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When modeling the propagation of elastic guided waves in plates or cylinders, Finite Element based numerical methods such as the Scaled Boundary Finite Element Method (SBFEM) or the Semi-Analytical Finite Element (SAFE) Method lead to an eigenvalue problem to be solved at each frequency. For the particular case of shear horizontal modes in a homogeneous plate or torsional modes in a homogeneous cylinder, the problem can be drastically simplified. The eigenvalues become simple functions of the frequency, while the eigenvectors are constant. The current contribution discusses how this behavior is represented in the numerical formulation and derives the expressions for the eigenvalues and eigenvectors as well as the dynamic stiffness matrix of infinite elastic waveguides.
Guided waves hold great potential for applications in the field of ultrasonic nondestructive testing. Examples of possible applications are the ultrasonic testing and structural health monitoring of wheelset-axles as used in trains. Depending on the particular type, these axles can be described as either thick cylindrical rods or thick walled hollow cylinders with varying thickness. Wheelset-axles are safety relevant components that have to be inspected on a regular basis. The use of guided waves would allow a full inspection while accessing only the front faces of the axle, thus potentially speeding up the inspection procedure. In order to develop such an inspection technique, however, detailed knowledge of wave propagation through the axle is required. Established mesh-based procedures, like the finite element method, could be used to simulate guided wave propagation in such structures. However, due to the size of the axle itself and the comparatively fine mesh that is dictated by the wavelengths usually applied in ultrasonic testing, these mesh-based procedures would be very expensive in terms of computation times. The multimodal approach seems to be a very promising alternative that can be expected to provide results significantly faster. The multimodal method uses the guided wave modes of a corresponding waveguide with a constant cross-section as basis in which the local sound field at any given position in a waveguide with varying thickness can be expressed. Thereby the numerical effort is reduced to solving the one dimensional differential equations that govern the evolution of the coefficients in the mode spectrum along the waveguide. Once the sound field has been calculated, a time dependence can easily be included, which allows the simulation of pulse propagation through the waveguide. In this thesis, the multimodal approach, as described for the calculation of Lamb-waves in plates with non-constant thickness, is extended to other types of elastic waveguides such as cylindrical rods and thick walled hollow cylinders. For the sake of simplicity, investigations are restricted to axially symmetric wave modes. The results obtained with the multimodal approach are validated against FEM-simulations. It is shown that the multimodal method potentially holds a great advantage in terms of computation time over commercially available software based on the finite element method. Finally, the multimodal method is evaluated with respect to possible future applications on wheelset-axles.
The application of waveguides for acoustic measuring technologies and the development of non-destructive evaluation techniques with guided ultrasonic waves for plate like materials like carbon fiber reinforced plastic shells and layered structures require a good understanding of acoustic wave propagation inside the material. The well-known Finite Element Method can be used for simulations, however at least for higher frequencies, the ratio of wavelength and geometrical dimension demands a time-consuming fine grid. Using commercial simulation tools the computational costs increase considerably for ultrasonic frequencies.
In the recent years, the Federal Institute for Materials Research and Testing has developed a very efficient alternative for simulating acoustic wave propagation particularly in wave guides by extending the Scaled Boundary Finite Element Method (SBFEM). The SBFEM as a semi-analytical method has one main advantage over the classical Finite Element Method: It only demands a discretization of the boundary instead of the whole domain. This is pictured in the figures below. The method is still related to the Finite Element Method and uses their well-known solving strategies. SBFEM is shown to be highly efficient, especially in the frequency domain. Additionally, the efficiency can be increased by using higher-order spectral elements. In plates and cylinders, the SBFEM can be used to animate propagating modes and computes their wavenumber.
In this contribution, we present a short introduction into the basics of SBFEM formulation of the dynamic elastic wave equation. The applicability and efficiency of the approach is demonstrated by applying the method to layered structures and different wave guide geometries. As one example we present the wave propagation in a typical adhesive joint of different metal sheets as common in new designs in automotive industry. The analysis comprises the computation of dispersion curves as starting point of every development of non-destructive testing techniques for inspecting such structures as well as the analysis of the propagating modes. Additional examples presented handle special cases for axis-symmetric geometries, such as pipes and cylindrical rods which are common in various acoustic measurement applications.
The use of composite materials has been steadily growing during the last decades, as well as the requirements on quality, mechanical properties and geometries of the parts. Some processes, like the 3D UV pultrusion process, manufacture parts that are long and thin, whilst having a varying curvature radius along the same part or even no curvature at all. Studying their mechanical properties along the main fiber direction, which is of foremost interest, is not an easy task nor efficient with most nondestructive methods. The use of air-coupled ultrasonics to evaluate the properties of composite materials has been widely proved by several authors, mainly using guided waves that provide information on the orthotropic properties of this kind of materials. Most of this work has focused on analyzing straight plate-like geometries, due to the simplicity to generate desired Lamb modes in the plate and analyze the behavior of guided waves inside the plate. In our contribution, the differences in the propagation of Lamb waves for straight and curved geometry glass fiber reinforced polymers (GFRP) have been analyzed. A GFRP test sample cured with UV light with one straight and one curved area has been evaluated. The responses of the generated Lamb wave modes for the straight and curved geometries have been compared, accounting for variations in the transducer characteristics, e.g. resonance behavior and focusing.
Understanding on how a machine learning model interprets data is a crucial step to verify its reliability and avoid overfitting. While the focus of the scientific community is nowadays orientated towards deep learning approaches, which are considered as black box approaches, this work presents a toolbox that is based on complementary methods of feature extraction and selection, where the classification decisions of the model are transparent and can be physically interpreted. On the example of guided wave benchmark data from the open guided waves platform, where delamination defects were simulated at multiple positions on a carbon fiber reinforced plastic plate under varying temperature conditions, the authors could identify suitable frequencies for further investigations and experiments. Furthermore, the authors presented a realistic validation scenario which ensures that the machine learning model learns global damage characteristics rather than position specific characteristics.
Understanding on how a machine learning model interprets data is a crucial step to verify its reliability and avoid overfitting. While the focus of the scientific community is nowadays orientated towards deep learning approaches, which are considered as black box approaches, this work presents a toolbox that is based on complementary methods of feature extraction and selection, where the classification decisions of the model are transparent and can be physically interpreted. On the example of guided wave benchmark data from the open guided waves platform, where delamination defects were simulated at multiple positions on a carbon fiber reinforced plastic plate under varying temperature conditions, the authors could identify suitable frequencies for further investigations and experiments. Furthermore, the authors presented a realistic validation scenario which ensures that the machine learning model learns global damage characteristics rather than position specific characteristics.
Um aus messtechnisch ermittelten Dispersionsabbildungen geführter Ultraschallwellen Rückschlüsse auf die Materialparameter zu ziehen, werden in der aktuellen Forschung verschiedene inverse Methoden diskutiert. Maschinelles Lernen und insbesondere Convolutional-Neural-Networks (CNNs) stellen eine Möglichkeit der automatisierten inversen Modellierung und Evaluierung von Bilddaten dar. In diesem Vortrag wird anhand synthetischer Daten gezeigt, wie das Ausbreitungsverhalten von geführten Ultraschallwellen unter Verwendung von CNNs genutzt werden kann, um die isotropen elastischen Konstanten einer plattenförmigen Struktur zu bestimmen.
An approach to adhesive bond characterisation using guided acoustic waves in multi-layered plates
(2021)
An approach for the non-destructive characterisation of adhesive bonds using guided ultrasonic waves is presented. Pulsed laser radiation is used to thermoacoustically excite broadband ultrasonic waves in a multi-layered sample, consisting of a metal plate adhesively joined to a polymeric layer using synthetic resin. The resulting signals are received by a purpose-built piezoelectric transducer. Varying the distance between excitation and detection yields spatio-temporal measurement data, from which the dispersive properties of the propagating waves can be inferred using a two-dimensional Fourier transform, assuming the plates to act as coupled waveguides. Coupled multi-layered waveguides show an effect referred to as mode repulsion, where the distance between certain modes in the frequency-wavenumber domain is assumed to be a measure of coupling strength. Measurements at different stages of curing of the adhesive layer are performed and evaluated. A comparison of the results shows changes in the dispersive properties, namely an increased modal bandwidth for the fully cured sample as well as an increased modal distance.
Understanding on how a machine learning model interprets data is a crucial step to verify its reliability and avoid overfitting. While the focus of the scientific community is nowadays orientated towards deep learning approaches, which are considered as black box approaches, this work presents a toolbox that is based on complementary methods of feature extraction and selection, where the classification decisions of the model are transparent and can be physically interpreted. On the example of guided wave benchmark data from the open guided waves platform, where delamination defects were simulated at multiple positions on a carbon fiber reinforced plastic plate under varying temperature conditions, the authors could identify suitable frequencies for further investigations and experiments. Furthermore, the authors presented a realistic validation scenario which ensures that the machine learning model learns global damage characteristics rather than position specific characteristics.
This presentation shows how the dispersive behavior of ultrasonic guided waves in isotropic materials can be used by means of Convolutional Neural Networks to determine the elastic parameters. For this purpose, the preprocessing, the training, the chosen architecture and the results are evaluated on the basis synthetic image data. This presentation was given at the SMSI 2021.