Development of a hybrid finite element-transfer matrix methodology for the modeling of vibroacoustic systems with attached noise control treatments

Résumé : Les véhicules aériens et terrestres sont constitués de systèmes bâtis complexes. La structure principale est généralement composée de panneaux légers renforcés par des éléments rigides. Cette solution de conception est répandue parce qu’elle allie la force et un faible poids. Cependant, on sait qu’elle offre des résultats vibroacoustiques médiocres, c’est à dire que l’effet des perturbations externes qui touchent le système peut générer un niveau de bruit excessif à l’intérieur de la cabine des passagers. C’est une préoccupation majeure chez les fabricants, parce que ce niveau de bruit nuit sensiblement au confort ressenti par les clients et peut causer de la fatigue chez les conducteurs et les pilotes. Pour cette raison, les composants passifs constitués de matériaux dissipatifs assemblés en mode multicouche sont généralement intégrés à la structure. Ces assemblées bordées intègrent surtout des matériaux poroélastiques, qui sont plutôt répandus, grâce à l’agencement intéressant de bonnes propriétés d’isolation sonore et de faible poids. L’intégration en amont des traitements de contrôle du bruit au processus de conception est la clé de succès d’un produit. Pour ce faire, des outils pratiques numériques en mesure de capter le comportement dynamique des systèmes vibroacoustiques impliquant les structures, les cavités et les matériaux d’insonorisation sont requis. D’une part, la modélisation de ces systèmes couplés en utilisant des procédés à base d’éléments finis peut être, bien que précis, irréalisable pour des applications pratiques. D’autre part, les approches analytiques telles que la méthode de matrice de transfert sont souvent préférées grâce à leur facilité d’utilisation, même si elles manquent de précision en raison des hypothèses rigoureuses inhérentes au cadre analytique. Dans ce contexte, les procédures de structuration hybrides sont récemment devenues très populaires. En effet, les différentes techniques de modélisation sont généralement recherchées pour décrire les systèmes vibroacoustiques complexes arbitraires sur la plus large gamme de fréquences possible. L’objectif du projet proposé est de mettre au point un cadre hybride offrant une mé- thodologie simple pour tenir compte des traitements de contrôle du bruit dans l’analyse vibroacoustique par éléments finis. A savoir, le modèle de calcul qui en découle conserve la souplesse et la précision de la méthode des éléments finis en bénéficiant de la simplicité et de l’efficacité de la méthode de matrice de transfert pour obtenir une réduction de la charge de calcul pour la modélisation de composants acoustiques passifs. La performance de la méthode pour prédire la réponse vibroacoustique de structures planes homogènes avec des traitements acoustiques attachées est évaluée. Les résultats démontrent que la méthode hybride proposée est très prometteuse, parce qu’elle permet une réduction de l’effort de calcul tout en conservant suffisamment de précision par rapport à l’analyse complète par éléments finis. En outre, la méthode de matrice de transfert proposée de modélisation des traitements de contrôle des bruits est générale, comme on peut l’appliquer dans d’autres cadres outre l’application de l’élément fini considéré dans ce travail. // Abstract : Aerial and terrestrial vehicles consist of complex built-up systems. The main structure is typically made of light panels strengthened by stiffer components. Such design solution is widely used as it combines strength and low weight. However, it is known to give poor vibroacoustic performances, i.e. the effect of external disturbances acting on the system may generate an excessive noise level inside the passengers cabin. This is a main concern for the manufacturers, as it significantly affects the comfort experienced by the costumers and may fatigue drivers and pilots. For this reason, passive components consisting of dissipative materials assembled in a multilayer fashion are typically integrated within the structure. These lined assemblies mainly involve poroelastic materials, which are commonly used thanks to the appealing combination of good noise insulation properties and low weight. The early integration of noise control treatments in the design process is the key to a successful product. For this purpose, practical numerical tools able to capture the dynamic behavior of vibroacoustic systems involving structures, cavities and noise proofing materials are demanded. On the one hand, modeling such coupled systems using finite element based methods can be, albeit accurate, time consuming for practical applications. On the other hand, analytical approaches such as the transfer matrix method are often preferred thanks to their ease of use, although they suffer from a lack of accuracy due to the stringent assumptions inherent within the analytical framework. In this context, hybrid substructuring procedures have recently become quite popular. Indeed, different modeling techniques are typically sought to describe arbitrarily complex vibroacoustic systems over the widest possible frequency range. The aim of this thesis is to devise a hybrid framework providing a simple methodology to account for noise control treatments in vibroacoustic finite element analysis. Namely, the resulting computational model retains the flexibility and accuracy of the finite element method while taking advantage from the simplicity and efficiency of the transfer matrix method to obtain a reduction of the computational burden in the modeling of passive acoustic components. The performance of the method in predicting the vibroacoustic response of flat structures with attached homogeneous acoustic treatments is assessed. The results prove that the proposed hybrid methodology is very promising, as it allows for a reduction of the computational effort while preserving enough accuracy with respect to full finite element analysis. Furthermore, the proposed transfer matrix based methodology for noise control treatments modeling is general, as it can be used in alternative frameworks besides the finite element application considered in this work

