On bifurcation analysis of implicitly given functionals in the theory of elastic stability
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BANICHUK, Nikolay; BARSUK, Alexander A.; JERONEN, J.; NEITTAANMAKI, Pekka; TUOVINEN, Tero. On bifurcation analysis of implicitly given functionals in the theory of elastic stability. In: Computational Methods in Applied Sciences. Volume 40, 6-7 martie 2014, Jyvaskyla. Berlin, Germania: Springer Science and Business Media B.V., 2016, pp. 175-188.
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Computational Methods in Applied Sciences
Volume 40, 2016
Conferința "International Conference for Mathematical Modeling and Optimization in Mechanics"
Jyvaskyla, Finland, 6-7 martie 2014

On bifurcation analysis of implicitly given functionals in the theory of elastic stability

DOI: https://doi.org/10.1007/978-3-319-23564-6_11

Pag. 175-188

Banichuk Nikolay1, Barsuk Alexander A.2, Jeronen J.3, Neittaanmaki Pekka3, Tuovinen Tero3
 
1 Institut pe Probleme Mecanice, Academia de Stiinte a Rusiei,
2 State University of Moldova,
3 Department of Mathematical Information Technology, University of Jyvaskyla
 
Disponibil în IBN: 7 iulie 2022


Rezumat

In this paper, we analyze the stability and bifurcation of elastic systems using a general scheme developed for problems with implicitly given functionals. An asymptotic property for the behaviour of the natural frequency curves in the small vicinity of each bifurcation point is obtained for the considered class of systems. Two examples are given. First is the stability analysis of an axially moving elastic panel, with no external applied tension, performing transverse vibrations. The second is the free vibration problem of a stationary compressed panel. The approach is applicable to a class of problems in mechanics, for example in elasticity, aeroelasticity and axially moving materials (such as paper making or band saw blades). 

Cuvinte-cheie
Axially moving, bifurcation, Eigenvalue problem, Elastic beam, Elastic panel, stability