Finite Element Method for Free Vibration Analysis of Rectangular FGM Plate Based on First Order Shear Deformation Theory

Functionally graded materials (FGMs) are advanced composites having two constituents (generally, metal, and ceramic) whose mechanical properties vary gradually along the thickness of the structure with an assumed mathematical model. The present study deals with free vibration analysis of rectangular FGM plates based on first-order shear deformation theory (FSDT). The variation of the in-plane displacement field is considered to be constant and hence suitable shear correction factor is selected in terms of Poisson’s ratio. The analysis was carried out on both relatively thick and thin FGM plates with varying power law indices (n) and at different boundary conditions. Two isoparametric quadrilateral elements were selected for mesh generation and to compare the obtained results. The governing equation was formed using Hamilton’s principle and solutions were done with finite element method. The findings are in good agreement with the existing literature. After validating the present model, parametric studies were carried out to show the effect of length to thickness ratio, aspect ratio, and volume fraction ‘n’ on the fundamental frequencies. The results showed that when the boundary conditions change from ‘ssss’, ‘scsc’ to ‘cccc’, the frequency increases. The same also increases with increase length to thickness ratio and decreases with increase in ‘n’.