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

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

*Kontaktforfatter

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1 Citationer (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.

OriginalsprogEngelsk
Artikelnummer20150703
TidsskriftProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Vol/bind472
Udgave nummer2186
Antal sider17
ISSN1364-5021
DOI
StatusUdgivet - 1 feb. 2016

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