Physical Modelling and the Associated Acoustic Behaviour of Trumpets and Trombones

Accurately modelling the production of realistic musical notes in brass instruments is no easy task. Compared to woodwind instruments, brass instruments are considerably longer and constructed with bends, valves or coils, a mouthpiece with a cup rather than a reed or double-reed, as well as a large flare. Mathematically, this means that the sound wave propagation through the instrument could exhibit various nonlinear behaviours that are not examined within the fi eld of linear acoustics. In this thesis, we attempt to accurately model the timbre of musical notes produced on the trumpet and trombone and study the associated acoustic behaviours of both instruments. To accomplish this, we investigate the relevance of the interaction between the player and instrument to ensure the problem is computationally reasonable, as we need to decipher what aspects and parameters can be neglected, and which are essential to consider. This was done through a series of physical experiments and numerical studies, which also provided verification of previous claims and findings published in the literature. Ultimately, we determined there are factors more essential to incorporate over modelling vibroacoustic and thermoviscous effects. We therefore focus on these components and model the nonlinear wave propagation through the instruments in the time-domain using the compressible Euler equations, and numerically solve the system via the discontinuous Galerkin method. Several musical notes played at various dynamic levels are simulated. The numerical solutions are compared against the measured data to evaluate how well the timbre of the different musical tones can be recreated. Although several simplifying assumptions were made, we found that our model produces the most accurate results compared to previous findings. Furthermore, to our knowledge, we are the first to numerically reproduce (from real data) the production of shock waves in the trombone, thereby theoretically and numerically verifying the experimental work published by Hirschberg et al. in 1996 (https://doi.org/10.1121/1.414698)

