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Les vibrations qui sont en général source de dérangement, d’usure et même destruction des machines et structures mécaniques doivent être contrôlées ou éliminées. Pour cette raison, la lutte contre les vibrations est devenue depuis des années un enjeu majeur pour les chercheurs de laboratoire et de développement dans l’industrie afin de développer des solutions efficaces contre ces problèmes. De nombreuses technologies ont donc été développées. Parmi ces technologies, les absorbeurs de vibration non linéaires présentent des performances importantes dans l’atténuation de vibration sur une large bande de fréquences. C’est dans ce contexte que cette thèse se focalise sur l’analyse et l’optimisation des absorbeurs de vibration non linéaires. L’objectif de cette thèse est d’analyser le comportement dynamique non linéaire des systèmes présentant des absorbeurs de vibration non linéaires. Pour cela, un modèle dynamique d’un système à deux degrés de liberté est développé mettant en équations le comportement non linéaire. La résolution des équations de mouvement est faite par la Méthode Asymptotique Numérique (MAN). La performance de cette méthode est montrée via une comparaison avec la méthode de Newton-Raphson. L’analyse des modes non linéaires du système ayant une non-linéarité cubique est faite par une formulation explicite des Fonctions de Réponse en Fréquence non linéaires (FRFs) et les Modes Normaux Non linéaires (MNNs). Un démonstrateur sur la base d’un système simple à deux degré de liberté est mis en place afin de recaler les modèles envisagés sur la base des résultats expérimentaux trouvés. / Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. For this reason, the vibrations attenuation became a major issue for scientists and researchers in order to develop effective solutions for these problems. Many technologies have been developed. Among these technologies, the nonlinear vibration absorbers have significant performance in the vibration attenuation over a wide frequency band. In this context, this thesis focuses on the analysis and optimization of nonlinear vibration absorbers. The objective of the thesis is to analyze the nonlinear dynamic behavior of systems with nonlinear vibration absorbers. For this, a dynamic model of a two degrees of freedom system is developed. The Asymptotic Numerical Method (ANM) is used to solve the nonlinear equations of motion. The performance of this method is shown via a comparison with the Newton-Raphson method. The nonlinear modal analysis system with cubic nonlinearity is made by an explicit formulation of the nonlinear Frequency Response Functions (FRFs) and Nonlinear Normal Modes (MNNs). An experimental study is performed to validate the numerical results.

No contexto da fonação, as pregas vocais são responsáveis pela produção primária do sinal de voz na laringe. Tão importantes quanto complexas, elas exibem uma dinâmica rica e uma série de comportamentos que determinam as características fundamentais do sinal emitido pela boca. Com o intuito de avaliar suas propriedades sob a luz dos métodos da dinâmica não-linear de sistemas, este trabalho tem por objetivo principal desenvolver uma técnica de extração e simulação de sua dinâmica. Para isto são empregados modelos determinísticos das pregas vocais e imagens de videolaringoscopia de alta velocidade. Estes elementos são usados para reproduzir a dinâmica e cinemática das pregas de indivíduos saudáveis através de um procedimento de otimização dos parâmetros mecânicos destes modelos de pregas. Feito isto, os modelos são usados para avaliar o comportamento não-linear das pregas vocais através de uma análise modal não-linear cujo propósito foi descrever como as não-linearidades estruturais das pregas podem influenciar na voz. Os resultados mostram a eficiência de um método capaz de reproduzir a maior parte dos padrões de vibração das pregas e uma relação de dependência entre sua energia mecânica e sua frequência fundamental de vibração, que é fruto das não-linearidades estruturais das pregas vocais. / As far as phonation is concern, the vocal folds produce the primary voice signal within larynx. As important as complex, they exhibit a rich dynamics capable to influence the fundamental voice features. In light of nonlinear dynamical methods, this work has as purpose to develop a method to extract and simulate the vocal folds dynamics. Deterministic vocal folds models and high-speed videolaryngoscopy are used to reproduce the dynamics of healthy subjects and evaluate their nonlinear behavior and some phenomena raised by the nonlinearities. Nonlinear normal modes are employed to understanding how the nonlinearities may influence the primary phonation. The results show that the method could reflect the most important vibratory patterns. Additionally, the nonlinear analysis has shown energy-frequency dependence and a complex dynamics with structural nonlinearities.

