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Title: Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates (English)
Author: Brilla, Igor
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 35
Issue: 3
Year: 1990
Pages: 237-251
Summary lang: English
Category: math
Summary: The paper deals with the analysis of generalized von Kármán equations which desribe stability of a thin circular viscoelastic clamped plate of constant thickness under a uniform compressible load which is applied along its edge and depends on a real parameter. The meaning of a solution of the mathematical problem is extended and various equivalent reformulations of the problem are considered. The structural pattern of the generalized von Kármán equations is analyzed from the point of view of nonlinear functional analysis. (English)
Keyword: von Kármán equations
Keyword: viscoelastic plates
Keyword: stability
Keyword: plate of constant thickness
Keyword: uniform compressive load
Keyword: nonlinear functional analysis
Keyword: operator
Keyword: integro-operator formulations
Keyword: post-buckling
Keyword: circular plate
MSC: 35D99
MSC: 35Q72
MSC: 73F15
MSC: 73H05
MSC: 73K10
MSC: 74G60
MSC: 74K20
idZBL: Zbl 0727.73030
idMR: MR1052745
DOI: 10.21136/AM.1990.104408
Date available: 2008-05-20T18:39:25Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. Brilla: Stability Problems in Mathematical Theory of Equadiif IV, Proceedings, Prague, August 22-26, 1977 (ed. /. Fábera), Springer, Berlin-Heidelberg-New York 1979. MR 0535322
Reference: [2] Ľ. Marko: Buckled States of Circular Plates.Thesis, 1985 (Slovak).
Reference: [3] Ľ. Marko: The Number of Buckled States of Circular Plates.Aplikace matematiky, 34 (1989), 113-132. Zbl 0682.73036, MR 0990299
Reference: [4] E. C. Titchmarsh: Eigenfunction Expansion Associated with Second-order Differential Equations.The Clarendon Press, Oxford 1958. MR 0094551
Reference: [5] F. G. Tricomi: Integral Equations.Interscience Publishers, New York 1957. Zbl 0078.09404, MR 0094665


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