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Many modern ultrasonic methods in the fields of Non-Destructive Testing (NDT) and Structural Health Monitoring (SHM) require simulations in research. Researchers either use simulation data initially during development to investigate certain aspects, or the simulation process is directly part of the research task. Examples of the second case are inverse methods for parameter estimation, model-assisted probability of detection analysis or the generation of training data for AI algorithms. All these applications require algorithms that are as efficient as possible. For methods based on explicit time-step methods, a significant increase in efficiency can be achieved if a so-called lumped mass matrix can be used, which approximates the consistent mass matrix but is easier to invert.
The finite element method has been the subject of many studies on approximations of the mass matrix. In contrast, the lumped mass matrix in the context of the Scaled Boundary Finite Element Method (SBFEM) is a current field of research [1,2]. In the time domain, the semi-analytical SBFEM is notable for its flexibility to be applied to polygonal meshes. In particular, image-based mesh generation using a quadtree algorithm is possible. In general, polygonal meshes have the same flexibility as triangular meshes, but polygonal meshes can have additional advantages such as greater tolerance to distortion.
In this contribution, the SBFEM formulation based on bubble functions [3] for the time domain is presented for two-dimensional elastic waves. The adjustments necessary for a good approximating lumped mass matrix are emphasized. Several grid generation methods for polygonal elements are shown. Figure 1 depicts the difference between the consistent mass matrix and the lumped mass matrix for a normal polygonal mesh. Finally, the accuracy of mass lumping for linear, quadratic and cubic shape functions is presented and the computational efficiency is demonstrated using exemplary waveguide geometries.
This article presents a method to use the dispersive behavior of ultrasonic guided waves and neural networks to determine the isotropic elastic constants of plate-like structures through dispersion images. Therefore, two different architectures are compared: one using convolutions and transfer learning based on the EfficientNetB7 and a Vision Transformer-like approach. To accomplish this, simulated and measured dispersion images are generated, where the first is applied to design, train, and validate and the second to test the neural networks. During the training of the neural networks, distinct data augmentation layers are employed to introduce artifacts appearing in measurement data into the simulated data. The neural networks can extrapolate from simulated to measured data using these layers. The trained neural networks are assessed using dispersion images from seven known material samples. Multiple variations of the measured dispersion images are tested to guarantee the prediction stability. The study demonstrates that neural networks can learn to predict the isotropic elastic constants from measured dispersion images using only simulated dispersion images for training and validation without needing an initial guess or manual feature extraction, independent of the measurement setup. Furthermore, the suitability of the different architectures for generating information from dispersion images in general is discussed.
Defect reconstruction is essential in non-destructive testing and structural health monitoring with guided ultrasonic waves. This paper presents an algorithm for reconstructing notches in steel plates, which can be seen as artificial defects representing cracks by comparing measured results with those from a simulation model. The model contains a parameterized notch, and its geometrical parameters are to be reconstructed. While the algorithm is formulated and presented in a general notation, a special case of guided wave propagation is used to investigate one of the simplest possible simulation models that discretizes only the cross section of the steel plate. An efficient simulation model of the plate cross section is obtained by the semi-analytical scaled boundary finite element method. The reconstruction algorithm applied is gradient-based, and algorithmic differentiation calculates the gradient. The dedicated experimental setup excites nearly plane wave fronts propagating orthogonal to the notch. A scanning laser Doppler vibrometer records the velocity field at certain points on the plate surface as input to the reconstruction algorithm. Using two plates with notches of different depths, it is demonstrated that accurate geometry reconstruction is possible.
