Free vibration response of functionally graded thick plates with shear and normal deformations effects

Abstract

Free vibration response of functionally graded (FG) elastic, rectangular, and simply (diaphragm) supported plates is presented based on higher order shear/shear-normal deformations theories (HOSTs/HOSNTs). The theoretical models are based on Taylor’s series expansion of in-plane and transverse displacements in thickness coordinate defining the plate deformations. Some of these advanced models account for the effects of transverse shear deformations, transverse normal deformation and non-linear variation of in-plane displacements through plate’s thickness. Functionally graded materials (FGMs) are idealized as continua with mechanical properties changing smoothly with respect to spatial coordinates. The material properties of FG plates are assumed here to be varying through thickness of plate in a continuous manner. Poisson’s ratios of FG plates are assumed constant, but their Young’s modulii and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as exponential and power law functions. The equations of motion are derived using Hamilton’s principle on the basis of HOSTs/HOSNTs. Numerical solutions are obtained using Navier solution method. The accuracy of numerical solutions is first established through comparison with the exact three dimensional (3D) elasticity solutions and then compared with available other models’ solutions. New solutions are then provided for future use.