TY - THES A1 - Gravenkamp, Hauke T1 - Numerical methods for the simulation of ultrasonic guided waves N2 - 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 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. T3 - BAM Dissertationsreihe - 116 KW - guided wave KW - numerical methods KW - scaled boundary finite element method KW - ultrasound PY - 2014 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-428 SN - 978-3-9816380-4-2 SN - 1613-4249 VL - 116 SP - 1 EP - 195 PB - Bundesanstalt für Materialforschung und -prüfung (BAM) CY - Berlin AN - OPUS4-42 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Song, C. T1 - Scaled Boundary Finite Element Method zur effizienten Simulation geführter Ultraschallwellen T2 - DGZfP-Jahrestagung 2013 CY - Dresden, Germany DA - 2013-05-06 PY - 2013 AN - OPUS4-28550 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Song, C. A1 - Birk, C. T1 - Modelling ultrasonic waves in solid waveguides of arbitrary cross-section T2 - AIA-DAGA 2013 Conference on Acoustics CY - Meran, Italy DA - 2013-03-18 PY - 2013 AN - OPUS4-28551 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Man, H. A1 - Song, Ch. A1 - Birk, C. T1 - Numerical computation of dispersion relations in three-dimensional waveguides T2 - Australian Conference on the Mechanics of Structures and Materials (ACMSM 22) CY - Sydney, Australia DA - 2012-12-11 PY - 2012 AN - OPUS4-28495 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Saputra, A. A1 - Birk, C. A1 - Song, Ch. T1 - Numerical modelling of Lamb waves in cracked plates using the scaled boundary finite element method T2 - Australian Conference on the Mechanics of Structures and Materials (ACMSM 22) CY - Sydney, Australia DA - 2012-12-11 PY - 2012 AN - OPUS4-28496 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Gravenkamp, Hauke A1 - Song, C. A1 - Prager, Jens T1 - A numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method N2 - In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities. KW - Scaled boundary finite element method KW - Lamb waves KW - Dispersion KW - Non-destructive testing KW - Composites KW - Functionally graded materials PY - 2012 DO - https://doi.org/10.1016/j.jsv.2012.01.029 SN - 0022-460X SN - 1095-8568 VL - 331 IS - 11 SP - 2543 EP - 2557 PB - Academic Press CY - London AN - OPUS4-25743 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke T1 - The simultion of ultrasonic guided waves using the Scaled Boundary Finite Element Method T2 - Forum Braunschweiger Akustiker CY - Helmstedt, Germany DA - 2012-05-31 PY - 2012 AN - OPUS4-25995 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Song, C. A1 - Prager, Jens T1 - Numerische Berechnung der Dispersionseigenschaften von Lambwellen in Platten mit beliebiger Materialzusammensetzung N2 - Für alle Anwendungen geführter Wellen, beispielsweise in der zerstörungsfreien Materialprüfung, ist die exakte und effiziente Berechnung von Dispersionseigenschaften erforderlich. Dabei müssen für eine gegebene Frequenz die Anzahl der ausbreitungsfähigen Moden und deren Wellenzahlen sowie Phasen- und Gruppengeschwindigkeiten berechnet werden. Für den Fall von Lambwellen in homogenen isotropen Platten existieren analytische Gleichungen für die Wellenzahlen, die sich mit numerischen Nullstellensuchverfahren lösen lassen. Für komplexere Strukturen oder dreidimensionale, nicht rotationssymmetrische Wellenleiter ist die Entwicklung numerischer Methoden erforderlich. In der vorliegenden Arbeit wird ein numerisches Verfahren, basierend auf der Scaled Boundary Finite Element Method (SBFEM) [1] vorgestellt. Mit diesem lassen sich Dispersionseigenschaften von beliebigen Wellenleitern sehr effizient berechnen. Ergebnisse werden für den Fall von Wellen in Platten mit komplexer Materialzusammensetzung präsentiert. T2 - DAGA 2012 - 38. Jahrestagung für Akustik - Fortschritte der Akustik CY - Darmstadt, Deutschland DA - 2012-03-19 KW - Ultraschall KW - Lambwellen KW - Dispersion KW - Scaled boundary finite element method PY - 2012 SP - 1 EP - 2 PB - Deutsche Gesellschaft für Akustik e.V. AN - OPUS4-25978 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Saputra, A. A. A1 - Song, C. A1 - Prager, Jens ED - Linde, B. B. J. ED - Paczkowski, J. ED - Ponikwicki, N. T1 - Detection of defects in thin-walled structures by means of lamb waves N2 - In this paper the Scaled Boundary Finite Element Method (SBFEM) is applied for the simulation of Lamb waves in cracked plates. This method is highly advantageous to study the interaction of different Lamb wave modes with cracks as the crack is not discretized and no refinement is required around the crack tip. Numerical examples are presented for the reflection of the fundamental symmetric and antisymmetric modes from cracks of different depth. The spatial Fourier transformation is employed to calculate the amplitudes of reflected Lamb wave modes. The results reveal possibilities to obtain details of the crack geometry in non-destructive testing and structural health monitoring applications. T2 - International congress on ultrasonics CY - Gdansk, Poland DA - 05.09.2011 KW - Lamb waves KW - Scaled boundary finite element method KW - Simulation KW - Crack detection PY - 2012 SN - 978-0-7354-1019-0 DO - https://doi.org/10.1063/1.3703223 SN - 0094-243X N1 - Serientitel: AIP conference proceedings – Series title: AIP conference proceedings IS - 1433 SP - 443 EP - 446 PB - American Institute of Physics CY - Melville, NY AN - OPUS4-26203 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Prager, Jens A1 - Gravenkamp, Hauke A1 - Rahman, Mehbub-Ur A1 - Köppe, Enrico T1 - Einsatz geführter Wellen für die Ultraschallprüfung N2 - Der Einsatz geführter Wellen für die zerstörungsfreie Prüfung mit Ultraschall eröffnet neue Möglichkeiten, räumlich ausgedehnte Bauteile mit begrenzter Zugänglichkeit auf ihre Integrität zu prüfen und gewinnt daher zunehmend an Bedeutung. Dieser Artikel behandelt die physikalischen Grundlagen der Schallausbreitung. Deren Verständnis bildet die Grundlage für die Entwicklung geeigneter Prüfsysteme. An Beispielen werden verschiedene Möglichkeiten zur Simulation der Schallausbereitung vorgestellt. Aktuelle Lösungsansätze zur Prüfung von plattenförmigen Strukturen und von Rohrleitungen werden beschrieben, wobei besonders auf die Sensortechnik und die speziellen Anforderungen an die Prüfhardware eingegangen wird. ----------------------------------------------------------------------------------------------------------------------------------- Guided waves are widely used for non-destructive testing using ultrasound. Recently, the method has become increasingly important for integrity tests of spatially extended components with limited accessibility. This article discusses the basic physics of the sound propagation of guided waves. Their understanding forms the basis for the successful development of adapted inspection systems. Examples for simulating the wave propagation using different methods are presented. Current approaches for the inspection of plate-like structures and pipelines are described with focus on sensor technology and the specific requirement on the test hardware. KW - Zerstörungsfreie Prüfung KW - Geführte Wellen KW - Ultraschallprüfung KW - Non-destructive evaluation KW - Guided waves KW - Ultrasound PY - 2012 DO - https://doi.org/10.1524/teme.2012.0168 SN - 0340-837X SN - 0178-2312 SN - 0171-8096 VL - 79 IS - 5 SP - 251 EP - 261 PB - Oldenbourg CY - München AN - OPUS4-26206 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Gravenkamp, Hauke A1 - Man, H. A1 - Song, C. A1 - Prager, Jens T1 - The computation of dispersion relations for three-dimensional elastic waveguides using the scaled boundary finite element method N2 - In this paper, a numerical approach for the computation of dispersion relations for three-dimensional waveguides with arbitrary cross-section is proposed. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM). It is an extension of the approach previously derived for plate structures. It is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the Z matrix, which is well known in the SBFEM. The Hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives. The cross-section of the waveguide is discretized using higher-order spectral elements. It is discussed in detail how symmetry axes can be utilized to reduce computational costs. In order to sort the solutions at different frequencies, a mode-tracking algorithm is proposed, based on the Padé expansion. KW - Guided waves KW - Simulation KW - Dispersion KW - Scaled boundary finite element method PY - 2013 DO - https://doi.org/10.1016/j.jsv.2013.02.007 SN - 0022-460X SN - 1095-8568 VL - 332 IS - 15 SP - 3756 EP - 3771 PB - Academic Press CY - London AN - OPUS4-28837 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Saputra, A. A. A1 - Chongmin, Song T1 - Detection of defects in thin-walled structures by means of Lamb waves T2 - International Congress on Ultrasonics 2011 CY - Gdansk, Poland DA - 2011-09-05 PY - 2011 AN - OPUS4-24332 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Gravenkamp, Hauke A1 - Song, C. A1 - Prager, Jens T1 - Numerical computation of dispersion relations in wave guides N2 - In this paper a numerical approach, based on the Scaled Boundary Finite Element Method (SBFEM), is described to obtain dispersion relations for propagating modes in wave guides. While the formulation is developed for plate structures, it can easily be extended to wave guides with arbitrary cross-section. The cross-section is discretized in the Finite Element sense while all equations remain analytical in the direction of propagation. The wave numbers of all propagating modes are obtained as the solutions of a standard eigenvalue problem. The group velocities can be calculated accurately as the eigenvalue derivatives. The use of higher-order elements drastically increases the efficiency and accuracy of the computation. This approach can be used for wave guides with arbitrary distribution of material parameters. KW - Guided waves KW - Dispersion KW - Group velocity KW - Scaled boundary finite element method PY - 2012 DO - https://doi.org/10.1002/pamm.201210256 SN - 1617-7061 VL - 12 IS - 1 SP - 535 EP - 536 PB - Wiley-VCH Verl. CY - Weinheim AN - OPUS4-27750 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Saputra, A. A. A1 - Birk, C. A1 - Song, C. A1 - Gravenkamp, Hauke ED - Samali, ED - Attard, ED - Song, T1 - Numerical modelling of lamb waves in cracked plates using the scaled boundary finite element method T2 - ACMSM 22 - Australasian conference on the mechanics of structures and materials CY - Sydney, Australia DA - 2012-12-11 KW - Lamb waves KW - Scaled boundary finite element method KW - Crack detection KW - Continued fractions PY - 2013 SN - 978-0-415-63318-5 SP - 927 EP - 932 PB - Taylor & Francis AN - OPUS4-27751 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Man, H. A1 - Birk, C. A1 - Song, C. ED - Samali, ED - Attard, ED - Song, T1 - Numerical computation of dispersion relations in three-dimensional waveguides T2 - ACMSM 22 - Australasian conference on the mechanics of structures and materials CY - Sydney, Australia DA - 2012-12-11 KW - Guided waves KW - Dispersion KW - Scaled boundary finite element method KW - Non-destructive testing KW - Structural health monitoring PY - 2013 SN - 978-0-415-63318-5 SP - 897 EP - 902 PB - Taylor & Francis AN - OPUS4-27752 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Song, C. T1 - Numerical computation of dispersion relations in wave guides T2 - GAMM 2012, 83rd Annual Meeting of the International Association of Applied Mathematics and Mechanics CY - Darmstadt, Germany DA - 2012-03-26 PY - 2012 AN - OPUS4-26220 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke A1 - Prager, Jens A1 - Song, C. T1 - Numerische Berechnung der Dispersionseigenschaften von Lambwellen in Platten mit beliebiger Materialzusammensetzung T2 - DAGA 2012. 38. Jahrestagung für Akustik CY - Darmstadt, Germany DA - 2012-03-19 PY - 2012 AN - OPUS4-26221 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Subhani, M. A1 - Li, J. A1 - Gravenkamp, Hauke A1 - Samali, B. T1 - Effect of elastic modulus and Poisson's ratio on guided wave dispersion using transversely isotropic material modelling N2 - Timber poles are commonly used for telecommunication and power distribution networks, wharves or jetties, piling or as a substructure of short span bridges. Most of the available techniques currently used for non-destructive testing (NDT) of timber structures are based on one-dimensional wave theory. If it is essential to detect small sized damage, it becomes necessary to consider guided wave (GW) propagation as the behaviour of different propagating modes cannot be represented by one-dimensional approximations. However, due to the orthotropic material properties of timber, the modelling of guided waves can be complex. No analytical solution can be found for plotting dispersion curves for orthotropic thick cylindrical waveguides even though very few literatures can be found on the theory of GW for anisotropic cylindrical waveguide. In addition, purely numerical approaches are available for solving these curves. In this paper, dispersion curves for orthotropic cylinders are computed using the scaled boundary finite element method (SBFEM) and compared with an isotropic material model to indicate the importance of considering timber as an anisotropic material. Moreover, some simplification is made on orthotropic behaviour of timber to make it transversely isotropic due to the fact that, analytical approaches for transversely isotropic cylinder are widely available in the literature. Also, the applicability of considering timber as a transversely isotropic material is discussed. As an orthotropic material, most material testing results of timber found in the literature include 9 elastic constants (three elastic moduli and six Poisson's ratios), hence it is essential to select the appropriate material properties for transversely isotropic material which includes only 5 elastic constants. Therefore, comparison between orthotropic and transversely isotropic material model is also presented in this article to reveal the effect of elastic moduli and Poisson's ratios on dispersion curves. Based on this study, some suggestions are proposed on selecting the parameters from an orthotropic model to transversely isotropic condition. KW - Timber KW - Guided wave KW - Transversely isotropic material KW - Orthotropic material KW - Dispersion curves PY - 2013 DO - https://doi.org/10.4028/www.scientific.net/AMR.778.303 SN - 1022-6680 SN - 1662-8985 VL - 778 SP - 303 EP - 311 PB - Trans Tech Publ. CY - Zurich AN - OPUS4-29019 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke T1 - Scaled Boundary Finite Element Method zur Simulation geführter Ultraschallwellen T2 - IZFP Seminar 2013 CY - Saarbrücken, Germany DA - 2013-07-15 PY - 2013 AN - OPUS4-29001 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Gravenkamp, Hauke T1 - Numerische Methoden zur Simulation geführter Ultraschallwellen T2 - Doktorandenkolloquium des Institutes für Konstruktionstechnik der TU Braunschweig CY - Braunschweig, Germany DA - 2013-08-15 PY - 2013 AN - OPUS4-29002 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -