An analytical solution for free vibration analysis of circular plates in axisymmetric modes based on the two variables refined plate theory

This paper presents, for the first time, an analytical solution for free vibrations of an isotropic circular plate in axisymmetric modes based on the two variables refined plate theory. This theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Governing equations are derived using Hamilton's principle and an analytical method on the basis of using Bessel functions is introduced to solve them. By this procedure, final form of the governing equations is obtained in matrix form. These equations are solved for classical boundary conditions and comparison studies are performed to verify the validity of the present results. It is found that the results obtained using RPT and TSDT are close to each other. As a benchmark, numerical results are presented in a dimensionless form for various values of thickness to radius ratio.