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Timoshenko's beam equation as limit of a nonlinear one-dimensional von Kármán system

Published online by Cambridge University Press:  11 July 2007

G. Perla Menzala  and
E. Zuazua
G. Perla Menzala
Affiliation:
National Laboratory of Scientific Computation, LNCC/CNPq, Rua Getulio Vargas 333, Quitandinha, Petrópolis, CEP 25651-070, RJ, BrasilInstitute of Mathematics, UFRJ, PO Box 68530, Rio de Janeiro, RJ, Brasil (perla@lncc.br)
E. Zuazua
Affiliation:
Universidad Complutense de Madrid, Dpto. de Matemática Aplicada, 28040, Madrid, Espana (zuazua@eucmax.sim.ucm.es)
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Abstract

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We consider a dynamical one-dimensional nonlinear von Kármán model depending on one parameter ε > 0 and study its weak limit as ε → 0. We analyse various boundary conditions and prove that the nature of the limit system is very sensitive to them. We prove that, depending on the type of boundary condition we consider, the nonlinearity of Timoshenko's model may vanish.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 4 , August 2000 , pp. 855 - 875
Copyright
Copyright © Royal Society of Edinburgh 2001