrations and critical buckling parameter of linearly varying thickness annular plates exhibiting polar orthotropic characteristics, on the basis of classical plate theory. The numerical solution of the governing differential equation derived by using Hamilton's energy principle is obtained by the spline technique method for three different boundary conditions: inner and outer both clamped; inner clamped and outer simply supported; inner free and outer clamped. Transverse displacements, moments in normalized form for a particular set of plate parameters and buckling loads in compression for different values of taper constant, foundation modulus and rigidity ratios have been computed for the first two modes of vibration. The numerical results are compared with exact values and with the results of other authors. The close agreement of the values illustrates the versatility of this simple and elegant method, provided the number of nodal points is taken appropriately.