Axisymmetric Flexural Vibrations of a Thick Free Circular Plate

A series solution of the general three-dimensional equations of linear elasticity is used to find accurate natural frequencies and mode shapes for the flexural vibrations of thick free circular plates. The approximate solution for thick plates, which includes shear and rotary inertia effects, is compared with the accurate series solution. It is found that the approximate solution yields frequencies of sufficient accuracy for most engineering applications within the range of applicability of the approximate theory.