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On the vibrations of rectangular plates

Published online by Cambridge University Press:  14 November 2011

Alain Haraux  and
Vilmos Komornik
Alain Haraux
Affiliation:
Université Pierre et Marie Curie, Laboratoire d'Analyse Numérique (U. A. 189), Tour 55-65, 5e étage, 4, place Jussieu, 75230 Paris Cedex 05, France
Vilmos Komornik
Affiliation:
Eötvös Loránd University, Department of Analysis, H-1088 Budapest, Múzeum krt. 6-8, Hungary; andUniversité de Bordeaux I, U.F.R. de Mathématiques et déInformatique, 351, cours de la Libération, 33405 Talence Cedex, France
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Synopsis

We prove that, for every non-empty open subset of a rectangular plate, there exists a positive number T such that no vibration of this plate with fixed edges can remain strictly above the rest position at all points of the subset during a period T. Moreover, the result remains valid for every non-empty segment parallel to one of the sides of the plate. Our proof is based on some results of non-harmonic analysis.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 1-2 , 1991 , pp. 47 - 62
Copyright
Copyright © Royal Society of Edinburgh 1991

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