This thesis highlights one of the most significant concerns that has preoccupied drivetrain engineers in recent times, namely drivetrain clonk. Clonk is an unacceptable audible sound, which is accompanied by a tactile drivetrain response. This may occur under several different driving conditions. Many drivetrain NVH concerns are related to impact loading of subsystems down-line of engine. These concerns are induced by power torque surge through engagement and disengagement processes, which may propagate through various transmission paths as structural waves. The coincidence of these waves with the acoustic modes of sub-system components leads to audible responses, referred to as clonk. The approach usually undertaken and reported in literature is either purely theoretical or constitutes experimental observation of vehicle conditions. A few research workers have reported rig-based investigations, but not under fully dynamic conditions with controlled and reproducible impulsive action. The research reported in this thesis combines experimental and numerical investigation of high frequency behaviour of light truck drivetrain systems, when subjected to sudden impulsive action, due to driver behaviour. The problem is treated as a multi-physics interactive phenomenon under transient conditions. The devised numerical method combines multi-body dynamics, structural modal analysis, impact dynamics in lash zones and acoustic analysis within an overall investigation framework. A representative drivetrain system rig is designed and implemented, and controlled tests simulating driver behaviour undertaken. The combined numerical predictions and experimental noise and vibration monitoring has highlighted the fundamental aspects of drivetrain behaviour. Good agreement is' also found between the detailed numerical approach and the experimental findings. Novel methods of measurement such as Laser Doppler Vibrometery have been employed. Simultaneous measurements of vibration and noise radiation confirm significant elasto-acoustic coupling at high impact energy levels. One of the major finds of the thesis is the complex nature of the clonk signal, being a combination of accelerative and ringing noise, with the latter also comprising of many other lower energy content as observed in the case of transmission rattle and bearing-induced responses. Therefore, the link between rattle and clonk, long suspected, but not hitherto shown has been confirmed in the thesis. Another major find of particular commercial interest is the insignificant contribution of torsional damping devices such as dual mass flywheels upon the accelerative component of the clonk response.

A very short and disagreeable audible and tactile response from a vehicle driveline may be excited when the throttle is abruptly applied or released, or when the clutch is rapidly engaged. The condition is most noticeable in low gear and in slow moving traffic, when other background engine and road noise levels are low. This phenomenon is known as clonk and is often associated with the first cycle of shuffle response, which is a low frequency longitudinal vehicle movement excited by throttle demand. It is often reported that clonk may coincide with each cycle of the shuffle response, and multiple clonks may then occur. The problem is aggravated by backlash and wear in the drivetrain, and it conveys a perception of low quality to the customer. Hitherto, reported investigations do not reveal or discuss the mechanism and causal factors of clonk in a quantitative manner, which would relate the engine impulsive torque to the elastic response of the driveline components, and in particular to the noise radiating surfaces. Crucially, neither have the issues of sensitivity, variability and non-linearity been addressed and published. It is also of fundamental importance that clonk is seen as a total system response to impulsive torque, in the presence of distributed lash at the vibro-elastic impact sites. In this thesis, the drivetrain is defined as the torque path from the engine flywheel to the road wheels. The drivetrain is a lightly damped and highly non-linear dynamic system. There are many impact and noise emitting locations in the driveline that contribute to clonk, when the system is subjected to shock torque loading. This thesis examines the clonk energy paths, from the initial impact to many driveline lash locations, and to the various noise radiating surfaces. Both experimental and theoretical methods are applied to this complex system. Structural and acoustic dynamics are considered, as well as the very important frequency couplings between elastic structures and acoustic volumes. Preliminary road tests had indicated that the clonk phenomenon was a, very short transient impact event between lubricated contacts and having a high frequency characteristic. This indicated that a multi-body dynamics simulation of the driveline, in conjunction with a high frequency elasto-acoustic coupling analysis, would be required. In addition, advanced methods of signal analysis would be required to handle the frequency content of the very short clonk time histories. These are the main novelties of this thesis. There were many successful outcomes from the investigation, including quantitative agreement between the numerical and experimental investigations. From the experimental work, it was established that vehicle clonk could be accurately reproduced on a driveline rig and also on a vehicle chassis dynamometer, under controlled test conditions. It then enabled Design of Experiments to be conducted and the principal causal factors to be identified. The experimental input and output data was also used to verify the mathematical simulation. The high frequency FE analysis of the structures and acoustic cavities were used to predict the dynamic modal response to a shock input. The excellent correlation between model and empirical data that was achieved, clearly established the clonk mechanism in mathematical physics terms. Localised impact of meshing gears under impulsive loads were found to be responsible for high frequency structural wave propagation, some of which coupled with the acoustics modes of cavities, when the speed of wave propagation reached supersonic levels. This finding, although previously surmised, has been shown in the thesis and constitutes a major contribution to knowledge.

