# Bifurcations of generalized von Kármán equations for circular viscoelastic plates

Aplikace matematiky (1990)

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

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topBrilla, 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

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

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