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On Bifurcation Analysis of Implicitly Given Functionals in the Theory of Elastic Stability

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Book cover Mathematical Modeling and Optimization of Complex Structures

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 40))

Abstract

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).

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Author information

Authors and Affiliations

  1. Institute for Problems in Mechanics RAS, Prospect Vernadskogo 101, Bld. 1, 119526, Moscow, Russian Federation

    Nikolay Banichuk

  2. Moldova State University, A. Mateevici 60, MD-2009, Kishinev, Moldova

    Alexander Barsuk

  3. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), 40014, Jyväskylä, Finland

    Juha Jeronen, Pekka Neittaanmäki & Tero Tuovinen

Authors
  1. Nikolay Banichuk
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  2. Alexander Barsuk
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  3. Juha Jeronen
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  4. Pekka Neittaanmäki
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  5. Tero Tuovinen
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Corresponding author

Correspondence to Nikolay Banichuk .

Editor information

Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmäki

  2. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Sergey Repin

  3. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Tero Tuovinen

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Banichuk, N., Barsuk, A., Jeronen, J., Neittaanmäki, P., Tuovinen, T. (2016). On Bifurcation Analysis of Implicitly Given Functionals in the Theory of Elastic Stability. In: Neittaanmäki, P., Repin, S., Tuovinen, T. (eds) Mathematical Modeling and Optimization of Complex Structures. Computational Methods in Applied Sciences, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-319-23564-6_11

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

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23563-9

  • Online ISBN: 978-3-319-23564-6

  • eBook Packages: EngineeringEngineering (R0)

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