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Zur Messung von Konzentrationen in Flüssigkeiten können akustische Sensoren genutzt werden. Ziel der vorliegend Arbeit ist es einen Sensor zu entwerfen der sehr hohe Messgenauigkeiten erzielen kann. Der Sensor besteht aus einem rechteckigen Rohr, welches auf einem Halbraum angebracht ist. Die Konzentrationsbestimmung erfolgt anhand des Resonanzverhaltens der Struktur, wodurch eine hohe Messgenauigkeit erreicht werden kann. Um den Sensors zu verwirklichen, muss eine Optimierung der Geometrie mit vielen Iterationsschritten durchlaufen werden. Da keine analytische Beschreibung des akustischen Verhaltens vorliegt, wird eine effiziente Simulationsmethode benötigt. Die Scaled Boundary Finite Element Method (SBFEM) für prismatische Strukturen erscheint für die Simulation geeignet, da Teile der Geometrie ohne neue Vernetzung geändert werden können. Für die Berechnung des Sensors wird ein Modell der akustischen Fluid-Struktur Interaktion benötigt, das bisher nicht vorhanden ist.
Die Präsentation behandelt die Implementierung des Fluidmodells in die SBFEM und deren Validierung. Für die Validierung werden die Ergebnisse mit analytischen Beispielen ohne Fluid-Struktur Kopplung und mit Comsol-Ergebnissen der Dispersionskurven mit Wasser gefüllter Rohre verglichen.
Schließlich wird das neuartige Verfahren für die Modellierung der Sensorgeometrie angewendet. An einer einfachen Geometrie wird das Sensorprinzip zur Bestimmung der Salzkonzentration demonstriert.
The Scaled Boundary Finite Element Method (SBFEM) for prismatic structures is an efficient method for the simulation of acoustic behavior. Hence a further development of the method is of great interest. The wave propagation can be calculated for isotropic and anisotropic materials in solids. As for many applications the acoustic behavior in fluids and the behavior in case of fluid-structure interaction (FSI) is subject of research, the implementation of a fluid model in SBFEM for prismatic structures is needed. In case of FSI the coupling between fluid and solid domains can be performed without additional effort when describing both domains in the same variables. Hence a displacement-based fluid description is used. As the discretized formulation leads to spurious modes, a penalty method to suppress the unphysical behavior is chosen. To validate the derived model a comparison with analytical solutions of purely fluid domains is made. As to verify that in case of FSI the model shows the right behavior, dispersion curves of water-filled pipes are calculated and compared to results obtained with Comsol.
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.
Ultrasonic guided waves (UGW) have been shown to be suitable for non-destructive testing (NDT) and structural health monitoring (SHM) of many engineering structures. Development of a technique based on UGWs requires careful understanding obtained through modelling and analysis of wave propagation and mode-damage interaction due to their dispersion and multimodal character. This presentation will provide insights into the Scaled Boundary Finite Element Method and its applicability for tackling wave propagation problems. Features and limitations of the SBFEM will be presented on an example of a multi-layered plate structure consisting of isotropic and anisotropic materials bonded together. You will be guided through the process of picking up the wave modes for your application. Starting from the calculation of dispersion curves and mode shapes to the analysis of wave propagation and mode-damage interaction. The main highlight of the presentation lies in the ability to detect damage in a certain layer depending on the mode used. The resulting deeper understanding of the wave propagation in multi-layered structures is the key to further developments of NDT and SHM for engineering structures consisting of multiple layers.
In recent years carbon über polymers have become a popular light-weight substitute for high-weight materials such as steel. One advantage of carbon fiber polymers is the high strength-to-weight ratio, thus some popular application areas are weight sensitive such as aeronautics or automobiles. As these application areas are especially sensitive to material failure it is of significant interest to characterize material defects which may arise. In this talk we will propose a method to characterize material defects in carbon fiber reinforced polymers using gradient-based optimization methods. The procedure is based on the solution of an inverse problem where simulation data and experimental data is fitted. Here,
gradients of the simulation will be supplied by an Algorithmic Differentiation (AD) tool which greatly enhances the quality of the solution. Numerical examples will be provided.
Acoustic methods are ideally suited for determining the mechanical properties of different materials non-destructively. The availability of such methods is particularly important for fiber-reinforced polymers (FRPs) because their properties strongly depend on the manufacturing process and in-service conditions. Since FRPs are mostly used in thin-walled components, properties can be derived from the dispersion curves of ultrasonic guided waves (UGWs).
Our approach is based on an inverse procedure in which the numerically calcu-lated dispersion curves are fitted to the measured curves. The acquisition is done by applying a broadband piezoelectric transducer (PZT) to excite and a 3D laser Doppler vibrometer (3D LDV) to record the waves. Compared to the ap-proaches based on laser excitation, the PZT provides a better signal-to-noise ra-tio because more energy is brought into the structure. Whereas the 3D LDV compared to a 1D LDV or a PZT allows capturing in-plane and out-of-plane components and thus providing more dispersion information. Since the inverse procedure requires many iterations before elastic properties are retrieved, an ef-ficient tool for the calculation of the dispersion curves is necessary. For this, the Scaled Boundary Finite Element Method is used. All in all, a good agreement between theoretical and experimental curves is demonstrated.