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Finding the Density of a Membrane from Nodal Lines

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Inverse Problems in Wave Propagation

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 90))

Abstract

We solve an inverse nodal problem for a rectangular membrane using two different algorithms, the ratio method and the method of parameter identification. The algorithms use nodal positions and the corresponding natural frequencies to construct a piecewise constant approximation to the density distribution of the membrane. Both algorithms are numerically implemented using numerically simulated data.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Rensselaer Polytech Institute, Troy, NY, 12181, USA

    Ching-Ju Ashraf Lee & Joyce R. Mclaughlin

Authors
  1. Ching-Ju Ashraf Lee
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  2. Joyce R. Mclaughlin
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Editor information

Editors and Affiliations

  1. Domaine de Voluceau, INRIA, B.P. 105, 78153 Le Chesnay, Cedex, France

    Guy Chavent

  2. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    Paul Sacks

  3. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    George Papanicolaou

  4. Department of Computer and Applied Mathematics, Rice University, Houston, TX, 77251-1892, USA

    William W. Symes

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© 1997 Springer Science+Business Media New York

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Lee, CJ.A., Mclaughlin, J.R. (1997). Finding the Density of a Membrane from Nodal Lines. In: Chavent, G., Sacks, P., Papanicolaou, G., Symes, W.W. (eds) Inverse Problems in Wave Propagation. The IMA Volumes in Mathematics and its Applications, vol 90. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1878-4_15

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  • DOI: https://doi.org/10.1007/978-1-4612-1878-4_15

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7322-6

  • Online ISBN: 978-1-4612-1878-4

  • eBook Packages: Springer Book Archive

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