Free Vibration Analysis of Single and Multilayered Sandwich FGM Plates-Assessment of Higher Order Refined Theories

Abstract

Analytical formulations and solutions for natural frequency analysis of functionally graded material (FGM) plates based on two higher-order refined shear deformation theories with 9 and 12 degrees-of-freedom are presented. The displacement model with 12 degrees-of-freedom considers the effect of both transverse shear and normal strain/stress while the other considers only the effect of transverse shear deformation. In addition another higher-order model and the first-order model developed by other investigators and available in the literature are also presented for the evaluation purpose. For mathematical modeling purposes, the Poissons ratio of the material is considered as constant whereas Youngs modulus is assumed to vary through the thickness according to the power law function. The equations of motion are derived using Hamiltons principle. Solutions are obtained in closed-form using Naviers technique and solving the eigenvalue equation. The accuracy of the theoretical formulations and the solution method using the present two higher-order refined models is first established by comparing the results generated in the present investigation with the 3D elasticity solutions already reported in the literature. After establishing the accuracy of predictions, benchmark results for the natural frequencies using all the four models are presented for single layer FGM plate and multi layered FGM sandwich plate with varying edge ratios and side-to-thickness ratios.