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Numerical methods for the simulation of ultrasonic guided waves

  • Ultrasonic guided waves offer a wide range of applications in fields such as non-destructive testing, structural health monitoring or material characterization. They can be excited in thin-walled structures and propagate over comparably long distances. Due to their complex and dispersive propagation behavior, numerical methods are often required in order to analyze the guided wave modes that can be excited in a given structure and to simulate their interaction with defects. In the work presented in this thesis, highly efficient numerical methods have been developed that are specifically optimized for guided wave problems. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM). The SBFEM is a semi-analytical method which evolved from the concept of Finite Elements but requires the discretization of the boundary of the computational domain only. To compute dispersion curves and mode shapes of guided waves, only the cross-section of the waveguide is discretized inUltrasonic guided waves offer a wide range of applications in fields such as non-destructive testing, structural health monitoring or material characterization. They can be excited in thin-walled structures and propagate over comparably long distances. Due to their complex and dispersive propagation behavior, numerical methods are often required in order to analyze the guided wave modes that can be excited in a given structure and to simulate their interaction with defects. In the work presented in this thesis, highly efficient numerical methods have been developed that are specifically optimized for guided wave problems. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM). The SBFEM is a semi-analytical method which evolved from the concept of Finite Elements but requires the discretization of the boundary of the computational domain only. To compute dispersion curves and mode shapes of guided waves, only the cross-section of the waveguide is discretized in the Finite Element sense, while the direction of propagation is described analytically. The wavenumbers of guided wave modes and the corresponding mode shapes are obtained as the eigenvalues and eigenvectors of a frequency-dependent Hamiltonian matrix. For the discretization, higher-order spectral elements are employed, leading to very low computational costs compared to traditional Finite Elements. Particular formulations are presented for plate structures as well as axisymmetric waveguides, where only the throughthickness direction has to be discretized. For the cases where the waveguide is embedded in or coupled to a quasi-infinite medium, a dashpot boundary condition is proposed in order to account for the effect of waves being transmitted into the surrounding medium. Though this approach is not exact, it leads to sufficiently accurate results for practical applications, while the computational costs are typically reduced by several orders of magnitude compared to other Finite Element based approaches. As a particular application, an experimental set-up for material characterization is discussed, where the elastic constants of the waveguide’s material are obtained from the analysis of waves propagating through the waveguide. A novel solution procedure is proposed in this work, where each mode of interest is traced over the required frequency range. The solutions are obtained by means of inverse iteration. To demonstrate the potential of the SBFEM for non-destructive testing applications, the interaction of guided wave modes with cracks in plates is simulated in the time domain for several examples. Particularly for the modeling of cracked structures, the SBFEM is very well suited, since the side-faces of the crack do not require discretization and the stress-singularity at the crack tip does not introduce additional difficulties. Hence, the computational costs can be reduced by typically a factor 100 compared to traditional Finite Elements and the meshing is straightforward.zeige mehrzeige weniger

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Metadaten
Autor*innen:Hauke Gravenkamp
Dokumenttyp:Dissertation
Veröffentlichungsform:Eigenverlag BAM
Schriftenreihe (Bandnummer):BAM Dissertationsreihe (116)
Sprache:Englisch
Jahr der Erstveröffentlichung:2014
Veröffentlichende Institution:Bundesanstalt für Materialforschung und -prüfung (BAM)
Titel verleihende Institution:Technische Universität Carolo-Wilhelmina zu Braunschweig, Fakultät Architektur, Bauingenieurwesen und Umweltwissenschaften
Gutachter*innen:Sabine Langer, Marc Kreutzbruck, Chongmin Song
Datum der Abschlussprüfung:14.04.2014
Verlag:Bundesanstalt für Materialforschung und -prüfung (BAM)
Verlagsort:Berlin
Jahrgang/Band:116
Erste Seite:1
Letzte Seite:195
DDC-Klassifikation:Naturwissenschaften und Mathematik / Physik / Physik
Freie Schlagwörter:guided wave; numerical methods; scaled boundary finite element method; ultrasound
URN:urn:nbn:de:kobv:b43-428
ISSN:1613-4249
ISBN:978-3-9816380-4-2
Verfügbarkeit des Dokuments:Datei für die Öffentlichkeit verfügbar ("Open Access")
Lizenz (Deutsch):License LogoAllgemeines Deutsches Urheberrecht
Datum der Freischaltung:23.01.2015
Referierte Publikation:Nein
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