Geodesic
Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates
Applications of Mathematics, Tome 35 (1990) no. 3, pp. 237-251
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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.
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.
DOI : 10.21136/AM.1990.104408
Classification : 35D99, 35Q72, 73F15, 73H05, 73K10, 74G60, 74K20
Keywords: von Kármán equations; viscoelastic plates; stability; plate of constant thickness; uniform compressive load; nonlinear functional analysis; operator; integro-operator formulations; post-buckling; circular plate 
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     title = {Equivalent formulations of generalized von {K\'arm\'an} equations for circular viscoelastic plates},
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Brilla, Igor. Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates. Applications of Mathematics, Tome 35 (1990) no. 3, pp. 237-251. doi: 10.21136/AM.1990.104408

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[2] Ľ. Marko: Buckled States of Circular Plates. Thesis, 1985 (Slovak).

[3] Ľ. Marko: The Number of Buckled States of Circular Plates. Aplikace matematiky, 34 (1989), 113-132. | MR | Zbl

[4] E. C. Titchmarsh: Eigenfunction Expansion Associated with Second-order Differential Equations. The Clarendon Press, Oxford 1958. | MR

[5] F. G. Tricomi: Integral Equations. Interscience Publishers, New York 1957. | MR | Zbl

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