Relationship between vibration frequencies of Reddy and Kirchhoff polygonal plates with simply supported edges

This paper presents an exact relationship between the natural frequencies o f Reddy third-order plate theory and hose of classical Kirchhoff plate theo ry for simply supported, polygonal isotropic plates, including rectangular plates. The relationship SOY the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plat e theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relation ship.