Kompressible CFD-Simulationen von Aeroakustik für Automobilanwendungen

In this work, a direct noise computation method based on a low-Mach number flow solver is investigated. The new solver is implemented in the finite volume framework of the software OpenFOAM, accompanied with a new acoustic damping model for reducing spurious noise. The new solver is utilised to calculate noise generation and propagation for automotive applications. In order to validate the applicability of the low-Mach flow solver, a benchmark consisting of two-struts is calculated. The simulated aerodynamic near field as well as aeroacoustic far field are compared to wind tunnel measurements. The acoustic far field is computed using the direct method as well as a hybrid method. Both methods are evaluated based on comparing far field spectra and directivity patterns with experimental results. After validating the applicability of the low-Mach number solver, the topic of spurious noise generation in direct noise computation is addressed. Different spurious noise sources are presented and their generation mechanisms are investigated. Afterwards, two different strategies for spurious noise reduction, namely selective acoustic damping and numerical grid stretching, are discussed and validated. The acoustic damping model can substantially damp out spurious noise generated at grid interfaces without affecting the turbulence. It is also observed that the direction of grid refinement determines the direction of propagation of spurious noise. The strategies for spurious noise reduction are then applied on a side-mirror test case. For this, a new algorithm for automated and directional grid stretching is implemented. Spurious noise generation in the vicinity of the mirror’s surface as well as in the mirror’s wake could be substantially reduced and a quantitative analysis based on frequency-wavenumber spectra in the wake of the mirror is performed. Finally, the proposed flow solver, along with the strategies for spurious noise reduction, is used to directly compute noise generation on a generic vehicle model. Two different variants are calculated and the effect of the A-pillar and the side-mirror regarding their contribution to the acoustic waves on the side-window is investigated. Aerodynamic as well as aero- and vibroacoustic spectra on the side-window are calculated and compared to wind-tunnel measurements. For both variants, the results calculated using the direct method show good agreement with experimental data.In dieser Arbeit wird eine Methode zur direkten Berechnung von Aeroakustik basierend auf einen Strömungslöser für kleine Mach-Zahlen untersucht. Der Strömungslöser wird mit einem neuen Dämpfungsmodell für die Reduktion numerischer Schallwellen im finite Volumen Code OpenFOAM implementiert, und für die Berechnung der Entstehung und Ausbreitung von Schallwellen im Automobilbereich angewandt. Zur Validierung des neuen Strömungslösers, wird ein Benchmark, der aus zwei parallelen Streben besteht, berechnet. Das simulierte aerodynamische Nahfeld sowie das aeroakustische Fernfeld werden mit Windkanalmessungen verglichen. Das akustische Fernfeld wird mit der direkten sowie mit einer hybriden Methode berechnet. Beide Methoden werden anhand der Fernfeldspektren sowie der Richtcharakteristiken mit experimentellen Daten bewertet. Nach der Validierung des Strömungslösers wird die Entstehung von numerischen Störungen in der direkten Methode analysiert. Es werden verschiedene Quellen numerischer Störungen sowie deren Entstehungsmechanismen dargestellt. Anschließend werden zwei verschiedene Strategien zur Reduktion von Störungen diskutiert und validiert. Das Dämpfungsmodell zeigt sein Potenzial bei der Reduktion von numerischen Schallwellen ohne Beeinflussung der Turbulenz. Es wird außerdem gezeigt, dass die Richtung einer Verfeinerung des numerischen Gitters die Richtung der Ausbreitung numerischer Schallwellen bestimmt. Die Strategien zur Reduktion numerischer Störungen werden weiterhin an einem einzelnen Seitenspiegel angewandt. Dafür wird ein neuer Algorithmus für eine automatisierte und richtungsdefinierte Gitterexpansion implementiert. Die Amplitude numerischer Störungen, die im Spiegelnachlauf entstehen, werden mit Hilfe einer Frequenz-Wellenzahl Analyse quantitativ untersucht. Es zeigt sich, dass das Dämpfungsmodell diese Störungen deutlich reduziert. Abschließend wird der Strömungslöser zusammen mit den vorgeschlagenen Strategien in einer direkten Aeroakustikberechnung eines generischen Fahrzeugmodells angewandt. Es werden zwei unterschiedliche Varianten berechnet und der Einfluss der A-Säule und des Seitenspiegels bezüglich ihres akustischen Beitrags auf der Seitenscheibe untersucht. Sowohl aerodynamische als auch aero- und vibroakustische Spektren werden auf der Seitenscheibe berechnet und mit Windkanalmessungen verglichen. Für beide Varianten zeigen die Ergebnisse der direkten Methode gute Übereinstimmung mit den experimentellen Daten

Modelling, Simulation and Data Analysis in Acoustical Problems

Modelling and simulation in acoustics is currently gaining importance. In fact, with the development and improvement of innovative computational techniques and with the growing need for predictive models, an impressive boost has been observed in several research and application areas, such as noise control, indoor acoustics, and industrial applications. This led us to the proposal of a special issue about “Modelling, Simulation and Data Analysis in Acoustical Problems”, as we believe in the importance of these topics in modern acoustics’ studies. In total, 81 papers were submitted and 33 of them were published, with an acceptance rate of 37.5%. According to the number of papers submitted, it can be affirmed that this is a trending topic in the scientific and academic community and this special issue will try to provide a future reference for the research that will be developed in coming years

Análise dinâmica de estruturas periódicas utilizando uma abordagem de propagação de ondas e técnicas de sub-estruturação

