La mécanique des fluides numérique a permis d'optimiser de nombreux systèmes dont, notamment, les moteurs d'avions. Dans l'industrie aéronautique, les calculs numériques d'écoulements sont principalement limités à des approches stationnaires de par le coût prohibitif des simulations instationnaires. Néanmoins, les écoulements qui se développent dans les machines tournantes, à savoir les principaux composants d'un moteur d'avion, sont majoritairement périodiques en temps. En partant de cette hypothèse de périodicité temporelle, des approches dites spectrales en temps ont vus le jour il y a plus de quinze ans. Elles restent principalement limitées à des écoulements mono-fréquentiels, à savoir composés d'une seule fréquence de base et de ses harmoniques. Récemment, une méthode d'équilibrage harmonique multi-fréquentielle a été développée et implémentée dans le code de calcul elsA, élargissant le champ des applications possibles. En particulier, l'étude de l'aéroélasticité des machines tournantes multi-étagées devient alors envisageable.Cette thèse se propose d'appliquer la méthode d'équilibrage harmonique multi-fréquentielle pour étudier l'aéroélasticité d'une configuration nouvelle de moteur d'avion: les doublets d'hélices contra-rotatives. La méthode est tout d'abord validée analytiquement et numériquement sur des cas tests linéaires et non-linéaires avec succès. Deux problèmes sont soulevés pour l'utilisation d'une telle méthode sur des configurations aéroélastiques arbitraires: le conditionnement du terme source et la convergence de la méthode. Des approches originales ont été développées afin d'améliorer le conditionnement et de fournir une estimation a priori du nombre d'harmoniques nécessaire pour obtenir un certain niveau de convergence. La méthode d'équilibrage harmonique est ensuite validée sur un cas standard d'aéroélasticité des machines tournantes et montre des résultats très proches de ceux expérimentaux. L'applicabilité de la méthode est finalement démontrée pour la simulation de l'aéroélasticité des doublets d'hélices contra-rotatives. / Computational Fluid Dynamics (CFD) has allowed the optimization of many configurations among which aircraft engines. In the aeronautical industry, CFD is mostly restricted to steady approaches due to the high computational cost of unsteady simulations. Nevertheless, the flow field across the rotating parts of aircraft engines, namely turbomachinery blades, is essentially periodic in time. Years ago, Fourier-based time methods have been developed to take advantage of this time periodicity. However, they are, for the most part, restricted to mono-frequential flow fields. This means that only a single base-frequency and its harmonics can be considered. Recently, a multi-frequential Fourier-based time method, namely the multi-frequential Harmonic Balance (HB), has been developed and implemented into the elsA CFD code, enabling new kinds of applications as, for instance, the aeroelasticity of multi-stage turbomachinery.The present PhD thesis aims at applying the HB approach to the aeroelasticity of a new type of aircraft engine: the contra-rotating open rotor. The method is first validated on analytical, linear and non-linear numerical test problems. Two issues are raised, which prevent the use of such an approach on arbitrary aeroelastic configurations: the conditioning of the multi-frequential HB source term and the convergence of the method. Original methodologies are developed to improve the condition number of the simulations and to provide a priori estimates of the number of harmonics required to achieve a given convergence level. The HB method is then validated on a standard configuration for turbomachinery aeroelasticity. The results are shown to be in fair agreement with the experimental data. The applicability of the method is finally demonstrated for aeroelastic simulations of contra-rotating open rotors.

