O fenômeno de vibração induzida por vórtices (VIV) é um problema fundamental dentro da Mecânica dos Fluidos e um exemplo importante de interação fluido-estrutura. Esta tese investiga fenômeno de VIV quando um cilindro rígido, submetido a escoamento uniforme, está livre para oscilar na direção transversal e alinhada com a corrente incidente. A tese foi estruturada ao redor de sete perguntas relacionadas ao fenômeno de VIV: 1) O fenômeno e os resultados experimentais são repetitivos? 2) Como ocorre a transição entre ramos de resposta? 3) Qual é o papel da inércia da estrutura oscilante? 4) Qual é o papel de sua rigidez? 5) Quais são as frequências naturais mais importantes da estrutura? 6) Quais padrões de esteira se desenvolvem para VIV com dois graus de liberdade? 7) Quais são os efeitos do movimento na direção alinhada com a corrente no processo de formação e desprendimento de vórtices? O fenômeno de VIV é estudado de maneira experimental em uma base elástica pendular capaz de oscilar com o mesmo momento de inércia e frequência natural nas duas direções. Os experimentos de VIV foram realizados em canal de água recirculante e com diferentes condições de inércia e rigidez. A técnica de velocimetria por imagem de partículas foi usada e permitiu identificar diferentes padrões de esteira de vórtices. Verificou-se que o VIV é repetitivo a nível de amplitudes médias e frequências dominantes. A transição dos ramos pode ocorrer de maneira intermitente ou com histerese. Os parâmetros de inércia e rigidez da estrutura são capazes de mudar o regime de oscilação e, para algumas condições, suprimir as vibrações alinhadas com a corrente. Dentre os padrões de esteira observados, um deles não havia sido relatado na literatura e é definido nesta tese. O novo modo de emissão apresenta dois vórtices com circulação oposta e elevada intensidade emitidos por ciclo. A influência da direção alinhada com o escoamento está relacionada a dois efeitos: a velocidade relativa entre o cilindro e o fluido, responsável pelo aumento da circulação dos vórtices na esteira, e o ângulo de fase do movimento nas direções alinhada e transversal, capaz de mudar o processo de formação dos vórtices. / Vortex-induced vibration (VIV) phenomenon is a fundamental problem of Fluid Mechanics and a typical example of fluid-structure interaction. This thesis explores the VIV phenomenon for a rigid circular cylinder immersed in a uniform fluid current. The cylinder is free to oscillate in two degrees of freedom (2dof): in-line and cross flow. The thesis was structured in order to answer seven questions regarding VIV: 1) Are the phenomenon and its experimental results repetitive? 2) How do the branches transition occur? 3) What is the role played by the inertia of the oscillating structure? 4) What is the role of its stiffness? 5) Which are the most relevant natural frequencies of the structure? 6) Which are the vortex wake patterns developed in VIV 2dof? 7) What are the influences of the in-line movement to the process of vortex formation and shedding? The phenomenon is experimentally investigated using an elastic base similar to a pendulum and able to oscillate with the same moment of inertia and natural frequencies in both directions. All the experiments were conducted in a recirculating water channel facility and with several combinations of moment of inertia and stiffness of the structure. Particle image velocimetry provided visualization of different vortex wake patterns. The phenomenon is repetitive in terms of its mean amplitudes and dominant frequencies. The transitions between dfferent branches can be hysteretic or intermittent. It is shown that both the moment of inertia and the stiffness of the structure are able to change the regime of oscillations and, for some cases, suppress the in-line movement. Among the different vortex wake patterns observed, one has not been reported previously in the literature. The new wake pattern shows two large vortices with high and opposite circulations shed per cycle. The influence of the displacement in the current direction is related to two different effects: the relative velocity between the incoming flow and the structure motion, responsible for the increase in the net circulation shed in the vortex wake, and the influence of the phase angle between the displacement in the in-line and cross-flow directions, capable of changing the vortex formation process.

