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Eingeladener Vortrag
- nein (22)
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.
Numerical modelling of lamb waves in cracked plates using the scaled boundary finite element method
(2013)
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.
In the field of guided waves for non-destructive testing, the interaction of these waves with damages or other discontinuities in a structure is critical. When a guided wave mode travels and hits a defect, it scatters in all directions, converting to other modes and reflecting the existing one. These interactions are captured in scattered far field complex amplitudes. The amplitudes are stored in scattering matrices, which characterise the elastodynamic behaviour of a defect completely. Scattering matrices are also useful to simulate backpropagation from a defect using ray-tracing methods.
Simulating these interactions is challenging, and analytical solutions only exist for simple geometries. Still, using general tools like the finite element method results in large, usually costly models. Recently, researchers proposed a method based on a numerical implementation of the Kirchhoff–Helmholtz integral that allows the computation of the scattering matrices using a model containing only the damaged region. However, classical methods to resolve the far field and low-order elements were used, leading to large models yet more efficient than using other techniques.
We propose using the SBFEM as an alternative to enhance the computation of the far field scattering. The damaged region is discretised using high-order polyhedral elements, while the far field is constructed using a modified version of the SBFEM. Examples compared to the literature demonstrate the validity of the approach.
We introduce a novel approach that combines the scaled boundary finite element method (SBFEM) with a mortar coupling to enhance the computational modelling of elastic wave propagation and interaction with local features in the ultrasonic range. The key objective is to achieve decoupling between different regions of interest, enabling independent meshes for the zones where waves either propagate or interact with localised discontinuities in the elastic media. This decoupling allows us to exploit the benefits offered by various SBFEM formulations. Thus, we can select the most suitable solution for each specific region. An important concept we emphasise is the differentiation between the near field and far field regions. The near field encompasses zones where the precise representation of small features compared to the wavelength is crucial. At the same time, the far field comprises homogeneous regions where the waves propagate without interactions, eventually radiating towards infinity if the domain is unbounded. By separating these two zones, we can improve the computational performance by employing finer discretisation only where necessary. Furthermore, this decoupling enables the reuse of far field models in parametric analyses, making it highly valuable for scenarios focused particularly on local elastic wave interactions. This approach offers considerable potential in such cases. The modelling technique is validated, and its potential is demonstrated through practical applications.
This paper presents a mode-tracing approach for elastic guided waves based on analytically computed derivatives and includes a study of interesting phenomena in the dispersion curve representation. Numerical simulation is done by means of the Scaled Boundary Finite Element Method (SBFEM). Two approaches are used to identify the characteristics of the resulting wave modes: Taylor approximation and Padé approximation. Higher order differentials of the underlying eigenvalue problem are the basis for these approaches. Remarkable phenomena in potentially critical frequency regions are identified and the tracing approach is adapted to these regions. Additionally, a stabilization of the solution process is suggested.
The modeling of waveguides by means of the Scaled Boundary Finite Element Method (SBFEM) has recently been addressed and is considered an effective procedure for the simulation of ultrasonic guided waves in plates and uniform structures, as well as their interaction with defects. This work presents the extension of the known applications like uniform concrete foundation cylinders to structures with more complex shapes and defects. The main focus is the required modeling of 3-D structures in SBFEM to solve these efficiently. Furthermore the coupling of different models is discussed. This involves models like a mainly uniform foundation cylinder with varying material behavior or geometry in certain areas which has to be modeled in 3-D SBFEM. With the presentation of numerical examples the accuracy and performance of the modeling is discussed and the advantages in improving numerical stability are shown.
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 the achievable accuracy is given.
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.
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.