Ces travaux s'articulent autour du calcul des solutions périodiques dans les systèmes dynamiques non linéaires, au moyen de méthodes numériques de continuation. La recherche de solutions périodiques se traduit par un problème avec conditions aux limites périodiques, pour lequel nous avons implémenté deux méthodes d'approximation : - Une méthode spectrale dans le domaine fréquentiel, l'équilibrage harmonique d'ordre élevé, qui repose sur une formulation quadratique des équations. Nous proposons en outre une extension de cette méthode aux cas de non-linéarités non rationnelles. - Une méthode pseudo-spectrale dans le domaine temporel, la collocation à l'aide fonctions polynômiales par morceaux. Ces méthodes transforment le problème continu en un système d'équations algébriques non linéaires, dont les solutions sont calculées par continuation à l'aide de la méthode asymptotique numérique. L'ensemble de ces outils, complétés d'une analyse linéaire de stabilité, sont intégrés au code de calcul MANLAB. Applications : Un modèle physique non-régulier de clarinette est étudié en détail : à partir de la branche de solutions statiques et ses bifurcations, on calcule les différentes branches de solutions périodiques, ainsi que leur stabilité et leurs bifurcations. Ce modèle est ensuite adapté au cas du saxophone, pour lequel on intègre une caractérisation acoustique expérimentale, afin de mieux tenir compte de la géométrie complexe de l'instrument. Enfin, nous étudions un modèle physique simplifié de violon, avec une non-régularité liée frottement de Coulomb. / Periodic solutions of nonlinear dynamical systems are the focus of this work. We compute periodic solutions through a BVP formulation, solved with two numerical methods: - a spectral method, in the frequency domain: the hogh-order Harmonic Balance Method, using a quadratic formulation of the original equations. We also propose an extension to nonrational nonlinearities. - a pseudo-spectral method, in the time domain : the arthogonal collocation at Gauss point, with piece-wise polynomial interpolation. Both methods lead to a system of nonlinear algebraic equations, and its solutions are computed by a continuation algorithm : the Asymptotic Numerical Method. These methods are embeded in the numerical package MANLAB, together with a linear stability analysis. Application We then apply these methods to physical models of several instruments : a clarinet, a saxophone, and a violin. The clarinet model contains a non-smooth contact between the reed and the mouthpiece. The study focuses on the evolution of frequency, loudness, and spectrum along the branch of periodic solutions when varying the mouth pressure. The saxophone model is very similar, but an experimental characterization of the bore is used in that case. Finally, the violin model with a non-smooth Coulomb contact law and a simplified resonator is studied, showing the variety of models that can be treated using this method.

Ces travaux de thèse portent sur l'étude expérimentale et numérique de structures mécaniques non-linéaires soumises à des vibrations sinusoïdales et aléatoires. L'étude prend en compte l'existence d'incertitudes au sein du protocole expérimentale et de la modélisation. Les études expérimentales menées au CEA/CESTA montrent que la réponse des structures assemblées à des sollicitations vibratoires est fortement dépendante du niveau d'excitation d'une part, et que la réponse obtenue possède une variabilité, parfois importante. Ces résultats expérimentaux ne peuvent pas être reproduits en simulation avec la méthode de simulation vibratoire linéaire déterministe classique.L'objectif de ces travaux est de proposer et de mettre en place des méthodes numériques pour étudier ces réponses non-linéaires, et de quantifier et propager les incertitudes pertinentes au sein des calculs. Cet objectif passe par l'étude de maquettes d'essai de complexité croissante et sujettes aux mêmes phénomènes vibratoires que les objets d'étude industriels du CEA/CESTA. Les méthodes de simulation vibratoire non-linéaires et les techniques numériques développées dans le monde académique sont adaptées et utilisées dans le contexte industriel du CEA/CESTA.Le premier objet d'étude est une poutre métallique bi-encastrée, dont la non-linéarité est d'origine géométrique. Le modèle associé à cette poutre est un oscillateur de Duffing à un degré de liberté très détaillé dans la littérature scientifique, et qui permet de valider les développements numériques effectués, sur les aspects de l'excitation aléatoire et de la propagation d'incertitudes. Dans un premier temps, les méthodes de tir et d'équilibrage harmonique sont étendues au cas de l'excitation aléatoire et validées sur cette structure académique par comparaison à l'expérience. Dans un second temps, une méthode de propagation d'incertitude non-intrusive est implémentée pour prendre en compte les incertitudes de modélisation identifiées.Le second objet d'étude est une maquette comportant un plot élastomère reliant une masselotte à un bâti. Le comportement non-linéaire de l'élastomère est au c\oe ur de ces travaux de thèse. De nombreux essais vibratoires sont réalisés dans un premier temps pour identifier un modèle non-linéaire de l'élastomère juste suffisant. Dans un second temps, le modèle développé est validé par comparaison aux essais en utilisant et adaptant les méthodes étendues lors de l'étude de la poutre bi-encastrée.Enfin, une maquette d'étude se rapprochant d'un cas d'application industriel est étudiée : la maquette Harmonie-Gamma. Elle compte des interfaces frottantes et des liaisons élastomères. Les essais vibratoires réalisés permettent d'identifier le