Mode jumping in the von Karman equations

We study numerical approximations of bifurcating solution curves of the von Karman equations with simply supported and clamped boundary conditions, re spectively. Of special interest here is the splitting of a double bifurcati on point into two simple bifurcation points, and the tracing of the associa ted secondary solution branches, which corresponds to the phenomenon of mod e jumping in the buckling of a rectangular plate. A continuation-unsymmetri c Lanczos algorithm is utilized for curve-tracking. Our numerical results v erify the theoretical prediction of Schaeffer and Golubitsky, namely, mode jumping occurs when the boundary is partially clamped, but not if it is mer ely simply supported.