Bifurcations near a multiple eigenvalue of the rectangular plate problem
Z. Sadovský · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1986
Synopsis We consider the bifurcation problem of the Föppl–Kármán equations for a thin elastic rectangular plate near a multiple eigenvalue allowing for a small perturbation parameter related to the aspect ratio of the plate. The first step in the study is to introduce equivalent operator equations in the energy spaces of the problem which explicitly contain the perturbation parameter. By dealing partially with a general formulation, we obtain the main results for the double eigenvalue andZ2⊓Z2symmetry of bifurcation equations. We are chiefly interested in the degenerate cases of bifurcation equations.