Vibrations of Thick Free Circular Plates, Exact Versus Approximate Solutions

An exact solution for the natural frequencies of a thick free circular plate is compared to approximate solutions. The exact solution is a series solution of the general linear elasticity equations that converges to the correct natural frequencies. The approximate solutions to which this exact solution is compared are the Mindlin plate theory and a modification of a solution method proposed by Pickett. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Mindlin plate theory is considered by evaluating the shear coefficient that would make the exact and modified Pickett method match the Mindlin plate solution.