comportement dynamique linéaire et non-linéaire du système et d'étudier l'évolution de la réponse en fonction du niveau d'excitation. Un modèle numérique est réalisé par éléments finis puis réduit par une méthode de sous-structuration. Les relations non-linéaires sont introduites au niveau des liaisons frottantes et élastomères. La réponse vibratoire de la structure est simulée par la méthode d'équilibrage harmonique couplée à un algorithme de continuation. Les comparaisons essais / calculs sont menées pour les excitations de type sinus balayé et aléatoire, et permettent d'analyser l'apport de chaque non-linéarité dans la réponse de la structure. / This PhD work focuses on the experimental and numerical study of nonlinear structures subjected to both harmonic and random vibrations, in the presence of modeling and experimental uncertainties. Experimental studies undertaken at the CEA / CESTA show a strong dependence of the jointed structures towards the excitation level, as well as a variability in the response for a given excitation level. These experimental results cannot be simulated using the classical determinist linear vibration simulation method.The objective of this work is to propose and set up numerical methods to study these nonlinear responses, while quantifying and propagating the relevant uncertainties in the simulations. This objective involves the study of structural assemblies of increasing complexity and subjected to the same vibratory phenomena as CEA / CESTA industrial structures. Advanced nonlinear numerical methods developed in academia are applied in the CEA / CESTA industrial context.The first test structure is a clamped-clamped steel beam that has a geometrical nonlinearity. The beam is modeled by a Duffing oscillator which is a widely studied model in the field of nonlinear dynamics. This allows for a validation of the numerical developments proposed in this work, first on the issue of random vibrations, and second on the issue of the propagation of uncertainties. The simulations are based on two techniques of reference (shooting method and harmonic balance method). Firstly, the simulation results are validated by comparison with the experimental results for random vibrations. Secondly, the harmonic balance method is used in adequation with a non-intrusive polynomial chaos in order to take into accounts the modeling uncertainties.The second test structure is a mass linked to a solid casing via a vibration-absorbing elastomeric material of biconical shape surrounded by a cage of aluminum. The nonlinear behavior of the elastomer is at the heart of this work. Various vibration tests were performed on this structure in order to identify the simplest nonlinear model possible to answer our queries. The identified model is validated through comparisons between the simulation results and the experimental results for both sine-swept and random vibrations.The central assembly of this work is an industrial assembly with friction joints and vibration-absorbing elastomeric joints, named Harmonie-Gamma. The vibration tests performed exhibit resonance modes as well as a strong dependency of the response with the excitation level. A numerical finite element model is developed and reduced with a substructuration technique. The resulting nonlinear reduced model is simulated using an harmonic balance method with a continuation method. The simulated responses are compared with the experiments and allow for an analysis of coupled nonlinearities in the CEA / CESTA industrial context.

The recent advancement of superconducting nano devices has allowed for making a Superconducting Nanowire Single Photon Detector (SNSPD), whose extraordinary features have strongly motivated the research community to exploit it in many practical applications. In this thesis, an experimental setup for testing the SNSPD has been established. It contains an in-house packaging that meets the requirements of RF/microwave and optoelectronic characterizations. The quantum efficiency and detection efficiency measurements have confirmed that our approach is satisfactory. The dark count performance has reached the anticipated level. The factors affecting rise and fall times of the photoresponses are addressed. Based on the successful setup, the characterizations including dc, small signal ac measurements have been undertaken. The measurements are aimed at quantitatively investigating Cooper pair density in the superconducting nanowire. The experimental method involves a two-step, small signal S-parameter measurement either in the presence or absence of optical powers. The subsequent measurements by varying the temperature and dc bias current have achieved remarkable understanding on the physical properties of SNSPD nanowires. Then, the electrically induced nonlinearity is studied via the large signal RF and Microwave measurements. The experiments are a set of one-tone and two-tone measurements, in which either the RF driving power is varied at a fixed frequency, or vice versa. Two major nonlinear microwave circuit analysis methods, i.e. time-domain transient and hybrid-domain harmonic balance analysis, are employed. The simulation result reveals the optimized conditions of reaching the desired nonlinearity. Finally, we have successfully measured the optoelectronic mixing products in an electrically pumped optoelectronic mixer, which has identical structures as that of the SNSPD. The experiments confirm that this mixer is not only sensitive to the classical light intensities, but also to that of the single photon level. Meanwhile, the quantum conversion matrices is derived to interpret the quantum optoelectronic mixing effects.