Das Ausbreitungsverhalten geführter Ultraschallwellen ermöglicht die großflächige Prüfung von Platten und schalenförmigen Bauteilen wie Rohren und Laminaten auf Fehlstellen von wenigen Prüfpunkten aus. Während die beschränkte Divergenz der geführten Wellen die Ultraschallprüfung begünstigt, erschwert das dispersive und multimodale Verhalten der Lamb-Wellen die Auswertung der Ultraschallsignale. Die dispersive und multimodale Wellenausbreitung verkompliziert die Bestimmung der Fehlerposition bei der Auswertung der Geschwindigkeiten einzelner Wellenpakete. Zudem ist es herausfordernd, einen einfachen Zusammenhang zwischen den Reflexionen der Fehlstelle und deren Größe und Form herzustellen. Eine Möglichkeit zur genauen Bestimmung der Fehlerposition und -geometrie bietet der direkte Vergleich der Messsignale mit den Signalen aus einem Simulationsmodell. Die Nachbildung des Schadens im Simulationsmodell stellt ein inverses Problem dar, das iterativ gelöst werden kann, indem ein Vorwärtsmodell immer weiter optimiert wird. Klassische Ansätze wie die Finite Elemente Methode (FEM) sind für die Simulation von Ultraschallwellen aufgrund der kleinen Wellenlängen im Vergleich zur Bauteilgröße meist ineffizient. Aus diesem Grund basiert das vorgestellte Vorwärtsmodell auf der semi-analytischen Scaled Boundary Finite Element Method (SBFEM), die große Teile der Wellenausbreitung analytisch berechnet. In diesem Beitrag wird die Validierung des zweidimensionalen Modells an Platten mit einer rechteckigen Nut als Ersatzfehler präsentiert und es werden erste Schritte zur Validierung von 3D-Modellen vorgestellt.
Das Ausbreitungsverhalten geführter Ultraschallwellen ermöglicht die großflächige Prüfung von Platten und schalenförmigen Bauteilen wie Rohren und Laminaten auf Fehlstellen von wenigen Prüfpunkten aus. Während die beschränkte Divergenz der geführten Wellen die Ultraschallprüfung begünstigt, erschwert das dispersive und multimodale Verhalten der Lamb-Wellen die Auswertung der Ultraschallsignale. Die dispersive und multimodale Wellenausbreitung verkompliziert die Bestimmung der Fehlerposition bei der Auswertung der Geschwindigkeiten einzelner Wellenpakete. Zudem ist es herausfordernd, einen einfachen Zusammenhang zwischen den Reflexionen der Fehlstelle und deren Größe und Form herzustellen. Eine Möglichkeit zur genauen Bestimmung der Fehlerposition und -geometrie bietet der direkte Vergleich der Messsignale mit den Signalen aus einem Simulationsmodell. Die Nachbildung des Schadens im Simulationsmodell stellt ein inverses Problem dar, das iterativ gelöst werden kann, indem ein Vorwärtsmodell immer weiter optimiert wird. Klassische Ansätze wie die Finite Elemente Methode (FEM) sind für die Simulation von Ultraschallwellen aufgrund der kleinen Wellenlängen im Vergleich zur Bauteilgröße meist ineffizient. Aus diesem Grund basiert das vorgestellte Vorwärtsmodell auf der semi-analytischen Scaled Boundary Finite Element Method (SBFEM), die große Teile der Wellenausbreitung analytisch berechnet. In diesem Beitrag wird die Validierung des zweidimensionalen Modells an Platten mit einer rechteckigen Nut als Ersatzfehler präsentiert und es werden erste Schritte zur Validierung von 3D-Modellen vorgestellt.
Adhesively bonded composite joints can develop voids and porosity during fabrication, leading to stress concentration and a reduced load-carrying capacity. Hence, adhesive porosity analysis during the fabrication is crucial to ensure the required quality and reliability. Ultrasonic-guided wave (UGW)-based techniques without advanced signal processing often provide low-resolution imaging and can be ineffective for detecting small-size defects. This article proposes a damage imaging process for adhesive porosity analysis of bonded composite plates using UGWs measured by scanning laser Doppler vibrometer (LDV). To implement this approach, a piezoelectric transducer is mounted on the composite joint specimen to generate UGWs, which are measured over a densely sampled area. The signals obtained from the scan are processed using the proposed signal processing in different domains. Through the utilization of filter banks in frequency and wavenumber domains, along with the root-mean-square calculation of filtered signals, damage images of the adhesive region are obtained. It has been observed that different filters provide information related to different void sizes. Combining all the images reconstructed by filters, a final image is obtained which contains damages of various sizes. The images obtained by the proposed method are verified by radiography results and the porosity analysis is presented. The results indicate that the proposed methodology can detect the pores with the smallest detectable pore area of 2.41 mm^2, corresponding to a radius of 0.88 mm, with an overall tendency to overestimate the pore size by an average of 11%.
