Article
MSC:
35B32,
47H15,
73F15,
73H05,
73K10,
74G60,
74K20 | MR 1065004 | Zbl 0725.73044 | DOI: 10.21136/AM.1990.104412
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Keywords:
von Kármán equations; viscoelastic plates; bifurcations; Volterra operator; relations between critical points and bifurcation points; circular clamped von Kármán plates; linearized viscoelastic stability problem; operator formulation
von Kármán equations; viscoelastic plates; bifurcations; Volterra operator; relations between critical points and bifurcation points; circular clamped von Kármán plates; linearized viscoelastic stability problem; operator formulation
Summary:
The paper deals with the analysis of generalized von Kármán equations which describe stability of a thin circular clamped viscoelastic plate of constant thickness under a uniform compressive load which is applied along its edge and depends on a real parameter, and gives results for the linearized problem of stability of viscoelastic plates. An exact definition of a bifurcation point for the generalized von Kármán equations is given. Then relations between the critical points of the linearized problem and the bifurcation points are analyzed.
References:
[1] I. Brilla: Bifurcation Theory of the Time-Dependent von Karman Equations. Aplikace matematiky, 29 (1984), 3-13. MR 0729948 | Zbl 0538.45006
[2] I. Brilla: Equivalent Formulations of Generalized von Kármán Equations for Circular Viscoelastic Plates. Aplikace matematiky, 35 (1990), 237-251. MR 1052745 | Zbl 0727.73030
[3] N. Distéfano: Nonlinear Processes in Engineering. Academic press, New York, London 1974. MR 0392042
[4] Ľ. Marko: The number of Buckled States of Circular Plates. Aplikace matematiky, 34 (1989), 113-132. MR 0990299 | Zbl 0682.73036
[5] F. G. Tricomi: Integral equations. lnterscience Publishers, New York, 1957. MR 0094665 | Zbl 0078.09404
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