A Higher Order Shear Deformation Theory for the Vibration of Thick Plates

Abstract

Several first order, shear deformation theories for thick plates have been formulated during the past half-century (e.g., by Reissner, Hencky, Mindlin and Ambartsumyan). The Mindlin theory has been widely used for vibration analysis. It is well known that consideration of shear flexibility corrects the flexural frequencies by reducing them. However, it has been found that first order shear deformation theories result in over-correction. In the present work a higher order theory is presented which provides additional freedom to the displacements through the plate thickness and essentially eliminates the over-correction. A complete theory is developed, including energy functionals, equations of motion and boundary conditions. Comparisons of frequencies arising from classical thin plate theory, Mindlin theory and the present theory are made for completely free rectangular plates of moderate and large thickness. Completely free boundaries, rather than simply supported ones, are chosen because they are more consistent with physical models in the theories used.