Abstract
Free vibrations of a simply supported thick elastic plate subjected to in-plane stresses are studied. Taking into account the effects of rotatory inertia and shear deformations with thickness changes, natural frequencies and vibration modes of thick plates are obtained. A set of fundamental equations of a two-dimensional higher-order plate theory is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a thick plate. It is noticed that the present higher-order theories can predict the natural frequencies of an extremely thick plate more accurately compared to other refined theories.
