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The computation of dispersion relations for axisymmetric waveguides using the Scaled Boundary Finite Element Method

  • This paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computationalThis paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computational efficiency, depending on the elasticity matrix. In the case of solid cylinders, the singularity of the governing equations that occurs in the center of the cross-section is avoided by changing the quadrature scheme. Numerical examples show the applicability of the approach to homogeneous as well as layered structures with isotropic or anisotropic material behavior.zeige mehrzeige weniger

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Metadaten
Autor*innen:Hauke Gravenkamp, C. Birk, C. Song
Dokumenttyp:Zeitschriftenartikel
Veröffentlichungsform:Verlagsliteratur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Ultrasonics
Jahr der Erstveröffentlichung:2014
Verlag:Elsevier B.V.
Verlagsort:Amsterdam
Jahrgang/Band:54
Ausgabe/Heft:5
Erste Seite:1373
Letzte Seite:1385
Freie Schlagwörter:Cylinders; Dispersion; Guided waves; Numerical methods; Scaled Boundary Finite Element Method
DOI:10.1016/j.ultras.2014.02.004
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:07.04.2014
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