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|標題:||Mode jumping in the von Karman equations||作者:||Chien, C.S.
|關鍵字:||von Karman equations;mode jumping;bifurcation;continuation methods;unsymmetric Lanczos method;continuation problems;buckling problem;bifurcations;algorithm;systems||Project:||Siam Journal on Scientific Computing||期刊/報告no：:||Siam Journal on Scientific Computing, Volume 22, Issue 4, Page(s) 1354-1385.||摘要:||
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.
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