A class of reduced-order models in the theory of waves and stability

C. J. Chapman*, S. V. Sorokin

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

1 Citation (Scopus)

Abstract

This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation.

Original languageEnglish
Article number20150703
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume472
Issue number2186
Number of pages17
ISSN1364-5021
DOIs
Publication statusPublished - 1 Feb 2016

Keywords

  • Barycentric representation
  • Elastic wave
  • Euler truncation
  • Fourier series
  • Lamb wave
  • Rayleigh wave

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