Non-axisymmetric warping of a heavy circular plate on a flexible ring support

In this paper, we study the deformation and stability of a circular plate under its own weight and supported by a flexible concentric ring. Both bilateral and unilateral supports are considered. Von Karman’s plate model is adopted to formulate the equations of motion. A nonlinear Galerkin’s method based on two sets of assumed functions is used to discretize and solve the governing equations. Vibration method is used to predict the stability of the deformations. The linear analysis conducted previously predicts that the deformation is always axisymmetric. The current nonlinear analysis, however, shows that the axisymmetric deformation may become unstable when the dimensionless load, i.e., a ratio between the weight per unit area and the flexural rigidity of the plate, reaches a critical value. At this critical load, a stable non-axisymmetric deformation of the form cos nθ emerges following a pitch-fork bifurcation, where the integer n depends on the stiffness and the radius of the ring support. When the load increases further, more than one stable non-axisymmetric deformation may coexist. In a stable non-axisymmetric deformation with bilateral support, tension on the ring support may develop when the load reaches another critical value. In this situation, the circular plate will separate from the supporting ring in part of the angular region if the bilateral support is replaced by a unilateral one. The deformation with unilateral support is in general larger than the one with bilateral support.