A free boundary problem and stability for the circular plate

In the recent paper [6] we have answered the question of stability for the nonlinear beam which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. The basic idea that was first used in a numerical solution and subsequently in the mathematical analysis was to consider the free boundary problem in the interval in which the beam is not in contact with the obstacle. In this work we consider the analogous problem for the linear circular plate. Numerical computations are crucial here to establish conditions essential for the problem of stability and they also yield the critical parameter values, i.e., the secondary bifurcation points.