Este trabalho pode ser dividido em três etapas principais. Inicialmente é proposta uma formulação estabilizada do método dos elementos finitos (MEF) para solução de problemas de escoamento incompressível governado pela equação de Navier-Stokes. Esta formulação foi implementada em um código computacional e testada através de diversos exemplos numéricos. Alguns elementos finitos com diferentes pares de função de interpolação da velocidade e pressão, consagrados na literatura, e também elementos finitos menos populares, foram investigados e seus resultados e performance comparados. A segunda etapa consiste na formulação do problema estrutural. Buscou-se por uma formulação dinâmica, não linear, capaz de simular movimentos complexos de estruturas sujeitas a grandes deslocamentos e grandes deformações durante longos intervalos de tempo. A etapa final deste trabalho é a proposição de um método para solução de problemas de Interação Fluido Estrutura (IFE) que utiliza o conceito de fronteiras imersas como alternativa a abordagens ALE (Arbitrary Lagrangian Eulerian) clássicas. Elementos Finitos Generalizados, juntamente com Multiplicadores de Lagrange, são utilizados para prover descontinuidade nos campos de velocidade e pressão do fluido ao longo da interface com a estrutura. O acoplamento dos dois problemas é realizado utilizando um método implícito e alternado (staggered scheme), que possui a vantagem de permitir, facilmente, a implementação de códigos computacionais desenvolvidos para resolver isoladamente o problema fluido e/ou estrutural. / This work is divided in three parts. Initially, it is presented a stabilized Finite Element Method formulation to solve fluid flow problems governed by the incompressible Navier-Stokes Equations. This formulation was implemented in a computer code and validated throughout several numeric simulations. Some well-known finite elements with different pairs of velocity/pressure approximations, as well as some other less popular elements, were investigated and their performance compared. The second part describes the Structural Problem formulation. This formulation is able to simulate nonlinear dynamic problems involving large displacements and finite strains during long period of time. In the final part of this work, it is proposed a Fluid-Structure Interaction method based on an immersed interface approach in opposition to classical ALE (Arbitrary Lagrangian Eulerian) approaches. Generalized Finite Elements, together with Lagrange Multipliers, are used to provide velocity and pressure discontinuities on the fluid domain across the immersed interface. To couple both fluid and structural problems, an implicit staggered scheme is adopted, which allows the easy implementation of already developed black box computer codes.

Several nuclear research reactors use or are planned with cores containing flat-plate- type fuel elements. The nuclear fuel is contained in parallel plates that are separated by narrow channels through which the fluid flows to remove the heat generated by fission reactions. One of the problems of this fuel element design is the mechanical stability of the fuel plates. High-velocity coolant flowing through the channels can cause large deflections of these plates leading to local overheating, structural failure or plate collapse. As a consequence, the safe operation of the reactor may be affected. In this work, a numerical fluid-structure interaction study was conducted for evaluating the mechanical stability of nuclear fuel plates under axial flow conditions. Five different cases were analyzed. In all cases, the system consisted of two fuel plates bounded by fluid channels but, in case 5, a support comb at the leading edge of the plates was inserted. The pressure loadings caused by the fluid flow were calculated using a Computational Fluid Dynamics model created with ANSYS CFX. The structural response was determined by means of a Finite Element Analysis model generated with ANSYS Mechanical. Both models were coupled using the two-way fluid-structure interaction approach. The results from Case 1 allowed proposing a methodology to predict the critical velocity of the assembly without an inlet support comb. The maximum deflection of the plates was detected at their leading edges. It was detected that, for flow rates in the channels less than a certain value, the maximum deflection increased linearly with the square of the coolant velocity. In contrast, for greater flow rates, a nonlinear behavior was observed. Therefore, that fluid velocity was identified as the critical velocity of the system. Besides, above the critical velocity, an extra deflection peak was observed near the trailing edge of the plates. In cases 2, 3 and 4, the influence of manufacturing deviations and the change of materials properties due to the increment of temperature on the critical velocity was investigated. With these conditions, the critical velocity of the system was found at lower values. Lastly, in Case 5, the effectiveness of using a support comb at the leading edge of the plates was investigated. The results showed that the static divergence at the inlet end is effectively eliminated with the installation of the comb. In addition, the flow-induced deflections along the length of the plates were significantly diminished with the comb. / Muitos reatores nucleares de pesquisa usam ou são planejados com elementos combustíveis tipo placas planas. O combustível nuclear está contido em placas paralelas que são separadas por canais estreitos através dos quais o fluido refrigerante passa para remover o calor gerado pelas reações de fissão. Um dos problemas deste tipo de elemento combustível é a estabilidade mecânica das placas de combustível. O líquido refrigerante a alta velocidade pode causar deflexões excessivas dessas placas, bloqueando o canal de escoamento e levar ao superaquecimento nas placas, falha estrutural ou colapso da placa. Como consequência, a operação segura do reator pode ser afetada. Neste trabalho, foi realizado um estudo numérico de interação fluido-estrutura para avaliar a estabilidade mecânica de placas de combustível nuclear sob condições de fluxo axial. Cinco diferentes casos foram analisados. Em todos os casos, o sistema consistiu em duas placas de combustível delimitadas por canais de fluido, mas, no caso 5, um pente de suporte na borda de ataque das placas foi inserido. As cargas de pressão causadas pela vazão foram calculadas usando um modelo de Dinâmica dos Fluidos Computacional, criado com ANSYS CFX. A resposta estrutural foi determinada por meio de um modelo de elementos finitos, gerado com ANSYS Mechanical. Os modelos foram acoplados usando a abordagem de interação fluido-estrutura bidirecional. Os resultados do Caso 1 permitiram propor uma metodologia para prever a velocidade crítica do sistema sem o pente de suporte. A deflexão máxima das placas foi observada em suas bordas de ataque. Foi detectado que, para velocidades nos canais inferiores a um determinado valor, a deflexão máxima aumentava linearmente com o quadrado da velocidade do líquido refrigerante. Em contraste, para maiores vazões, um comportamento não linear foi observado. Portanto, essa velocidade do fluido foi identificada como a velocidade crítica. Além disso, acima da velocidade crítica, um pico extra de deflexão foi observado próximo à borda de saída das placas. Nos casos 2, 3 e 4, a influência dos desvios de fabricação e da alteração das propriedades dos materiais devido ao incremento de temperatura na velocidade crítica foi investigada. Sob essas condições, a velocidade crítica foi encontrada a valores mais baixos. Por fim, no Caso 5, a eficácia do uso do pente de suporte na borda de entrada das placas foi estudada. Os resultados mostraram que a divergência estática na extremidade de entrada foi efetivamente eliminada com a instalação do pente. Além disso, as deflexões induzidas pelo fluido ao longo do comprimento das placas foram significativamente diminuídas com o pente.