No contexto da fonação, as pregas vocais são responsáveis pela produção primária do sinal de voz na laringe. Tão importantes quanto complexas, elas exibem uma dinâmica rica e uma série de comportamentos que determinam as características fundamentais do sinal emitido pela boca. Com o intuito de avaliar suas propriedades sob a luz dos métodos da dinâmica não-linear de sistemas, este trabalho tem por objetivo principal desenvolver uma técnica de extração e simulação de sua dinâmica. Para isto são empregados modelos determinísticos das pregas vocais e imagens de videolaringoscopia de alta velocidade. Estes elementos são usados para reproduzir a dinâmica e cinemática das pregas de indivíduos saudáveis através de um procedimento de otimização dos parâmetros mecânicos destes modelos de pregas. Feito isto, os modelos são usados para avaliar o comportamento não-linear das pregas vocais através de uma análise modal não-linear cujo propósito foi descrever como as não-linearidades estruturais das pregas podem influenciar na voz. Os resultados mostram a eficiência de um método capaz de reproduzir a maior parte dos padrões de vibração das pregas e uma relação de dependência entre sua energia mecânica e sua frequência fundamental de vibração, que é fruto das não-linearidades estruturais das pregas vocais. / As far as phonation is concern, the vocal folds produce the primary voice signal within larynx. As important as complex, they exhibit a rich dynamics capable to influence the fundamental voice features. In light of nonlinear dynamical methods, this work has as purpose to develop a method to extract and simulate the vocal folds dynamics. Deterministic vocal folds models and high-speed videolaryngoscopy are used to reproduce the dynamics of healthy subjects and evaluate their nonlinear behavior and some phenomena raised by the nonlinearities. Nonlinear normal modes are employed to understanding how the nonlinearities may influence the primary phonation. The results show that the method could reflect the most important vibratory patterns. Additionally, the nonlinear analysis has shown energy-frequency dependence and a complex dynamics with structural nonlinearities.

La dynamique des structures assemblées est un sujet de recherche actuel. En particulier, une prédiction correcte de l'amortissement apporté par les liaisons vissés est devenu une condition essentiel pour un certain nombre d'applications, comme par exemple les avions et les véhicules spatiaux. En effet, pour ces applications, l’utilisation de matériaux avec un coefficient d'amortissement plus élevée, comme des matériaux visco-élastiques, est limité par les conditions de fonctionnement.Ces travaux apportent deux contributions principales. La première porte sur la phase de conception et modélisation, avec la création d'un système de connecteurs pour la reproduction des comportements normal et tangentiel d'une liaisons vissée. Cela est accomplie en considérant seulement les données physiques de la liaison et des surfaces en contact.La deuxième contribution concerne l’évaluation des propriétés dynamiques non-linéaires des assemblages. Un set d'outils de post-traitement utilisant le filtre de Kalman est développé pour réaliser une analyse modale non-linéaire pour les types d'essais les plus communs: les essais aux chocs, les essais en balayage sinus, et les essais en sinus aléatoire.Les méthodes développées ont été appliqués et évaluées sur une structure boulonnée réel, en soulignant les avantages et les inconvénients. Notamment, le filtre de Kalman permet une meilleure précision sur les paramétrés identifiés, mais le procédé d’initialisation du filtre est le problème principal. Une automatisation partiel de l’initialisation est prévu, ainsi que des conseils pratiques grâce à l’expérience acquise sur le sujet. / Bolted structures dynamics is an ongoing research topic. In particular, a correct prediction of the damping provided by bolted joints has became an essential requirement for a certain number of applications, such as aircrafts and space vehicles. In fact, for these applications, the use of materials with higher damping coefficients is limited by environmental conditions.This work provides two main contributions. The first one concerns the design and modeling phase, with the creation of a finite element connectors' system, that reproduces the bolted joint normal and tangential behaviors. The latter is accomplished only by taking into account readily available physical data, such as the bolted joint dimensions and the properties of the surfaces in contact. The second contribution regards the evaluation of assembled structures' nonlinear dynamic properties. A set of post-processing tools making use of the Kalman filter is developed to perform a nonlinear modal analysis for the most common types of experimental tests: impact hammer tests, sweep sine tests, and random vibration tests.The developed methods are then applied and evaluated on a real bolted structure, pointing out advantages and drawbacks. In particular, the Kalman filter allows for a higher accuracy in the determination of modal parameters, but the filter initialization is the main problem. A partial automation of the initialization task is provided, together with practical tips thanks to the experience gained on the subject.