Finite Element Formulations for Free Vibration Analysis of Isotropic and Orthotropic Plates using Two-Variable Refined Plate Theory

In this paper, a finite element formulation based on two-variable refined plate theory is developed for free vibration analysis of isotropic and orthotropic plates. The two-variable refined plate theory, which can be used for both thin and thick plates, predicts parabolic variation of transverse shear stresses across the plate thickness, satisfies the zero traction condition on the plate surfaces and does not need the shear correction factor. After constructing weak form equations using the Hamilton principle for vibration formulation, a new 4-node rectangular plate element with six-degrees of freedom at each node is introduced for discretization of the domain. The natural frequencies of isotropic plates with different boundary condition and the fundamental natural frequencies of levy type orthotropic plates are obtained. Comparison of results with exact solutions and other common plate theories shows that beside the simplicity of presented finite element formulations, it presents accurate and efficient results. Also the effects of orthotropy ratio, side-to-thickness ratio and types of boundary conditions on the natural frequencies are studied.