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.
The dispersive properties of Lamb waves can be utilised for material characterisation because the frequency-wavenumber-relationship, as well as the group velocity, depend on material parameters. These dependencies make a non-destructive estimation of an elastic constant possible. This preliminary study investigates the sensitivity of dispersion curves caused by a change in elastic constants. The Scaled Boundary Finite Element Method is used to compute special dispersion curves, which show the sensitivity value of the frequency and group velocity as a colour value. This representation allows for easy identification of patterns and local effects. Two sets of dispersion curves are presented, one set for a steel plate and the other set for a plate made of a carbon fibre reinforced polymer. In general, we notice that the sensitivity often increases with the frequency and that higher-order modes seem to be more suitable for material characterisation. Moreover, specific modes respond to material changes while others are relatively unaffected, which must be taken into consideration for material characterisation.
Die Messung von Flüssigkeitskonzentrationen in Rohrsystemen ist von großem Interesse für viele unterschiedliche Anwendungen. Die meisten Messsysteme sind jedoch nicht in der Lage, die Flüssigkeit direkt im Rohr zu untersuchen und es muss eine zusätzliche Vorrichtung, wie z.B. einem Bypass, angebracht werden, welche den Kontakt zwischen Flüssigkeit und Sensor ermöglicht.
Um den Einbauaufwand gering zu halten und die Strömungseigenschaften des Rohres nicht zu beeinflussen, wird ein neuartiges Messsystem entwickelt, welches als Teil der Rohrwand ausgeführt werden kann. Dieses neuartige System ist angelehnt an die Idee der phononischen Kristallen (PnK). PnK’s bestehen im Allgemeinen aus einem Matrixmaterial, in welchem Streuzentren periodisch angeordnet sind. Dies führt beim Eintreffen einer akustischen Welle in definierten Frequenz-bereichen, sogenannter Bandlücken, zu zunehmender destruktiven Interferenz. Wird innerhalb einer solchen Bandlücke durch Einbringen einer flüssigkeitsgefüllten Kavität ein Resonanzverhalten erzeugt, kann dies genutzt werden, um die Flüssigkeit zu analysieren.
Im Rahmen von Voruntersuchung wird zunächst das akustische Verhalten des PnK’s, welcher für die Sensorentwicklung genutzt werden soll, unter Vernachlässigung der Flüssigkeit ausführlich untersucht. Hierbei werden zunächst die Bandlücken ermittelt und das Übertragungsverhalten betrachtet. Dieses wird im Anschluss experimentell überprüft.
The Scaled Boundary Finite Element Method (SBFEM) is a semi-analytical method that shows promising results in modelling of guided ultrasonic waves. Efficiency and low computational cost of the method are achieved by a discretisation of the boundary of a computational domain only, whereas for the domain itself the analytical solution is used. By means of the SBFEM different types of defects, e.g. cracks, pores, delamination, corrosion, integrated into a structure consisting of anisotropic and isotropic materials can be modelled.
In this contribution, the SBFEM is used to analyse the propagation of guided waves in a structure consisting of an isotropic metal bonded to anisotropic carbon fibre reinforced material. The method allows appropriate wave types (modes) to be identified and to analyse their interaction with different defects. Results obtained are used to develop a structural health monitoring system for composite pressure vessels used in automotive and aerospace industries.