The recent advancement of superconducting nano devices has allowed for making a Superconducting Nanowire Single Photon Detector (SNSPD), whose extraordinary features have strongly motivated the research community to exploit it in many practical applications. In this thesis, an experimental setup for testing the SNSPD has been established. It contains an in-house packaging that meets the requirements of RF/microwave and optoelectronic characterizations. The quantum efficiency and detection efficiency measurements have confirmed that our approach is satisfactory. The dark count performance has reached the anticipated level. The factors affecting rise and fall times of the photoresponses are addressed. Based on the successful setup, the characterizations including dc, small signal ac measurements have been undertaken. The measurements are aimed at quantitatively investigating Cooper pair density in the superconducting nanowire. The experimental method involves a two-step, small signal S-parameter measurement either in the presence or absence of optical powers. The subsequent measurements by varying the temperature and dc bias current have achieved remarkable understanding on the physical properties of SNSPD nanowires. Then, the electrically induced nonlinearity is studied via the large signal RF and Microwave measurements. The experiments are a set of one-tone and two-tone measurements, in which either the RF driving power is varied at a fixed frequency, or vice versa. Two major nonlinear microwave circuit analysis methods, i.e. time-domain transient and hybrid-domain harmonic balance analysis, are employed. The simulation result reveals the optimized conditions of reaching the desired nonlinearity. Finally, we have successfully measured the optoelectronic mixing products in an electrically pumped optoelectronic mixer, which has identical structures as that of the SNSPD. The experiments confirm that this mixer is not only sensitive to the classical light intensities, but also to that of the single photon level. Meanwhile, the quantum conversion matrices is derived to interpret the quantum optoelectronic mixing effects.

Forced response analysis of bladed disk assemblies plays a vital role in rotor blade design and has been drawing a great deal of attention both from research community and engine industry for more than half a century. However because of the phenomenon called &lsquo / mistuning&rsquo / , which destroys the cyclic symmetry of a rotor, there have been several difficulties related to forced response analysis ever since, two of which are addressed in this thesis: efficient non-linear forced response analysis of mistuned bladed disks and mistuning identification. On the nonlinear analysis side, a new solution approach is proposed studying the combined effect of non-linearity and mistuning, which is relatively recent in this research area and generally conducted with methods whose convergence and accuracy depend highly on the number of degrees of freedom where non-linear elements are attached. The proposed approach predicts nonlinear forced response of mistuned bladed disk assemblies considering any type of nonlinearity. In this thesis, special attention is given to the friction contact modeling of bladed disks which is the most common type of nonlinearity found in bladed disk assemblies. In the modeling of frictional contact a friction element which enables normal load variation and separation of the contact interface in three-dimensional space is utilized. Moreover, the analysis is carried out in modal domain where the differential equations of motions are converted to a set of non-linear algebraic equations using harmonic balance method and modal superposition technique. Thus, the number of non-linear equations to be solved is independent of the number of non-linear elements used. On the mistuning identification side, a new method is enclosed herein which makes use of neural networks to assess unknown mistuning parameters of a given bladed disk assembly from its assembly modes, thus being suitable for integrally bladed disks. The method assumes that a tuned mathematical model of the rotor under consideration is readily available, which is always the case for today&rsquo / s realistic bladed disk assemblies. A data set of selected mode shapes and natural frequencies is created by a number of simulations performed by mistuning the tuned mathematical model randomly. A neural network created by considering the number of modes, is then trained with this data set for being used to identify mistuning of the rotor from measured data. On top of these, a new adaptive algorithm is developed for harmonic balance method, several intentional mistuning patterns are investigated via excessive Monte-Carlo simulations and a new approach to locate, classify and parametrically identify structural non-linearities is introduced.

