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Acoustic-structure interaction in the scaled boundary finite element method for primsatic geometries
(2019)
Due to the short wavelength compared to the dimensions of the structure, the simulation of ultrasonic waves is still a challenging task. A numerical method well suited for this purpose is the semi-analytical Scaled Boundary Finite Element Method (SBFEM). When applying this method, only the boundary of a computational domain is discretized using finite elements, while the interior is described by an analytical ansatz. Hence, the number of degrees of freedom is reduced significantly compared to the classical Finite Element Method (FEM).
In recent years, a particular formulation of the SBFEM for the simulation of ultrasonic guided waves was developed. The method constitutes an efficient algorithm for prismatic structures of arbitrary length, such as plates, pipes, or beams. Wave propagation phenomena in such structures can be modeled for isotropic and anisotropic inhomogeneous waveguides. Even though the method is an efficient tool for the simulation of guided waves in solid media, a reliable model for the simulation of acoustic wave propagation in fluids as well as acoustic-structure interaction in terms of SBFEM is still missing. In principle, the fluid can be described by a displacement-based formulation and thus be implemented in existing SBFEM algorithms for solid bodies. However, due to the discretization with classical finite elements, spurious modes occur, which cannot be separated from the physical modes straightforwardly. The spurious modes can be suppressed using a penalty parameter. Although very accurate results were achieved for some problems, this procedure has been proven unreliable for certain cases.
For this reason, we propose a different approach in this contribution. We employ a pressure model to simulate the acoustic behavior of fluids. The implementation of the pressure model results in a higher effort due to the necessity of incorporating coupling terms, but it presents a stable alternative without spurious modes. The accuracy of the method is demonstrated in comparison with analytical solutions and results obtained using the FEM.
Geführte Ultraschallwellen sind für die Materialcharakterisierung hervorragend geeignet, da ihr Ausbreitungsverhalten abhängig von den Materialeigenschaften des untersuchten Werkstoffs ist.
Um aus dem messtechnisch ermittelten Ausbreitungsverhalten geführter Ultraschallwellen Rückschlüsse auf die Materialparameter zu ziehen, werden in der aktuellen Forschung verschiedene inverse Methoden diskutiert. Dispersionsabbildungen im Frequenz-Wellenzahl-Bereich repräsentieren das Ausbreitungsverhalten geführter Ultraschallwellen. Maschinelles Lernen und insbesondere Convolutional-Neural-Networks (CNNs) sind eine Möglichkeit der automatisierten inversen Bestimmung der Materialparameter aus den Dispersionsabbildungen.
In diesem Beitrag wird anhand synthetischer Daten gezeigt, wie das Ausbreitungsverhalten von geführten Ultraschallwellen unter Verwendung von CNNs und Dispersionsabbildungen genutzt werden kann, um die elastischen Konstanten einer isotropen plattenförmigen Struktur zu bestimmen. Anhand dieses Beispiels wird das generelle Vorgehen zur Anwendung maschineller neuronaler Lernverfahren aufgezeigt. Hierfür werden die verwendeten Daten analysiert, das Preprocessing erläutert und eine einfache CNN-Architektur gewählt. Im Rahmen der Auswertung wird insbesondere Wert auf die Erklärbarkeit und Zuverlässigkeit des verwendeten CNNs gelegt und so Grenzen und Möglichkeiten aufgezeigt.
The application of composite overwrapped pressure vessels (COPV) to store hydrogen and other compressed gases, especially when operating at high pressures, imposed the need for an innovative and reliable approach to ensure the safe operation of the system. Continuous structural health monitoring (SHM) based on ultrasonic guided waves (GWs) is a promising approach due to the ability of the wave to propagate for long distances and go around complex structures, moreover the high sensitivity to various failure modes such as delamination, matrix cracking and debonding. In this study, we scrutinize the behavior of (GWs) within the COPV using a network of PZT elements that are used for excitation and sensing. A laser doppler vibrometer (LDV) was also used to scan the surface of the vessel in various directions. L(0,1) and L(0,2) were observed in the captured signal. The L(0,2) appeared to be a dominant mode in the COPV and was capable of propagating along the entire length and maintaining a good signal-to-noise ratio. The L(0,2) mode maintained the same phase velocity when it is captured at various excitation angles (0, 45, and 90 degrees). The reduced effect of the orthotropy of the materials on the propagating waves is an important result as it will reduce the complexity in data processing when performing damage identification.
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.