Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations

In this paper, natural frequencies characteristics of a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on three-dimensional equations of elasticity is considered. The axisymmetric conditions are assumed for the 2D-FGM cylinder. The material properties of the cylinder are varied in the radial and axial directions with power law functions. Effects of volume fraction distribution and FGM configuration on the natural frequencies of a simply supported cylinder are analyzed. Also, the effects of length and thickness of the cylinder are considered for different material distribution profiles. Three-dimensional equations of motion are used and the eigen value problem is developed based on direct variational method. Finite element method with graded material characteristics within each element of the structure is used for solution. The study shows that the 2D-FGM cylinder exhibit interesting frequency characteristics when the constituent volume fractions and its configuration are varied.