Submitted by Maria Medeiros (maria.dilva1@ufcg.edu.br) on 2018-08-29T14:12:32Z No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS - DISSERTAÇÃO (PPGF) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) / Made available in DSpace on 2018-08-29T14:12:32Z (GMT). No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS - DISSERTAÇÃO (PPGF) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) Previous issue date: 2015-04-10 / Capes / Nesta dissertação, analisamos a dinâmica de osciladores parametricamente forçados, com enfoque na amplificação de pequenos sinais. Iniciamos por uma revisão da ressonância paramétrica e da amplificação paramétrica em um oscilador linear parametricamente excitado. Em seguida, estudamos dois tipos de osciladores não-lineares parametricamente forçados e concluímos a dissertação com a análise de um dímero parametricamente excitado. Basicamente, analisamos os fenômenos de ressonância paramétrica e de amplificação paramétrica, comparando os resultados obtidos analiticamente (via métodos da média ou do balanço harmônico) com os obtidos via integração numérica das equações do movimento. Em todos os casos, obtivemos a linha de transição para a instabilidade paramétrica do oscilador paramétrico. Nós excitamos os amplificador paramétrico com e sem dessintonia entre entre o bombeamento e o sinal externo ac. Verificamos que o ganho da amplificação paramétrica depende da sensitivamente na fase do sinal externo ac e na amplitude do bombeamento. Mostramos que tais sistemas podem ser facilmente utilizados para recepção e decodificação de sinais com modulação de fase. Além disso, obtivemos séries temporais, envelopes e transformadas de Fourier para a resposta da amplificação paramétrica de pequenos sinais ac. Especificamente nos casos dos osciladores de Duffing parametricamente forçados, obtivemos e analisamos linhas de bifurcação e a amplitude dos ciclos limites como função da frequência e da amplitude de bombeamento. Adicionalmente, conseguimos obter uma relação analítica para os ganhos do sinal e do idler dos osciladores não-lineares parametricamente forçados pelo método do balanço harmônico. Os resultados obtidos implicam que os amplificadores paramétricos não-lineares podem ser excelentes detectores, especialmente em pontos próximos a bifurcações para instabilidade, em que apresentam altos ganhos e largura de banda bem estreitas. Por último, investigamos também o comportamento de dois osciladores lineares acoplados e parametricamente estimulados, com e sem força externa ac. Tais sistemas são muito sensíveis à fase do sinal a ser amplificado e podem ser utilizados para criar amplificadores sintonizáveis em função do parâmetro de acoplamento. / In this dissertation, we studied the dynamics of parametrically-driven oscillators, with a focus on the amplification of small signals. We begin with a revision of parametric resonance and parametric amplification in a linear oscillator parametrically excited. Next, we studied two types of nonlinear parametrically-driven oscillators and finished the dissertation with an analysis of a parametric dimer. Basically, we analyzed the phenomena of parametric resonance and parametric amplification by comparing the results obtained analytically (via the averaging or harmonic balance methods) with those of numerical integration of the equations of motion. In all cases, we obtained the transition line to parametric instability of the parametric oscillator. We excited the parametric amplifier with and without detuning between the pump and the external signal. We found that the parametric amplification depends sensitively on the phase of the external ac signal and on the internal pump amplitude. We showed that such amplifiers can be easily used for the reception and decoding of signals with phase modulation. Furthermore, we obtained time series, envelopes, and Fourier transforms of the response of the parametric amplifier to small external ac signals. Specifically in the cases of the parametrically-driven Duffing oscillators, we obtained and analysed the bifurcation lines and the amplitude of limit cycles as function of the pump amplitude and frequency. In addition, we derived an expression for the signal and idler gains of the nonlinear parametrically-driven oscillators with the harmonic balance method. The results imply that the nonlinear parametric amplifiers can be excellent detectors, specially near bifurcations to instability, due to their high gains and narrow bandwidths. Finally, we studied the dynamics of two linear oscillators coupled and parametrically excited, with and without external ac driving. We found that such systems have a wealth of dynamical responses. They present parametric amplification that is dependent on the coupling parameter and on the phases of the external ac signals. Such systems may be used as tunable amplifiers.

