Abstract
A three-dimensional modelling of free vibrations of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and mode shapes are determined by using the finite element method within the ABAQUS code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal analysis are demonstrated for square metal–ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fractions of the material constituents. The through-the-thickness distributions of effective material properties at a point are defined based on the Mori–Tanaka scheme. First, exact values of natural frequencies, displacements and stresses available in the literature are used to estimate the accuracy of the developed 3-D graded finite element for FGM sandwich plates. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the length-to-thickness ratio.
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