Circular Elastic Plate Resting on Tensionless Pasternak Foundation

Abstract

In this technical note, a thin circular plate resting on a two-parameter (Pasternak-type) foundation is studied under concentrated central and distributed loads. The governing equations of the plate are derived for static loading case considering the lift off (uplift) of the plate from the foundation. For the approximate solution, a Galerkin technique is adopted and the free vibration mode shapes of the completely free plate are chosen as the displacement functions. The technique yields a system of algebraic nonlinear equations, and its solution is accomplished by using an iterative method. The numerical results are obtained for evaluation of the behavior of the plate and then given comparatively in figures. Although in the case of a tensionless Winkler foundation, the lift off of the plate from the foundation takes place, when the displacement of plate is negative, while in case of the two-parameter foundation the lift off appears when the slopes of the foundation surface and that of the plate are not equal.