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Leichtbaustrukturen kommen in vielen Branchen und Bereichen zum Einsatz. Vor allem der Fahrzeugbau sowie die Luft- und Raumfahrt profitieren von dem geringen Materialeinsatz und der Einsparung in der Nutzungsphase. Neben den genannten Potenzialen bieten Leichtbaustrukturen die Möglichkeit, gezielt eine hohe Dämpfung von Vibrationen bei geringem Materialeinsatz zu kombinieren. In diesem Zusammenhang werden häufig sog. Sandwichstrukturen verwendet. Die Sandwichstrukturen bestehen in der Regel aus kraftaufnehmenden Deckschichten und weicheren Kernschichten aus einer Wabenstruktur oder Vollmaterial aus Kunststoffen. Letztere übernehmen häufig die Aufgabe der Dämpfung.
In diesem Beitrag wird die Dämpfung einer ebenen Sandwichstruktur bestehend aus einer metallischen Deckschicht und einer viskoelastischen Polymerschicht untersucht. Die Herausforderung liegt in der physikalischen Modellierung der Materialdämpfung sowie der Übertragung der experimentell gewonnenen Daten in ein Finite-Elemente Simulationsmodell. Hierzu werden bestehende Methoden der Dämpfungsidentifikation evaluiert. Anschließend wird die Struktur mithilfe einer experimentellen Schwingungsanalyse unter vorgegebenen Randbedingungen analysiert. Aus den gewonnenen Messdaten werden Parameter ermittelt, um ein frequenzabhängiges Materialmodell zu generieren. Neben dem Vergleich der experimentellen und berechneten Ergebnisse liegt der Schwerpunkt dieses Beitrags auf der Betrachtung von Unsicherheiten während des Prozesses.
When considering noise propagation in flow in frequency domain computations, the standard Helmholtz equation is not sufficient to describe these effects. Therefore, using the linearized Euler equations (LEE) is common practice to describe sound propagation based on displacement perturbation. Galbrun reformulated the LEE in terms of an arbitrary Eulerian-Lagrangian description, which resulted in the displacement based Galbrun equation. This equation can also be formulated in terms of pressure and displacements.
We want to include sources (monopoles, dipoles and quadrupoles) in the harmonic analysis of Galbrun equation when a volume flow is present. In a first step we will solve Galbrun equation considering a volume flow. The velocity field is obtained in a CFD computation. Afterwards, the sources will be included in the acoustic computations as well.
Preliminary computational results are discussed and implications for future directions of research are addressed.
Transfer path analysis (TPA) is a proven method for identifying critical structure-borne and airborne sound paths. The basic idea is to divide the overall system into an exciting active component (source) and a passive component, e.g. the mechanical structure to be investigated, with their respective measurement points. By separating them, two independent systems are created, whereby on one hand, the excitation behaviour can be characterised and on the other hand, the transmission behaviour can be assessed. Finally, both systems are validated by comparing them to each other and deciding whether changes to source or structure are required or not. The advantage is the simple description of the source as a black box without complex modelling. In this contribution, this systematic is applied to window regulator systems as they are found in vehicles. The focus is on a hybrid approach between experimental and numerical transfer path analysis. For this purpose, the basic workflow of suitable TPA methods is discussed. This includes the operational measurement of different exciting electric motors variants, the determination of the transfer functions of the structure, the calculation of the contact forces and the analysis of the individual transfer paths.
A main research topic in acoustics is the reduction of indoor noise, which has increasingly received attention in recent years. A commonly used solution to solve these problems is reducing noise using damping structures, which absorb sound. This work aims at the numerical optimization of damping structures in interior problems, following three goals. First, the optimal damping structure for the required frequency range has to be determined. Second, the optimal position of the damping material has to be found. Third, we are focusing on lightweight design, which means that the amount of damping material used, has to be kept to a minimum. We present the implementation of a genetic algorithm into our open source code, which we use to optimize the damping behaviour and in consequence, the sound propagation for interior problems. We show an example of the application of this code.
Einfluss der absorbierenden akustischen Leistung auf die Eigenschaften von Resonanzfrequenzen
(2021)
Versatile model order reduction techniques for the reduction of dynamic systems have been presented in the last decades. Krylov subspace based methods are considered as efficient in terms of computational effort and reduction order and can be used in order to match the transfer function locally. However, they lack of a simple and efficient automatisation and error estimation. On the other hand, modal reduction is popular because it leads to exactly matching eigenfrequencies. The static behaviour and the overall accuracy of the frequency response, though, are poor. In this paper, a combination of both methods is presented and discussed.
