Three-dimensional free vibration of thick circular plates on Pasternak foundation

This paper describes a study of the three-dimensional vibration characteristics of thick circular plates resting on elastic foundation. The analysis is based on the three-dimensional small-strain, linear and exact elasticity theory. The foundation is described by the Pasternak model. The Ritz method is used to derive the frequency equation of the plate-foundation system by augmenting the strain energy of the plate with the elastic potential energy of the foundation. A set of Chebyshev polynomials multiplied by a boundary function is adopted as the admissible functions of the displacement components in each direction. For plates with free edges, the effect of foundation medium beyond the edge of the plate has been considered by introducing the generalized shearing force concept in the analysis. The convergence and comparison studies demonstrate the correctness and accuracy of the present method. It is shown that the present method has rapid convergent rate, stable numerical operation and very high accuracy. Parametric investigations on the dynamic behavior of thick circular plates resting on elastic foundation have been carried out with respect to various thickness–radius ratios, foundation stiffness parameters and boundary conditions. Results known for the first time have been reported and discussed in detail. Some significant conclusions have been drawn.