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Curve Veering for the Parameter-dependent Clamped Plate

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Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9553))

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Abstract

The computation of vibrations of a thin rectangular clamped plate results in an eigenvalue problem with a partial differential equation of fourth order. If we change the geometry of the plate for fixed area, this results in a parameter-dependent eigenvalue problem. For certain parameters, the eigenvalue curves seem to cross. We give a numerically rigorous proof of curve veering, which is based on the Lehmann-Goerisch inclusion theorems and the Rayleigh-Ritz procedure.

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Authors and Affiliations

  1. Institut für Mathematik, TU Clausthal, Erzstraße 1, 38678, Clausthal-Zellerfeld, Germany

    Henning Behnke

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  1. Henning Behnke
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Correspondence to Henning Behnke .

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Editors and Affiliations

  1. Institute of Computer Science, University of Würzburg, Würzburg, Germany

    Marco Nehmeier

  2. Universität Würzburg, Würzburg, Germany

    Jürgen Wolff von Gudenberg

  3. Department of Mathematics, Uppsala University, Uppsala, Sweden

    Warwick Tucker

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Behnke, H. (2016). Curve Veering for the Parameter-dependent Clamped Plate. In: Nehmeier, M., Wolff von Gudenberg, J., Tucker, W. (eds) Scientific Computing, Computer Arithmetic, and Validated Numerics. SCAN 2015. Lecture Notes in Computer Science(), vol 9553. Springer, Cham. https://doi.org/10.1007/978-3-319-31769-4_21

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  • DOI: https://doi.org/10.1007/978-3-319-31769-4_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31768-7

  • Online ISBN: 978-3-319-31769-4

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