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Bifurcations near a multiple eigenvalue of the rectangular plate problem

Published online by Cambridge University Press:  14 November 2011

Zoltán Sadovský
Zoltán Sadovský
Affiliation:
Institute of Construction and Architecture of the Slovak Academy of Sciences, 842-20 Bratislava, Czechoslovakia
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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 and Z2 ⊓ Z2 symmetry of bifurcation equations. We are chiefly interested in the degenerate cases of bifurcation equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 1-2 , 1986 , pp. 35 - 62
Copyright
Copyright © Royal Society of Edinburgh 1986

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