Free vibration of polar orthotropic circular plates of quadratically varying thickness resting on elastic foundation

Classical plate theory is used to study free vibration of polar orthotropic circular plates of quadratically varying thickness resting on Winkler elastic foundation. Boundary characteristic orthonormal polynomials are used in the Rayleigh–Ritz method to analyze the plate for free, simply supported and clamped edge conditions. The numerical convergence of the method is tested and comparisons are made in particular case with the results already available in the literature. First twelve frequencies for various values of parameters describing the elastic foundation, thickness profile and orthotropy of the plate are given in tabular form. Two dimensional graphs for nodal lines and three dimensional graphs for mode shapes are plotted.