Bifurcations of generalized von Kármán equations for circular viscoelastic plates

Igor Brilla

Aplikace matematiky (1990)

  • Volume: 35, Issue: 4, page 302-314
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Brilla, Igor. "Bifurcations of generalized von Kármán equations for circular viscoelastic plates." Aplikace matematiky 35.4 (1990): 302-314. <http://eudml.org/doc/15632>.

@article{Brilla1990,
abstract = {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.},
author = {Brilla, Igor},
journal = {Aplikace matematiky},
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; Volterra operator; relations between critical points and bifurcation points; circular clamped von Kármán plates; linearized viscoelastic stability problem; operator formulation},
language = {eng},
number = {4},
pages = {302-314},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bifurcations of generalized von Kármán equations for circular viscoelastic plates},
url = {http://eudml.org/doc/15632},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Brilla, Igor
TI - Bifurcations 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 - 4
SP - 302
EP - 314
AB - 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.
LA - eng
KW - 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; Volterra operator; relations between critical points and bifurcation points; circular clamped von Kármán plates; linearized viscoelastic stability problem; operator formulation
UR - http://eudml.org/doc/15632
ER -

References

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  1. I. Brilla, Bifurcation Theory of the Time-Dependent von Karman Equations, Aplikace matematiky, 29 (1984), 3-13. (1984) Zbl0538.45006MR0729948
  2. I. Brilla, Equivalent Formulations of Generalized von Kármán Equations for Circular Viscoelastic Plates, Aplikace matematiky, 35 (1990), 237-251. (1990) Zbl0727.73030MR1052745
  3. N. Distéfano, Nonlinear Processes in Engineering, Academic press, New York, London 1974. (1974) Zbl0328.73060MR0392042
  4. Ľ. Marko, The number of Buckled States of Circular Plates, Aplikace matematiky, 34 (1989), 113-132. (1989) Zbl0682.73036MR0990299
  5. F. G. Tricomi, Integral equations, lnterscience Publishers, New York, 1957. (1957) Zbl0078.09404MR0094665

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