Finite Element Analysis For Free Vibration Of Functionally Graded Material Plates

Functionally graded materials (FGM) is a new type of non-uniform composite materials. It consists of two or more component materials according to the requirements of design. The constituents of component materials varies continuously from one side to the other side so that the properties of FGM also change continuously in the gradient field to eliminate the discontinuity of material property. With the wide use of FGMs in modern structure engineering, the research on mechanical properties of FGM plate has become an important direction. Based on the classical plate theory (CPT) and the first-order shear deformation plate theory (FSDT), the linearly free vibration of FGM plates was studied by using the finite element method (FEM) in this paper. The relationship between the natural frequencies of FGM plates and those of the reference homogenous ones is investigated. The work basically includes:(1) Based on the classical thin plate theory and physical neutral surface, free vibration responses of FGM plates was presented. Firstly, a FEM type of free vibration equation about FGM plate under arbitrary shape and arbitrary boundary condition was deduced by using the Hamilton’s principle and a computer program was formulated by using the MATLAB. The analogous transformation relation of natural frequencies was obtained by comparing free vibration equation of FGM plates with that of homogenous plates. Then the excellent accuracy and correctness of the results is confirmed by making some comparisons with those results available in the literature. At last, vibration mode shapes of the rectangular plate for various boundary conditions were plotted according to the FEM results. The effects of aspect ratios, gradient indices, boundary conditions, and thickness to length ratios on the free vibration of the FGM plates were also presented.(2) A FEM type of undamped free vibration equation about FGM plate under arbitrary shape and arbitrary boundary condition was deduced by using the Hamilton’s principle based on the first-order shear deformation plate theory and physical neutral surface, also, a computer program was formulated by using the MATLAB. With the help of the computer program, free vibration response under arbitrary boundary condition of moderately thick FGM plats was studied. By comparing to the CPT results and those available in literature, the effect of shear deformation on the free vibration of the moderately thick FGM plates, constrained by different combinations of classical boundary conditions, was also presented for various values of the aspect ratios, the gradient index, and the thickness to length ratio.