In order to characterise a method for the reduction of mechanical models for the simulation of machine tools and similar mechatronic systems, first, the requirements on the model reduction method are derived. Criteria for the relative error of the frequency response function, the transmission zeros, and the poles are defined and the idea of defining a frequency range of interest is established.
Subsequently, a combination of Krylov and modal subspaces for the reduction of dynamic systems with second-order structure and proportional damping is presented. It is shown that the combination of the bases of the two methods leads to a combination of the advantages and an elimination of the drawbacks of them both. Moreover, an estimation for the upper bound of the defined error criteria is developed and verified with numerical results.
The result of this paper is an a priori parametrisable and numerically efficient model reduction method, which leads to reduced systems of low order with a definable error limit within a definable frequency range.
In this article, we compare the finite element solution of the pressure and the displacement formulations for the acoustic problem in the frequency domain. The Helmholtz differential equation is solved for both, the spectral and the source problems, and each of these is formulated in terms of pressure and displacement. The pressure formulation allows to use standard Lagrangian elements whereas Raviart–Thomas elements are applied for the displacement formulation. Both formulations are tested in several examples. It is shown that Raviart–Thomas elements account for a reasonable alternative to Lagrangian elements in some cases.
In der vorliegenden Arbeit wird ein Programmcode zur numerischen Modalanalyse dreidimensionaler Fluide in komplexen akustischen Systemen, speziell in Resonatoren, entwickelt. Mit diesem Code ist es möglich, turbulente Strömungen im Rahmen der Modalanalyse zu berücksichtigen. Hierzu wird ein realistisches Strömungsprofil, ermittelt mithilfe eines 3D-Navier-Stokes-Lösers, verwendet. Der Hauptteil der Arbeit befasst sich mit der Herleitung der für die Berechnung notwendigen Galbrun-Gleichung und deren Aufbereitung zur numerischen Analyse. Für die numerische Umsetzung kommt die Methode der finiten Elemente in Verbindung mit komplex konjugierten, infiniten Astley-Leis Elementen zur Anwendung. Die infiniten Elemente werden genutzt, um in den betrachteten Außenraumproblemen die Abstrahlung in das Fernfeld abzubilden. Nach der Anwendung des entwickelten Programmcodes auf einfachere Modelle erfolgen Untersuchungen zur Intonation einer Blockflöte. Hierzu wird das Fluid innerhalb und im Nahfeld des Instruments unter Berücksichtigung des turbulenten Strömungsprofils, welches sich beim Spielen der Blockflöte ausbildet, betrachtet. Im Ergebnis stehen die Eigenwerte des Instruments in Abhängigkeit von der gewählten Griffkombination. Zur Evaluierung der Ergebnisse und zur Untersuchung des Einflusses der Strömung auf den Klang erfolgt der Vergleich mit den exakten Eigenfrequenzen. Die Galbrun-Gleichung wurde bereits von anderen Autoren untersucht und auf akustische Problemstellungen angewendet. Im Rahmen dieser Arbeit erfolgt jedoch erstmalig die Anwendung der Galbrun-Gleichung auf Eigenwertprobleme. Darüber hinaus sind der Autorin keine Arbeiten bekannt, die sich mit dreidimensionalen Modellen befassen. In der vorliegenden Arbeit werden somit erstmals komplexe dreidimensionale Modelle unter Anwendung der Galbrun-Gleichung untersucht.
We present the sound propagation and sound radiation inside and around a three dimensional recorder model. The fluid inside and in the near field of the instrument is meshed by second order Lagrangian tetrahedra elements. To present the effects in the far field, infinite elements are added to the finite elements. As infinte elements we use complex conjugated Astley-Leis elements. The goal of our studies is the computation of the eigenmodes of all playable notes, as well as the determination of the radiation behaviour for different fingerings. In a first step, the results obtained by considering a static fluid are presented. When playing a recorder, the inserted air flow leads to an oscillation of the air column inside the instrument. The musician is able to influence the frequency of the note by varying the blowing pressure and therefore a fine-tuning of the sound can be achieved. In rotation afflicted flows, the sound propagation can be described by the Galbrun equation. In a first instance, we present the influence of the flow velocity on the eigenfrequencies for simple geometries. Those results are compared to the frequencies obtained with Helmholtz equation for static fluids.