Cette étude porte sur la simulation dynamique de structures présentant des interfaces non linéaires et plus particulièrement sur le développement de diverses extensions à la méthode de balance harmonique. Cette méthode, qui permet le calcul de réponses vibratoires stationnaires, est basée sur l’approximation en série de Fourier tronquée de la réponse. En fonction de caractère plus ou moins non linéaire de la réponse, le nombre d’harmoniques à retenir pour approcher de façon satisfaisante la réponse peut être important et varier fortement sur l’ensemble de la plage de fréquence de simulation. Un des objectifs principaux de cette recherche a été de proposer une stratégie de calcul qui permette d’adapter le nombre d’harmoniques à chaque fréquence. Dans l’optique d’approcher le mouvement global de la structure, la méthodologie proposée se base sur le suivi de l’énergie de déformation du système en fonction de la richesse du contenu fréquentiel. La formulation développée reste simple à calculer et compatible avec les étapes de condensation interne à la méthode de balance harmonique. L’extension de cette technique au calcul de réponses quasi-stationnaires est en outre possible en redéfinissant les stratégies de choix des harmoniques à retenir. Parallèlement à ce but principal, la présence de variables internes dans les modèles non linéaires d’interface (modèle de frottement par exemple) a été prise en compte dans la formulation des équations de la balance harmonique adaptative. Ces méthodes spécifiques ont ensuite été mises en oeuvre sur des modèles numériques de structures aéronautiques. Un isolateur d’équipement utilisant un matériau viscoélastique non linéaire a ainsi pu être simulé. Ensuite, la méthode de balance harmonique adaptative a pu être appliquée à l’étude des effets dynamiques non linéaires observée sur les structures boulonnées. Enfin, le calcul de réponses quasi périodiques s’est effectué sur un tronçon de lanceur intégrant des amortisseurs à frottement sec. / The study deals with the dynamic simulation of structures with non linear interfaces and particularly with the development of various extensions of the harmonic balance method. This method, applied for steady state vibrations, is based on the response approximation with a truncated Fourier series. Depending on the more or less pronounced non linear response behavior, the number of harmonics to retain to correctly approach the response may be important and may strongly vary over all the frequency band. One of the main objectives of this research work has been to propose a calculation strategy which allows adapting the number of harmonics for each frequency. In order to globally approach the structure vibration, the proposed methodology basics is to observe the strain energy evolution functions of frequency contents. The developed formulation is easy to calculate and may be employed with internal reduction steps of the harmonic balance method. Moreover, an extension of this technique for quasi-periodic vibrations is possible by redefining harmonic choice strategies. In conjunction with this main objective, internal variables in non linear interface models (friction models for example) have been considered in a specific adaptive harmonic balance method formulation. Then, these specific methods have been applied on numerical aeronautical structure models. An equipment isolator integrating a non linear viscoelastic material has been simulated. Secondly, adaptive harmonic balance method has been employed for the study of non linear dynamic effects of bolted structures. Finally, quasi periodic vibration calculation has been carried out on a launcher stage integrating dry friction dampers.

