Three-dimensional elasticity solutions for free vibrations of circular plates: A polynomials-Ritz analysis Original Research Article

This paper presents accurate three-dimensional elasticity solutions for free vibration of circular plates. The derivation of a linear frequency equation based on an exact three-dimensional, small-strain, linearly elastic principle is detailed. The solution to this problem is made possible by using the Ritz method with a set of orthogonal polynomial series to approximate the spatial displacements of the circular plate in cylindrical polar coordinates. The perturbation of frequency responses due to the variations of boundary conditions and thickness is investigated. First known frequency parameters and three-dimensional deformed mode shapes are presented in vivid graphical forms. The accuracy of these results are verified by appropriate convergence studies and, when possible, are checked with existing solutions.