Vibration Analysis of Functionally Graded Plates Using Higher Order Shear Deformation Theories (HSDT)

Abstract

    A higher order shear deformation theory (HSDT) was presented for free vibration analysis of simply supported (diaphragm), elastic functionally graded (FG), rectangular, plates. Functionally graded materials (FGMs), although heterogeneous, are idealized as continua with their mechanical properties changing smoothly with respect to the spatial coordinates.. Poisson’s ratio was assumed to be constant, but their Young’s moduli and densities vary continuously in the thickness direction according to the volume fraction of constituents, which is mathematically modelled as power law function. The equations of motion were obtained using Hamilton’s principle employing HSDT. Navier’s solution was used to solve the equations of motion. The effect of variation of material properties in terms of gradation index, the effects of aspect ratios, thickness-to-side ratio on the natural frequencies of FG plates were studied in this article. The numerical results were compared with results available in the literature to validate theoretical model of the paper.