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Computation of dispersion relations for axially symmetric guided waves in cylindrical structures by means of a spectral decomposition method

  • In this paper, a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures is presented as an alternative to the currently established numerical procedures. The method is based on a spectral decomposition into eigenfunctions of the Laplace operator on the cross-section of the waveguide. This translates the calculation of real or complex wave numbers at a given frequency into solving an eigenvalue problem. Cylindrical rods and plates are treated as the asymptotic cases of cylindrical structures and used to generalize the method to the case of hollow cylinders. The presented method is superior to direct root-finding algorithms in the sense that no initial guess values are needed to determine the complex wave numbers and that neither starting at low frequencies nor subsequent mode tracking is required. The results obtained with this method are shown to be reasonably close to those calculated by other means and an estimate for theIn this paper, a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures is presented as an alternative to the currently established numerical procedures. The method is based on a spectral decomposition into eigenfunctions of the Laplace operator on the cross-section of the waveguide. This translates the calculation of real or complex wave numbers at a given frequency into solving an eigenvalue problem. Cylindrical rods and plates are treated as the asymptotic cases of cylindrical structures and used to generalize the method to the case of hollow cylinders. The presented method is superior to direct root-finding algorithms in the sense that no initial guess values are needed to determine the complex wave numbers and that neither starting at low frequencies nor subsequent mode tracking is required. The results obtained with this method are shown to be reasonably close to those calculated by other means and an estimate for the achievable accuracy is given.zeige mehrzeige weniger

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Metadaten
Autor*innen:Christian Höhne, Jens PragerORCiD, Hauke Gravenkamp
Dokumenttyp:Zeitschriftenartikel
Veröffentlichungsform:Verlagsliteratur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Ultrasonics
Jahr der Erstveröffentlichung:2015
Verlag:Elsevier B.V.
Verlagsort:Amsterdam
Jahrgang/Band:63
Erste Seite:54
Letzte Seite:64
Freie Schlagwörter:Cylinders; Dispersion; Guided waves; Numerical method; Spectral decomposition
DOI:10.1016/j.ultras.2015.06.011
ISSN:0041-624x
Verfügbarkeit des Dokuments:Datei im Netzwerk der BAM verfügbar ("Closed Access")
Datum der Freischaltung:20.02.2016
Referierte Publikation:Ja
Datum der Eintragung als referierte Publikation:13.11.2014
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