Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates

Abstract

A higher order shear and normal deformation theory (HOSNT) is presented for free vibration analysis of functionally graded (FG) elastic, rectangular, and simply supported (diaphragm) plates. Functionally graded materials (FGMs), although heterogeneous are idealized as continua with their mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of FG plates are assumed to be varying through thickness of the plate in a continuous manner. Poisson's ratio is 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 are obtained using Hamilton's principle employing HOSNT. Navier solution method is used to solve the equations of motion. The effect of variation of material properties in terms of gradation index on the natural frequencies of FG plates is studied in this article. In this study, the effects of aspect ratios, thickness ratio, material variations of FG plates on their natural frequencies are examined. It is thought that the tabulated results would be a reference for other researchers to compare their results.