Mode jumping in the von Kármán equations (Q2706441)

The authors study numerical approximations of bifurcating solutions, of von Kármán equations with simply supported and clamped boundary conditions. Of special interest is the splitting of double bifurcation point into two simply bifurcation points and the tracking of associated secondary solution branches, which corresponds to the phenomenon of mode jumping in the buckling of rectangular plate. A non-symmetric continuation method of Lanczos type is utilized for curve tracking. Numerical results verify theoretical predictions of \textit{D. Schaeffer} and \textit{M. Golubitsky} [Notes Pure Appl. Math. 54, 229-254 (1980; Zbl 0438.73044)], namely that the mode jumping occurs when the boundary is partially clamped, but not if it is merely simply supported.