Les ensembles turbo-alternateurs des centrales électriques sont de grandes machines tournantes de plus de 50 mètres de long et de plusieurs centaines de tonnes. Lors du fonctionnement normal d'une telle machine, une probabilité non nulle existe d'un détachement accidentel d'une aube. Dans une telle situation, un balourd important est généré et du contact apparaît entre les parties tournantes et non tournantes de la machine. Il est alors capital de pouvoir simuler efficacement la dynamique de ce type d'évènement faisant intervenir de fortes non linéarités dans le système. Cette thèse a été réalisée dans le cadre du projet ANR (Agence Nationale de la Recherche) IRINA (SImulation et maîtRise des rIsques en coNception des mAchines tournantes) et en particulier entre le LaMCoS (LAboratoire de Mécanique des Contacts et des Structures) de l'INSA de Lyon et le département AMA (Analyses Mécaniques et Acoustiques) d'EDF R et D à Clamart. Elle a pour objectif de mettre au point une technique rapide de simulation du comportement des lignes d'arbres de machines tournantes en cas de présence de non linéarité de type contact entre rotor et stator. Pour atteindre cet objectif, une double démarche a été mise en place. La première consiste à mettre au point des modèles simplifiés afin de réduire le nombre de degrés de liberté du problème. De surcroît, une technique de réduction de modèle adaptée au cas de non linéarité localisée est utilisée afin de réduire encore plus la taille du système à résoudre. La seconde démarche consiste à mettre au point une technique de résolution rapide du système réduit afin d'obtenir la solution encore plus rapidement. Pour cela, au lieu d'utiliser les traditionnelles techniques d'intégration temporelle directe, c'est la méthode de la balance harmonique qui est mise à profit. Cette technique permet d'obtenir directement la réponse stabilisée du système grâce à une résolution des équations dans le domaine fréquentiel. Dans ce cadre, une maquette numérique a été mise au point mettant en oeuvre les fonctionnalités citées. Cette dernière permet de reproduire les phénomènes physiques périodiques ainsi que quasi-périodiques et de déterminer leur stabilité. Des études paramétriques sur des exemples de problèmes de contact rotor-stator viennent illustrer cette démarche. Enfin, une application sur un cas industriel de groupe turbo alternateur EDF est présentée. / Power plants turbo-generator sets are large rotating machines of more than 50 meters long and weight several hundred tons. During normal operation of such a machine, there is a nonzero probability of an accidental disconnection of a blade. In such a situation, a significant imbalance is generated and contact may occur between the rotating and non-rotating parts. It is therefore essential to be able to effectively simulate the dynamics of this type of event involving strong nonlinearities in the system. This PhD was conducted within the framework of the ANR (Agence Nationale de la Recherche) IRINA (Simulation and risk control in rotating machinery design) and in particular between the LaMCoS (LAboratory of Contact Mechanics and Structures) of the INSA Lyon and the AMA department (Mechanical and Acoustic Analysis) at EDF R and D in Clamart. It aims to develop a fast technique for simulating the behavior of shafts of rotating machinery in case of presence of non-linearity of contact between rotor and stator. To achieve this goal, a dual approach was implemented. The first is to develop simplified models to reduce the number of degrees of freedom of the problem. In addition, a model reduction technique suitable for the case of localized nonlinearity is used to further reduce the size of the system to be solved. The second approach is to develop a technique for efficient resolution of the reduced system to obtain the solution more quickly. To do this, instead of using the traditional direct temporal integration techniques, the harmonic balance method is put to use. This technique allows to directly obtain the stabilized response of the system thanks to a resolution of the equations in the frequency domain. In this context, a numerical model has been developed to implement the features mentioned. The latter allows to reproduce the physical periodic and quasi-periodic phenomena and to determine their stability. Parametric studies of examples of problems of rotor-stator contact will illustrate this approach. Finally, an application on an industrial case of turbo generator EDF is presented.

The dissertation deals with simulations of the DC-DC converters in their basic configurations (Buck, Boost, Buck-boost, Cuk, SEPIC). In the first part of the thesis derivation of transfer functions Line-to-Output (LTO) and Control-To-Output (CTO) can be found. These symbolic responses are derived for three types of basic converters (Buck, Boost, Buck-boost) using well-known average model [1]. Derived expressions are very complicated. For reduction of these expressions symbolic approximation method was used, however the generality is lost. The average model was used to for decreasing the computational effort of analysis of DC-DC converters in the time domain. For these simulations VHDL-AMS language was used. The main topic of the thesis is harmonic balance method, which was adapted to DC-DC converters. Because conditions and assumptions for LTO and CTO functions are very different, harmonic balance method was derived into two variants. For obtaining of LTO response, duty cycle of switching signal can be considered as constant in time. Spectrum of this signal is simple as follows from well-known sinc function. For obtaining of CTO response PWM modulation must be used. Compared to sinc function spectrum of PWM modulation is richer (contains more combination frequencies). Many types of PWM modulation is described in [31]. For simulation PWM modulation with uniform sampling in two variants (single and double edge) was used. Non-ideal switching of PWM switch was modeled by PWM pulse with defined slew rate. Last section deals with comparison of all derived functions (LTO, CTO, modulation type, defined slew rate) with well-known averaged model.