Vibration of functionally graded elliptical plates resting on Winkler-type elastic foundation subjected to initial in-plane loading

In this paper, the free vibration behavior of functionally graded thin elliptical plates with simply supported and clamped boundary conditions is investigated using classical laminated plate theory. In contrast to previous studies, the geometry of the plate is considered to be as elliptical and in a more general form as super elliptical. Also, it is assumed that the considered plate is subjected to boundary in-plane preload and is rested on Winkler-type elastic foundation. It is assumed that the mechanical properties of the functionally graded plate vary continuously through the thickness according to a power law of the volume fraction of the constituents. The governing equations of motions are derived by employing the variational approach. The obtained equations are solved using Ritz method. In addition to the analytical modeling, for comparison, the problem is also modeled and analyzed numerically by using finite element software Abaqus. Correctness and accuracy of the present analytical model is confirmed through comparing the present analytical results by the results existed in the literature and by the present numerical results. After that, doing parametric study, the effects of some important parameters such as the boundary conditions, the in-plane forces, the plate geometry and the power-law index on the vibration behavior of the plate are studied and discussed. The results presented in this research are of great importance in design and application of the functionally graded elliptical plates.