Bifurcation theory of the time-dependent von Kármán equations. (English) Zbl 0538.45006

Brilla, Igor

Apl. Mat. 29, 3-13 (1984).

Author’s summary: 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.

Reviewer: J.Appell

MSC:

45G10	Other nonlinear integral equations
45M10	Stability theory for integral equations
74Hxx	Dynamical problems in solid mechanics

Keywords:

existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate

References:

[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. · Zbl 0439.73036
[2]	N. Distéfano: Nonlinear Processes in Engineering. Academic press, New York, London 1974. · Zbl 0227.73056
[3]	A. N. Kolmogorov S. V. Fomin: Elements of the theory of functions and functional analysis. (Russian). Izd. Nauka, Moskva 1976.
[4]	J. L. Lions: Quelques méthodes de résolution des problèmes aux limites no linéaires. Dunod, Gautier-Villars, Paris 1969. · Zbl 0189.40603
[5]	F. G. Tricomi: Integral equations. Interscience Publishers, New York, 1957. · Zbl 0078.09404