VIBRATION OF INITIALLY STRESSED REDDY PLATES ON A WINKLER–PASTERNAK FOUNDATION

Abstract

Treated herein is the vibration of isotropic Reddy plates. The plates considered are of general polygonal shape and their edges are all simply supported. Complicating effects such as the presence of initial stresses and a Winkler–Pasternak foundation are also considered. It is shown herein that the vibration solution can be readily obtained from the classical Kirchhoff plate vibration results because of the mathematical similarity of the two kinds of problems. The mathematical analogy permits the development of an exact relationship that links the natural frequencies of the initially stressed Reddy plates resting on a Winkler–Pasternak foundation to the corresponding classical Kirchhoff plate solutions without the presence of complicating effects.