Semianalytical Solution for Three-Dimensional Vibration Analysis of Thick Multidirectional Functionally Graded Annular Sector Plates under Various Boundary Conditions

Abstract

The free vibration of two-dimensional (2D) functionally graded annular sector plates is analyzed based on the three-dimensional (3D) theory of elasticity, using the 2D differential quadrature method. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. This paper presents a novel 2D power-law distribution for ceramic volume fraction of 2D functionally graded material that gives designers a powerful tool for flexible designing of structures under multifunctional requirements. Various material profiles along the thickness and radial direction are illustrated using the 2D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. A semianalytical approach composed of the differential quadrature method and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material.