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Dynamic Behaviour of a Travelling Viscoelastic Band in Contact with Rollers

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Numerical Methods for Differential Equations, Optimization, and Technological Problems

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 27))

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Abstract

The dynamic behaviour of an axially moving viscoelastic band, in contact with supporting rollers, is studied. A model of a thin, viscoelastic beam (panel) subjected to bending and centrifugal forces is used. An initial-boundary value problem for a fifth-order partial differential equation describing the movement of the band is formulated in detail. In this paper, five boundary conditions in total are used for the first time within the present model. An external force describing the normal force of the roller supports is included. Combining this viscoelastic model with the roller contact simulation is a new approach among moving band behaviour studies. The initial-boundary value problem is solved numerically using the fourth-order Runge-Kutta method and the central finite differences, and the band behaviour is illustrated for different band velocities and degrees of viscosity. It is found that the damping effect of viscoelasticity increases when the band velocity increases, and that the roller contact has a greater effect on the elastic panel behaviour than on the viscoelastic panel behaviour.

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Acknowledgements

This research has been supported by the Jenny and Antti Wihuri foundation, and the Academy of Finland (grant no. 140221).

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Authors and Affiliations

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

    Tytti Saksa, Juha Jeronen & Tero Tuovinen

  2. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences (RAS), Prospekt Vernadskogo 101, 119526, Moscow, Russia

    Nikolay Banichuk

  3. School of Technology, JAMK University of Applied Sciences, P.O. Box 207, 40101, Jyväskylä, Finland

    Matti Kurki

Authors
  1. Tytti Saksa
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  2. Nikolay Banichuk
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  3. Juha Jeronen
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  4. Matti Kurki
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  5. Tero Tuovinen
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Corresponding author

Correspondence to Tytti Saksa .

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Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Sergey Repin

  2. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Timo Tiihonen

  3. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Tero Tuovinen

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Saksa, T., Banichuk, N., Jeronen, J., Kurki, M., Tuovinen, T. (2013). Dynamic Behaviour of a Travelling Viscoelastic Band in Contact with Rollers. In: Repin, S., Tiihonen, T., Tuovinen, T. (eds) Numerical Methods for Differential Equations, Optimization, and Technological Problems. Computational Methods in Applied Sciences, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5288-7_22

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  • DOI: https://doi.org/10.1007/978-94-007-5288-7_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5287-0

  • Online ISBN: 978-94-007-5288-7

  • eBook Packages: EngineeringEngineering (R0)

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