Free Vibration Analysis of Moderately Thick Rectangular Plates on Pasternak Foundation with Point Supports and Elastically Restrained Edges by Using the Rayleigh–Ritz Method

In the present paper, free vibration analysis of moderately thick rectangular plates resting on an elastic foundation of Pasternak model with point supports and elastically restrained edges based on the first-order shear deformation plate theory is presented. The Rayleigh–Ritz method is applied to derive the eigenvalue equation of the plate. The Chebyshev polynomials multiplied by a boundary function which define the displacement components are adopted in this method as the admissible functions. The accuracy of the present method is examined via lots of convergence and comparison studies with the available data in the literature, and it is demonstrated that the present method has a rapid convergence rate and high accuracy. Many numerical results are presented in tabular and graphical forms in order to investigate the effects of various parameters such as thickness–span ratio, foundation parameters, the lateral and rotational stiffness of the edge supports, and locations of the point supports on the natural frequencies.