Orientadores: José Roberto de França Arruda, Jean-Mathieu MencikTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Nesta tese de doutorado, o método dos elementos finitos ondulatórios é utilizado para cálculo da resposta harmônica de sistemas mecânicos envolvendo estruturas com periodicidade unidimensional, i.e., estruturas compostas por subestruturas idênticas arranjadas ao longo de uma direção. Tais sistemas mecânicos podem ser complexos e são comumente encontrados em aplicações de engenharia como, por exemplo, nas fuselagens de aviões. A primeira parte da tese é dedicada ao cálculo das ondas que se propagam ao longo dessas estruturas. Uma breve revisão da literatura sobre as formulações disponíveis para o problema de autovalor associado ao método dos elementos finitos ondulatórios é apresentada, assim como um estudo dos erros numéricos induzidos por estes problemas de autovalor no caso de um guia de ondas sólido. Na segunda parte desta tese, modelagens de superelementos para estruturas periódicas são propostas. Neste contexto, matrizes de rigidez dinâmica e de receptância ou flexibilidade de estruturas periódicas são expressas a partir dos modos de onda. Comparadas às matrizes de rigidez dinâmica e receptância obtidas pelo método dos elementos finitos convencional, as matrizes baseadas no método dos elementos finitos ondulatórios são calculadas de forma bastante rápida e sem perda de acuracidade. Ademais, uma estratégia eficiente de redução de ordem de modelo é apresentada. Comparada às formulações que utilizam a base completa de ondas, esta estratégia proporciona redução do tempo computacional requerido para cálculo da resposta forçada de estruturas periódicas. De fato, é mostrado que elementos espectrais numéricos de alta ordem podem ser construídos a partir do método dos elementos finitos ondulatórios. Isto constitui uma alternativa ao método dos elementos espectrais convencional, cuja utilização está limitada a estruturas simples para as quais soluções analíticas por ondas existam. A motivação por trás das formulações de matrizes de superelementos a partir do método dos elementos finitos ondulatórios está na utilização do conceito de ondas numéricas para calcular a resposta harmônica de sistemas mecânicos acoplados que envolvam estruturas com periodicidade unidimensional e junções elásticas a partir de procedimentos de montagem clássicos de elementos finitos ou técnicas de decomposição de domínio. Este assunto é tratado na terceira parte desta tese. Nesse caso, o método de Craig-Bampton é usado para expressar as matrizes de superelementos de junções por meio de modos estáticos e de interface fixa. Um critério baseado no método dos elementos finitos ondulatórios é considerado para a seleção dos modos da junção que mais contribuem para a resposta forçada do sistema. Isto também contribui para o aumento da eficiência da simulação numérica de sistemas acoplados. Finalmente, na quarta parte desta tese, o método dos elementos finitos ondulatórios é utilizado para mostrar que é possível projetar estruturas periódicas com potencial para funcionar como filtros de vibração em bandas de frequência específicas. Com o intuito de destacar a relevância dos desenvolvimentos propostos nessa tese, ensaios numéricos envolvendo guias de onda sólidos, pórticos planos e estruturas tridimensionais do tipo fuselagem aeronáutica são realizadosAbstract: In this thesis, the wave finite element (WFE) method is used for assessing the harmonic forced response of mechanical systems that involve structures with one-dimensional periodicity, i.e., structures which are made up of several identical substructures along one direction. Such mechanical systems can be quite complex and are commonly encountered in engineering applications, e.g., aircraft fuselages. The first part of the thesis is concerned with the computation of wave modes traveling along these structures. A brief literature review is presented regarding the available formulations for the WFE eigenproblem, which need to be solved for expressing the wave modes, as well as a study of the numerical errors induced by these eigenproblems in the case of a solid waveguide. In the second part of the thesis, the WFE-based superelement modeling of periodic structures is proposed. In this context, the dynamic stiffness matrices and receptance matrices of periodic structures are expressed in terms of wave modes. Compared to the conventional FE-based dynamic stiffness and receptance matrices, the WFE-based matrices can be computed in a very fast way without loss of accuracy. In addition, an accurate strategy for WFE-based model order reduction is presented. It provides significant computational time savings for the forced response analysis of periodic structures compared to WFE-based superelement modeling, which makes use of the full wave basis. Indeed, it is shown that higher-order numerical spectral elements can be built by means of the WFE method. This is an alternative to the conventional spectral element method, which is limited to simple structures for which closed-form wave solutions exist. The motivation behind the formulation of WFE-based superelement matrices is the use of the concept of numerical wave modes to assess the forced response of coupled mechanical systems that involve structures with one-dimensional periodicity and coupling elastic junctions through classic finite element assembly procedures or domain decomposition techniques. This issue is addressed in the third part of this thesis. In this case, the Craig-Bampton method is used to express superelement matrices of coupling junctions by means of static and fixed-interface modes. A WFE-based criterion is considered to select among junction modes those that contribute most to the system forced response. This also contributes to enhancing the efficiency of the numerical simulation of coupled systems. Finally, in the fourth part of this thesis, the WFE method is used to show the potential of designing periodic structures which work as vibration filters within specific frequency bands. In order to highlight the relevance of the developments proposed in this thesis, numerical experiments which involve solid waveguides, two-dimensional frame structures, and three-dimensional aircraft fuselage-like structures are carried outDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutora em Engenharia Mecânica2010/17317-9FAPES

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA