Boundary Element and Finite Element Coupling for Aeroacoustics Simulations

We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary.Comment: 25 page

Analysis of Random Structure-Acoustic Interaction Problems Using Coupled Boundary Element and Finite Element Methods

A coupled boundary element(BEM)-finite element(FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels

Analysis of random structure-acoustic interaction problems using coupled boundary element and finite element methods

A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels

Utilisation d'une stratégie de contrôle actif vibratoire pour la réduction du bruit de roulement dans l'habitacle des automobiles

La réduction du bruit de roulement transmis jusqu'à l'habitacle automobile est étudiée en utilisant une stratégie de contrôle actif vibratoire (ASAC). Premièrement, la conception d'un banc de test vibro-acoustique, constitué d'un ensemble pneu/roue/suspension a été développé dans le but d'identifier les chemins de transmission vibro­ acoustique (jusqu'à 250 Hz) pour une excitation quasi identique au moyeu de la roue. Des mesures de fonctions de réponse en fréquence (FRF) entre l'excitation primaire au moyeu de la roue et chacune des jonctions de la suspension et du chassis ont été utilisées dans le but de caractériser et de préciser l'identification du trajet qu'emprunte l'énergie vibratoire, par des mesures du champ vibratoire aux jonctions suspension/châssis, partant du contact du pneu/route, passant par le châssis et se dirigeant jusqu'à l'habitacle. En second lieu, un modèle constitué d'élément finis (FEM) et d'éléments de frontière (BEM) a été développé afin de simuler la réponse acoustique d'un habitacle automobile. Ce modèle FEM/BEM a été utilisé dans le but de prédire le comportement vibro-acoustique d'un caisson de voiture suite aux forces mesurées aux jonctions de la suspension et du châssis. Finalement, un algorithme de contrôle actif vibratoire optimal a été développé afin de prédire l'effet la réduction de l'énergie vibratoire des différents chemins de transmission sur la mesure du niveau de pression acoustique à l'intérieur de l'habitacle automobile. L'approche du contrôle actif optimale est basée sur l'utilisation d'un actionneur électrodynamique, permettant de mo­difier le comportement vibratoire de la suspension et du châssis automobile, de façon à réduire le rayonnement acoustique de la structure du caisson de voiture. Afin de prédire la réduction du niveau de pression à l'intérieur de l'habitacle automobile, des fonctions de réponse en fréquence (FRF), d'un actionneur de contrôle positionné au centre du bras de suspension triangulé, ont été mesurées expérimentalement et ont été introduites dans l'algorithme de contrôle actif optimal. La contribution de l'actionneur de contrôle a été évaluée par une mesure de réduction du niveau de force mesuré aux jonctions de la suspension et du châssis et d'une diminution du niveau de bruit interne de l'habitacle par une mesure du niveau de pression acoustique localisé à la tête du conducteur.Abstract: The reduction of the structure-borne road noise inside the cabin of an automobile is investigated using an Active Structural Acoustic Control (ASAC) approach. First, a laboratory test bench consisting of a wheel/suspension/lower suspension A-arm assembly has been developed in order to identify the vibro-acoustic transmission paths (up to 250 Hz) for realistic road noise excitation of the wheel. Frequency Response Function (FRF) measurements between the excitation/control electrodynamic shakers and each suspension/chassis linkages are used to characterize the different transmission paths that transmit energy through the chassis of the car. Secondly, a FE/BE model (Finite/Boundary Elements) was developed to simulate the acoustic field of an automobile cabin interior. This model is used to predict the acoustic field inside the cabin as a response to the measured forces applied on the suspension/chassis linkages. Finally, an implemented optimal active control algorithm using a feedforward structure to perform the simulation of an optimal active structural acoustic control (ASAC) by using experimental and numerical FRFs is presented. The control approach relies on the use of an electrodynamic actuator to modify the vibration behavior of the suspension and the automotive chassis such that its noise radiation efficiency is decreased. To predict the noise level reduction inside the passenger compartment, the measured FRFs of a control actuator, connected to the lower suspension A-arm, have been implemented by using the optimal active control algorithm in MATLAB ª . Its contribution to noise reduction has been evaluated in term of acoustic radiation efficiency, as measured by the sound pressure level (SPL) located at the driver's head

PARTITION OF UNITY BOUNDARY ELEMENT AND FINITE ELEMENT METHOD: OVERCOMING NONUNIQUENESS AND COUPLING FOR ACOUSTIC SCATTERING IN HETEROGENEOUS MEDIA

The understanding of complex wave phenomenon, such as multiple scattering in heterogeneous media, is often hindered by lack of equations modelling the exact physics. Use of approximate numerical methods, such as Finite Element Method (FEM) and Boundary Element Method (BEM), is therefore needed to understand these complex wave problems. FEM is known for its ability to accurately model the physics of the problem but requires truncating the computational domain. On the other hand, BEM can accurately model waves in unbounded region but is suitable for homogeneous media only. Coupling FEM and BEM therefore is a natural way to solve problems involving a relatively small heterogeneity (to be modelled with FEM) surrounded by an unbounded homogeneous medium (to be modelled with BEM). The use of a classical FEM-BEM coupling can become computationally demanding due to high mesh density requirement at high frequencies. Secondly, BEM is an integral equation based technique and suffers from the problem of non-uniqueness. To overcome the requirement of high mesh density for high frequencies, a technique known as the ‘Partition of Unity’ (PU) method has been developed by previous researchers. The work presented in this thesis extends the concept of PU to BEM (PUBEM) while effectively treating the problem of non-uniqueness. Two of the well-known methods, namely CHIEF and Burton-Miller approaches, to overcome the non-uniqueness problem, are compared for PUBEM. It is shown that the CHIEF method is relatively easy to implement and results in at least one order of magnitude of improvement in the accuracy. A modified ‘PU’ concept is presented to solve the heterogeneous problems with the PU based FEM (PUFEM). It is shown that use of PUFEM results in close to two orders of magnitude improvement over FEM despite using a much coarser mesh. The two methods, namely PUBEM and PUFEM, are then coupled to solve the heterogeneous wave problems in unbounded media. Compared to PUFEM, the coupled PUFEM-PUBEM apporach is shown to result between 30-40% savings in the total degress of freedom required to achieve similar accuracy