Non-axisymmetric edge buckling of circular plates when heated

The paper presents the results of simple experiments on uniform heating of thin polymeric circular plates which edges are fixed on rigid rings; and the formation of non-axisymmetric buckling with different numbers of waves around the circumference localized near the plates’ edges. At the same time, buckling modes with a large number of waves around the circumference are observed for plates with a smaller thickness. The classical model of stability for a circular plate under radial compressive forces distributed on a plate contour is used for non-axisymmetric buckling of this kind. The model also describes the temperature swelling of the plate. It became possible to get the interrelation between the minimum critical load and number of waves around the circumference in the plate buckling mode. We compared a multiwave form of buckling for the plate with the modes of eigenoscillations similar to it, which are localized at the edge of the plate. The comparison is carried out based on the transitional line position which mathematically separates the area with an active oscillation from the plateau with an almost nondeformed central region of the plate (which is displaced as a rigid body); and also based on the location of the buckling mode extrema and oscillations modes with respect to the plate center. Using the same parameters, we compared non-axisymmetric plate buckling modes (observed in the experiment) with calculation results related to the theoretical model for rigid, hinged and elastic clamping of the plate edge. In the latter case, we show that it is possible to determine the support rigidity based on a good fit of theoretical and experimental values related to the transitional line radius and a circle radius where the plate buckling extrema are located. The given data illustrates a tendency of a shift of buckling extrema to the plate contour when the boundary conditions are weakened.