Search:
Computing and Library Services - delivering an inspiring information environment

Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity

Talbot, Chris J. and Crampton, Andrew (2005) Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity. Journal of Numerical Algorithms 38 Special Issue: Chebyshev Polynomials, 38. pp. 95-110. ISSN 1017-139

[img] PDF
Restricted to Registered users only

Download (154kB)

    Abstract

    A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considered using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional pole condition to deal with the r=0 coordinate singularity arising in the case of a 2D disc.

    Item Type: Article
    Additional Information: © Springer 2005
    Uncontrolled Keywords: spectral methods - collocation - differentiation matrices - boundary value problems - solid mechanics, elasticity
    Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
    Q Science > QA Mathematics
    Schools: School of Computing and Engineering
    School of Computing and Engineering > Automotive Engineering Research Group
    School of Computing and Engineering > Diagnostic Engineering Research Centre
    School of Computing and Engineering > Diagnostic Engineering Research Centre > Measurement System and Signal Processing Research Group
    School of Computing and Engineering > High-Performance Intelligent Computing
    School of Computing and Engineering > High-Performance Intelligent Computing > Planning, Autonomy and Representation of Knowledge
    School of Computing and Engineering > High-Performance Intelligent Computing > Planning, Autonomy and Representation of Knowledge

    ?? tserg ??
    School of Computing and Engineering > High-Performance Intelligent Computing > Information and Systems Engineering Group
    Related URLs:
    References:

    [1]. H. Chen, Y. Su and B.D. Shizgal, A direct spectral collocation Poisson solver in polar and cylindrical coordinates, J. Comput. Phys. 160 (2000) 453–469.

    [2]. A.C. Eringen and E.S. Suhubi, Elastodynamics, Vol. II (Academic Press, New York, 1975).

    [3]. B. Fornberg, The pseudospectral method: comparisons with finite differences for the elastic wave equation, Geophys. 52 (1987) 483–501.

    [4]. B. Fornberg, The pseudospectral method: accurate representation of interfaces in elastic wave calculations, Geophys. 53 (1988) 625–637.

    [5]. B. Fornberg, A Practical Guide to Pseudospectral Methods (Cambridge Univ. Press, Cambridge, 1996).

    [6]. W. Huang and D.M. Sloan, Pole conditions for singular problems: the pseudospectral approximation, J. Comput. Phys. 107 (1993) 254–261.

    [7]. M.-C. Lai, W.-W. Lin and W. Wang, A fast spectral/difference method without pole conditions for Poisson-type equations in cylindrical and spherical geometries, IMA J. Numer. Anal. 22 (2002) 537–548.

    [8]. J.C. Mason and D.C. Handscomb, Chebyshev Polynomials – Theory and Applications (Chapman and Hall/CRC Press, London, 2003).

    [9]. E. Tessmer and D. Kosloff, 3-D elastic modeling with surface topography by a Chebyshev spectral method, Geophys. 59 (1994) 464–473.

    [10]. L.N. Trefethen, Spectral Methods in MATLAB (SIAM, Philadelphia, PA, 2000).

    Depositing User: Briony Heyhoe
    Date Deposited: 26 Jul 2007
    Last Modified: 10 Dec 2010 13:30
    URI: http://eprints.hud.ac.uk/id/eprint/312

    Downloads

    Downloads per month over past year

    Repository Staff Only: item control page

    View Item

    University of Huddersfield, Queensgate, Huddersfield, HD1 3DH Copyright and Disclaimer All rights reserved ©