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This paper presents an automatic damage imaging technique by employing a signal processing approach based on applying hierarchically clustered filters across different domains. The technique involves time-frequency-wavenumber filter banks which are applied sequentially to ultrasonic guided wave (UGW) data. The study is conducted for a single lap joint composite specimen with a special focus on small voids which were formed due to manual adhesive component mixing. UGW data are acquired with a 3D Scanning Laser Doppler Vibrometer (LDV) over the scan area of the bonded plate. UGWs are excited at the central frequency of 100 kHz by a single piezoelectric transducer mounted on the surface of the single plate. Within each domain of time, frequency, and wavenumber, four filters are designed which results in 64 distinct filtered wavefields. From each filtered wavefield, an image is obtained by using root-mean-square (RMS) calculation of the signals. The obtained results are then combined to create a final, improved-resolution image of the scan area. The final image is compared to the image obtained through RMS calculation of full wavefield with interpolation through Delaunay triangulation and the image obtained by X-ray radiography. The results show that the smallest void that could be detected has a diameter of 2.14 mm.
Wavefield measurements by a scanning laser Doppler vibrometer are generally carried out in a cartesian coordinate. As a piezoelectric transducer generates Lamb waves following radial paths, the use of a polar coordinate can be a suitable alternative to the use of a cartesian coordinate. Therefore, in the proposed method, using a single transducer placed on the center of the specimen, the measured wavefields are transformed into polar coordinates, making several identical radial line inspections from the center in a direction of incident waves. Taking advantage of the properties of the polar coordinates, a signal processing technique is proposed through a frequency-wavenumber filtering process in these coordinates. In this technique, by using proper filters, unwanted wave modes of the incident wave along with all reflected waves are filtered out. In addition, the conventional features of RMS and Euclidean distance are adapted for the polar coordinate system to image the bonded plate. The proposed signal processing and damage imaging are first introduced through a numerical simulation. Then, the performance of the proposed technique is presented by experimental measurements of two specimens including adhesively bonded carbon fiber-reinforced plastic composite plates and bonded aluminum plates.
In plate-like structures, ultrasonic waves propagate as Lamb waves. Their use is important for many applications from non-destructive testing to structural health monitoring. Efficient simulation tools contribute to a significant value add e.g. in designing systems for these applications. Under which conditions an acceptable accuracy of these models with affordable computational costs can be achieved is an open question. Many of these applications include the usage of a plane wavefront, simulated in 2D crossesctional models to reduce complexity. In this contribution, a comparative case study between simulations and experiments is presented. The aim is to verify and compare a 2D cross-sectional model with experimental data. The experimental setup for this case study consists of an aluminum plate. A rectangular piezoelectric transducer is mounted for guided wave excitation. A laser Doppler vibrometer (LDV) measures out-of-plane velocities on the plate. A 2D cross-sectional model based on the Scaled Boundary Finite Element Method (SBFEM) is used to simulate the wave propagation of the experimental setup. The first data points near the transducer are used to fit the excitation tractions of the model, while additional points further away from the source are used to validate the model. The comparison between the recorded measurements and the simulated velocities shows a high degree of compatibility.
The simulation of ultrasonic waves in a linearly elastic body can be computationally intensive. The reason is the relatively short wavelength compared to the body size for high frequencies. One possible approach to counteract the high computational costs is to decompose the domain into small parts and strive for parallelization. The Mortar Method is a well-established approach for domain decomposition.
A rather new approach to discretize the emerging subdomains is the Scaled Boundary Finite Element Method. This semi-analytical method has many attractive properties. Some of these properties are listed subsequently. The grid consists of polygonal elements, which leaves much freedom in the meshing process. A variety of material distributions, including anisotropic materials, can be considered. High-order shape functions can be used for optimal convergence properties. The approach treats singularities at crack tips and corners analytically. Especially in the frequency domain, the Scaled Boundary Finite Element Method reduces the dimension of the approximation because only degrees of freedom which are associated with the boundary of a polygonal element are necessary. Those desirable properties make the method particularly suitable for calculating the dynamic responses in bodies with cracks, as it is essential for many non-destructive testing and structural health monitoring applications.
In this contribution, we present a combination of the Scaled Boundary Finite Element Method with the Mortar Method in two dimensions. The presentation starts with a theoretical overview of both approaches. Subsequently, numerical examples demonstrate the stability of the combination for the polygonal boundary of the elements. The numerical examples increase in complexity and are compared to results computed on non-divided domains with the Finite Element Method.
Eine zentrale Aufgabe der zerstörungsfreien Prüfung und der Strukturüberwachung (engl. Structural Health Monitoring - SHM) mit Ultraschallwellen ist die Bewertung von Schäden in Bauteilen. In vielen Bauteilen, wie zum Beispiel platten- und schalenförmigen Strukturen, Rohrleitungen oder Laminaten, breitet sich der Ultraschall in Form geführter Wellen aus. Zwar haben geführte Wellen eine relativ große Reichweite innerhalb des Bauteils und ermöglichen so eine großflächige Prüfung, ihre multimodalen und dispersiven Eigenschaften erschweren jedoch die Analyse der vom Schaden kommenden Reflexionen. Eine Möglichkeit, die Messsignale zu interpretieren und die Schäden zu charakterisieren, ist deren Vergleich mit der Wellenausbreitung in einem digitalen Modell. Hierbei stellt sich die Aufgabe, den Schaden im digitalen Modell anhand der Messdaten zu rekonstruieren. Diese Rekonstruktion beschreibt ein inverses Problem, das mehrere Vorwärtsrechnungen braucht, um das Schadensmodell an die Messdaten anzupassen.Durch die kleine Wellenlänge von Ultraschallwellen sind klassische Vorwärtsmethoden wie die Finte Elemente Methode rechenintensiv, weshalb die Autoren die semi-analytische Scaled Boundary Finite Element Method (SBFEM) benutzen, um den Rechenaufwand zu verringern. Im Beitrag wird ein inverses Verfahren basierend auf dem Automatischen Differenzieren in Kombination mit der SBFEM vorgestellt und an verschiedenen Schadenstypen in 2D-Querschnittmodellen von Wellenleitern getestet. In der präsentierten Vorstudie werden dafür „Messdaten“ aus unabhängigen Simulationen verwendet.
In der Zerstörungsfreien Prüfung und der Zustandsüberwachung sind geführte Wellen von großem Interesse, um Fehlstellen zu finden und zu charakterisieren. Die Interaktion der Wellen mit den Fehlstellen kann dabei aufgrund ihrer Komplexität häufig nicht analytisch beschrieben werden. Dies macht numerische Programme neben Experimenten unabdingbar. Aufgrund der kleinen Wellenlänge im Verhältnis zur Bauteilgröße ist jedoch eine effiziente Simulation noch immer Teil der aktiven Forschung.
Um die Effizienz der Simulationsalgorithmen zu steigern, ist es möglich, analytische Annahmen in die Finite Elemente Methode (FEM) zu integrieren. Beispiele für solche Methoden sind die Scaled Boundary Finite Element Method als ein semi-analytisches Verfahren und eXtended Finite Element Method. Diese beiden Möglichkeiten erlauben es, die Wechselwirkungen effizient zu simulieren.
In diesem Beitrag werden verschiedene Wechselwirkungen und Auswertungsmöglichkeiten von geführten Wellen mit Fehlstellen vorgestellt. Hierbei liegt der Fokus auf linearen und nicht-linearen Effekten. Zunächst wird auf Modenkonversion eingegangen und der Frage nachgegangen, ob diese ausreicht, um einen Riss zu charakterisieren. Diese Untersuchungen motivieren dann ein inverses Verfahren, mit dem einige Parameter eines simulierten Risses in einer Folge von Simulationen wieder rekonstruiert werden. Ein zweiter Teil beschäftigt sich mit nicht-linearen Risseffekten. Diese Risseffekte erzeugen im allgemeinen höhere harmonische Wellen. Hier werden Ergebnisse und Filtermethoden zur Auswertung vorgestellt.
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.