La caractérisation d’objets enfouis à partir de mesures d’ondes diffractées est un problème présent dans de nombreuses applications comme l’exploration géophysique, le contrôle non-destructif, l’imagerie médicale, etc. Elle peut être obtenue numériquement par la résolution d’un problème inverse. Néanmoins, c’est un problème non linéaire et mal posé, ce qui rend la tâche difficile. Une reconstruction précise nécessite un choix judicieux de plusieurs paramètres très différents, dépendant des données de la méthode numérique d’optimisation choisie.La contribution principale de cette thèse est une étude de la reconstruction complète d’obstacles élastiques immergés à partir de mesures du champ lointain diffracté. Les paramètres à reconstruire sont la frontière, les coefficients de Lamé, la densité et la position de l’obstacle. On établit tout d’abord des résultats d’existence et d’unicité pour un problème aux limites généralisé englobant le problème direct d’élasto-acoustique. On analyse la sensibilité du champ diffracté par rapport aux différents paramètres du solide, ce qui nous conduit à caractériser les dérivées partielles de Fréchet comme des solutions du problème direct avec des seconds membres modifiés. Les dérivées sont calculées numériquement grâce à la méthode de Galerkine discontinue avec pénalité intérieure et le code est validé par des comparaisons avec des solutions analytiques. Ensuite, deux méthodologies sont introduites pour résoudre le problème inverse. Toutes deux reposent sur une méthode itérative de type Newton généralisée et la première consiste à retrouver les paramètres de nature différente indépendamment, alors que la seconde reconstruit tous les paramètre en même temps. À cause du comportement différent des paramètres, on réalise des tests de sensibilité pour évaluer l’influence de ces paramètres sur les mesures. On conclut que les paramètres matériels ont une influence plus faible sur les mesures que les paramètres de forme et, ainsi, qu’une stratégie efficace pour retrouver des paramètres de nature distincte doit prendre en compte ces différents niveaux de sensibilité. On a effectué de nombreuses expériences à différents niveaux de bruit, avec des données partielles ou complètes pour retrouver certains paramètres, par exemple les coefficients de Lamé et les paramètres de forme, la densité, les paramètres de forme et la localisation. Cet ensemble de tests contribue à la mise en place d’une stratégie pour la reconstruction complète des conditions plus proches de la réalité. Dans la dernière partie de la thèse, on étend ces résultats à des matériaux plus complexes, en particulier élastiques anisotropes. / The characterization of hidden objects from scattered wave measurements arises in many applications such as geophysical exploration, non destructive testing, medical imaging, etc. It can be achieved numerically by solving an Inverse Problem. However, this is a nonlinear and ill-posed problem, thus a difficult task. A successful reconstruction requires careful selection of very different parameters depending on the data and the chosen optimization numerical method.The main contribution of this thesis is an investigation of the full reconstruction of immersed elastic scatterers from far-field pattern measurements. The sought-after parameters are the boundary, the Lamé coefficients, the density and the location of the obstacle. First, existence and uniqueness results of a generalized Boundary Value Problem including the direct elasto-acoustic problem are established. The sensitivity of the scattered field with respect to the different parametersdescribing the solid is analyzed and we end up with the characterization of the corresponding partial Fréchet derivatives as solutions to the direct problem with modified right-hand sides. These Fréchet derivatives are computed numerically thanks to the Interior Penalty Discontinuous Galerkin method and the code is validated thanks to comparison with analytical solutions. Then, two solution methodologies are introduced for solving the inverse problem. Both are based on an iterative regularized Newton-type methodology and the first one consists in retrieving the parameters of different nature independently, while the second one reconstructs all parameters together. Due to the different behavior of the parameters, sensitivity tests are performed to assess the impact of the parameters on the measurements. We conclude that material parameters have a weaker influence on the measurements than shape parameters, and therefore, a successful strategy to retrieve parameters of distinct nature should take into account these different levels of sensitivity. Various experiments at different noise levels and with full or limited aperture data are carried out to retrieve some of the physical properties, e.g. Lamé coefficients with shape parameters, density with shape parameters a, density, shape and location. This set of tests contributes to a final strategy for the full reconstruction and in more realistic conditions. In the final part of the thesis, we extend the results to more complex material parameters, in particular anisotropic elastic.

Cette thèse étudie le raffinement local de maillage à la fois en espace et en temps pour l’équation de l’elastodynamique du second ordre pour le calcul haute performance. L’objectif est de mettre en place des méthodes numériques pour traiter des hétérogénéités de petite taille ayant un impact important sur la propagation des ondes. Nous utilisons une approche par éléments finis de Galerkin discontinus avec pénalisation pour leur flexibilité et facilité de parallélisation. La formulation éléments finis que nous proposons a pour particularité d’être élasto-acoustique, pour pouvoir prendre en compte des hétérogénéités acoustiques de petite taille. Par ailleurs, nous proposons un terme de pénalisation optimisé qui est mieux adapté à l’équation de l’élastodynamique, conduisant en particulier à une meilleure condition CFL. Nous avons aussi amélioré une formulation PML du second ordre pour laquelle nous avons proposé une nouvelle discrétisation temporelle qui rend la formulation plus stable. En tirant parti de la p-adaptivité et des maillages non-conformes des méthodes de Galerkin discontinues combiné à une méthode de pas de temps local, nous avons grandement réduit le coût du raffinement local. Ces méthodes ont été implémentées en C++, en utilisant des techniques de template metaprogramming, au sein d’un code parallèle à mémoire distribuée (MPI) et partagée (OpenMP). Enfin, nous montrons le potentiel de notre approche sur des cas tests de validation et sur des cas plus réalistes avec des milieux présentant des hydrofractures. / This thesis studies local mesh refinement both in time and space for the second order elastodynamic equation in a high performance computing context. The objective is to develop numerical methods to treat small heterogeneities that have global impact on wave propagation. We use an internal penalty discontinuous Galerkin finite element approach for its flexibity and parallelization capabilities. The elasto-acoustic finite element formulation we discuss is elasto-acoustic in order to handle local acoustic heterogeneities. We also propose an optimized penalty term more suited to the elastodynamic equation that results in better CFL condition. We improve a second order PML formulation with an original time discretization that results in a more stable formulation. Using the p-adaptivity and nonconforming mesh capabilities of discontinuous Galerkin methods combined with a local time stepping method, we greatly reduce the high computational cost of local refinements. These methods have been implemented in C++, using template metaprogramming, in a distributed memory (MPI) and shared memory (OpenMP) parallel code. Finally, we show the potential of our methods on validation test cases and on more realistic test cases with medium including hydrofractures.