Free vibration of FG Lévy plate resting on elastic foundations

In this paper, free vibration of thin functionally graded (FG) Lévy plates resting on Winkler and Pasternak elastic foundations have been investigated. As a convention, Lévy plates have two opposite edges simply supported and the other two opposite edges are taken as a combination of clamped, simply supported and free edge conditions. A simple power-law form is assumed here to judge the variation of material properties of the FG constituents along the thickness direction. The numerical modelling has been performed using the displacement field of classical plate theory and Rayleigh–Ritz method to obtain the generalised eigenvalue problem. The displacement component is expressed as a linear combination of simple algebraic polynomials. The effect of different physical and geometrical parameters along with elastic foundations on the free vibration characteristics of FG Lévy plates has been investigated. New results of eigenfrequencies and their corresponding three-dimensional mode shapes are incorporated here after performing the test of convergence and validation of present results with the available literature in special cases.