Free Vibration Analysis of Second-Order Continuity Plate Element Resting on Pasternak Type Foundation Using Finite Element Method

Free vibration analyses of plate on elastic foundations are very common in mechanical and structural engineering and these types of structures are analysed using the concept of “plates on elastic foundation”. It is very important to build more practical and simple foundation models for safe and economical design of transversely loaded plate. In the present study, a workable approach for vibration analysis of laterally loaded plate on Pasternak foundation and second-order (C2) compatible plate bending elements based on the Kirchhoff theory is attempted. A Matlab code is developed for the present formulation. The results, thus obtained, are compared with similar studies done by other researchers, which show very good conformity. Parametric studies are carried out to obtain response for different soil parameters and boundary conditions. It is concluded that the influence of the Winkler coefficient on the frequency parameters are larger than that of the aspect ratio and Pasternak shear coefficient regardless of boundary conditions. The present approach is simple, effective and more reliable for vibration analysis of plates on Pasternak foundation and the convergence rate is very high and takes less computational efforts, resources and times.