Free vibration of simply supported rectangular plates on Pasternak foundation: An exact and three-dimensional solution

This paper deals with exact solution for free vibration analysis of simply supported rectangular plates on elastic foundation. The solution is on the basis of three dimensional elasticity theory. The foundation is described by the Pasternak (two-parameter) model. First, the Navier equations of motion are replaced by three decoupled equations in terms of displacement components. Then, these equations are solved in a semi-inverse method. The obtained displacement field satisfies all the boundary conditions of the problem in a point wise manner. The solution is in the form of a double Fourier sine series. Then free-vibration characteristics of rectangular plates resting on elastic foundations for different thickness/span ratios and foundation parameters are studied. The numerical results are compared with the available results in the literature. Important parameters on the accuracy of plate theories and free-vibration characteristics of rectangular plates resting on elastic foundations are discussed.