Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates

Igor Brilla

Aplikace matematiky (1990)

  • Volume: 35, Issue: 3, page 237-251
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Brilla, Igor. "Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates." Aplikace matematiky 35.3 (1990): 237-251. <http://eudml.org/doc/15629>.

@article{Brilla1990,
abstract = {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.},
author = {Brilla, Igor},
journal = {Aplikace matematiky},
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; stability; plate of constant thickness; uniform compressive load; nonlinear functional analysis; operator; integro-operator formulations; post-buckling; circular plate},
language = {eng},
number = {3},
pages = {237-251},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates},
url = {http://eudml.org/doc/15629},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Brilla, Igor
TI - Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 3
SP - 237
EP - 251
AB - 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.
LA - eng
KW - von Kármán equations; viscoelastic plates; stability; plate of constant thickness; uniform compressive load; nonlinear functional analysis; operator; integro-operator formulations; post-buckling; circular plate; stability; plate of constant thickness; uniform compressive load; nonlinear functional analysis; operator; integro-operator formulations; post-buckling; circular plate
UR - http://eudml.org/doc/15629
ER -

References

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  1. J. Brilla, Stability Problems in Mathematical Theory of Viscoelasticity, in Equadiif IV, Proceedings, Prague, August 22-26, 1977 (ed. /. Fábera), Springer, Berlin-Heidelberg-New York 1979. (1977) MR0535322
  2. Ľ. Marko, Buckled States of Circular Plates, Thesis, 1985 (Slovak). (1985) 
  3. Ľ. Marko, The Number of Buckled States of Circular Plates, Aplikace matematiky, 34 (1989), 113-132. (1989) Zbl0682.73036MR0990299
  4. E. C. Titchmarsh, Eigenfunction Expansion Associated with Second-order Differential Equations, The Clarendon Press, Oxford 1958. (1958) MR0094551
  5. F. G. Tricomi, Integral Equations, Interscience Publishers, New York 1957. (1957) Zbl0078.09404MR0094665

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