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Mode Jumping In The Von Kármán Equations

We study numerical approximations of bifurcating solution curves of the von Karman equations with simply supported and clamped boundary conditions, respectively. Of special interest here is the splitting of a double bifurcation point into two simple bifurcation points, and the tracing of the associated secondary solution branches, which corresponds to the phenomenon of mode jumping in the buckling of a rectangular plate. A continuation-unsymmetric Lanczos algorithm is utilized for curve-tracking. Our numerical results verify the theoretical prediction of Schaeffer and Golubitsky, namely, mode jumping occurs when the boundary is partially clamped, but not if it is merely simply supported.