Bifurcation theory of the time-dependent von Kármán equations

Igor Brilla

Aplikace matematiky (1984)

  • Volume: 29, Issue: 1, page 3-13
  • ISSN: 0862-7940

Abstract

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In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading.

How to cite

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Brilla, Igor. "Bifurcation theory of the time-dependent von Kármán equations." Aplikace matematiky 29.1 (1984): 3-13. <http://eudml.org/doc/15328>.

@article{Brilla1984,
abstract = {In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading.},
author = {Brilla, Igor},
journal = {Aplikace matematiky},
keywords = {existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate; existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate},
language = {eng},
number = {1},
pages = {3-13},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bifurcation theory of the time-dependent von Kármán equations},
url = {http://eudml.org/doc/15328},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Brilla, Igor
TI - Bifurcation theory of the time-dependent von Kármán equations
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 1
SP - 3
EP - 13
AB - In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading.
LA - eng
KW - existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate; existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate
UR - http://eudml.org/doc/15328
ER -

References

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  1. J. Brilla, Stability problems in mathematical theory of viscoelasticity, in Equadiff IV, Proceedings, Prague, August 22-26, 1977 (ed. J. Fabera). Springer, Berlin-Heidelberg- New York 1979. (1977) MR0535322
  2. N. Distéfano, Nonlinear Processes in Engineering, Academic press, New York, London 1974. (1974) MR0392042
  3. A. N. Kolmogorov S. V. Fomin, Elements of the theory of functions and functional analysis, (Russian). Izd. Nauka, Moskva 1976. (1976) MR0435771
  4. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites no linéaires, Dunod, Gautier-Villars, Paris 1969. (1969) MR0259693
  5. F. G. Tricomi, Integral equations, Interscience Publishers, New York, 1957. (1957) Zbl0078.09404MR0094665

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