Abstract
This article aims to investigate the free vibration of axial and bi-directional functionally graded (2D-FG) two-dimensional plane stress strip by using finite element method. The rule of mixture based on Vogit model is proposed to describe the change in the volume fractions of metal and ceramics constituents. The materials are graded continuously and smoothly in both axial and thickness directions according to the power law formula. Two-dimensional plane stress constitutive equations are proposed to describe the stress and strain across the beam domain. Finite element model using ANSYS software is developed to discretize the spatial domain of strip and modal solution is exploited to evaluate the eigenvalues (natural frequencies) and mode shapes of 2D FG strip beam. The effects of materials gradation in axial and bi-directional and boundary conditions on the natural frequencies are investigated. The proposed model can be used in design and analysis of 2D-FG structures manufactured from two different constituents and selecting the optimum gradation parameter based on the natural frequency's constraints, such as naval, nuclear and aerospace structures.