Effect of Poisson's ratio on the fundamental frequency of transverse vibration and buckling load of circular plates with variable profile

The problem described is solved by approximating the displacement function using simple polynomial coordinate functions which identically satisfy the boundary conditions. The numerical determinations of the eigenvalues under investigation are determined using the Rayleigh-Ritz method assuming that the plate thickness varies according to the functional relation h(r) = h(o)[1 + gamma(r/a)(n)], where n is an integer. It is shown that the frequency coefficients and critical bukling load parameters obtained by means of the analytical procedure are in excellent agreement with the results obtained employing a finite element algorithmic procedure. It is concluded that the value of Poisson's ratio has a significant effect upon the frequency and buckling parameters, especially in the case of plates of nonuniform thickness and with simply supported edges.