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

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, wavenumb...

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Published inProceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 472; no. 2186; p. 20150703
Main Authors Chapman, C. J., Sorokin, S. V.
Format Journal Article
LanguageEnglish
Published England The Royal Society Publishing 01.02.2016
Subjects
Barycentric Representation
Elastic Wave
Euler Truncation
Fourier Series
Lamb Wave
Rayleigh Wave
Lamb wave
elastic wave
Euler truncation
Rayleigh wave
Fourier series
barycentric representation
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2015.0703