Cette thèse vise à obtenir et à développer des modèles mathématiques pour comprendre certains aspects de la dynamique des fluides granulaires hétérogènes. Plus précisément, le résultat attendu consiste à développer trois modèles. Nous supposons dans un premier temps que la dynamique du matériau granulaire est modélisée à l’aide d’une approche fondée sur la théorie du mélange. D’autre part, pour les deux modèles restant, nous considérons que le fluide granulaire est modélisé à l’aide d’une approche multiphase associant des structures et des fluides rigides. Plus exactement : • Dans le premier modèle, nous avons obtenu un ensemble d’équations basées sur la théorie du mélange en utilisant des outils d’homogénéisation et une procédure thermodynamique. Ces équations reflètent deux propriétés essentielles des fluides granulaires : la nature visqueuse du fluide interstitiel et un comportement de type Coulomb de la composante granulaire. Avec nos équations, nous étudions le problème de Couette entre deux cylindres infinis d’un écoulement hétérogène granulaire dense, composé d’un fluide newtonien et d’une composante solide. • Dans le deuxième modèle, nous considérons le mouvement d’un corps rigide dans un matériau viscoplastique. Les équations 3D de Bingham modélisent ce matériau et les lois de Newton régissent le déplacement du corps rigide. Notre résultat principal est d’établir l’existence d’une solution faible pour le système correspondant. • Dans le troisième modèle, nous considérons le mouvement d’un corps rigide conducteur thermique parfait dans un fluide newtonien conducteur de la chaleur. Les équations 3D de Fourier-Navier-Stokes modélisent le fluide, tandis que les lois de Newton et l’équilibre de l’énergie interne modélisent le déplacement du corps rigide. Notre principal objectif dans cette partie est de prouver l’existence d’une solution faible pour le système correspondant. La formulation faible est composée de l’équilibre entre la quantité du mouvement et l’équation de l’énergie totale, qui inclut la pression du fluide, et implique une limite libre due au mouvement du corps rigide. Pour obtenir une pression intégrable, nous considérons une condition au limite de glissement de Navier pour la limite extérieure et l’interface mutuelle / This Ph.D. thesis aims to obtain and to develop some mathematical models to understand some aspects of the dynamics of heterogeneous granular fluids. More precisely, the expected result is to develop three models, one where the dynamics of the granular material is modeled using a mixture theory approach, and the other two, where we consider the granular fluid is modeled using a multiphase approach involving rigid structures and fluids. More precisely : • In the first model, we obtained a set of equations based on the mixture theory using homogenization tools and a thermodynamic procedure. These equations reflect two essential properties of granular fluids : the viscous nature of the interstitial fluid and a Coulomb-type of behavior of the granular component. With our equations, we study the problem of a dense granular heterogeneous flow, composed by a Newtonian fluid and a solid component in the setting of the Couette flow between two infinite cylinders. • In the second model, we consider the motion of a rigid body in a viscoplastic material. The 3D Bingham equations model this material, and the Newton laws govern the displacement of the rigid body. Our main result is the existence of a weak solution for the corresponding system. • In the third model, we consider the motion of a perfect heat conductor rigid body in a heat conducting Newtonian fluid. The 3D Fourier-Navier-Stokes equations model the fluid, and the Newton laws and the balance of internal energy model the rigid body. Our main result is the existence of a weak solution for the corresponding system. The weak formulation is composed by the balance of momentum and the balance of total energy equation which includes the pressure of the fluid, and it involves a free boundary (due to the motion of the rigid body). To obtain an integrable pressure, we consider a Navier slip boundary condition for the outer boundary and the mutual interface

O presente trabalho consiste no desenvolvimento de um código computacional baseado no método dos elementos finitos (MEF), para análise bidimensional de interação fluido-estrutura. Desenvolve-se um código bidimensional para dinâmica de fluidos compressíveis, viscosos ou não, em formulação Euleriana, com base no algoritmo CBS – characteristic based split. Então o código desenvolvido é adaptado para poder ser acoplado a um programa de formulação Lagrangeana para análise dinâmica de estruturas, o que é feito através do emprego da descrição Lagrangeana - Euleriana arbitrária (ALE). Por fim procede-se o acoplamento com um código para análise de estruturas, de formulação posicional e não linear geométrica, baseado no método dos elementos finitos. / The present work consists of the development of a computational code based on the element finite method for fluid-structure interaction analysis. A two-dimensional fluid dynamic Eulerian code is developed based on the CBS algorithm – characteristic based split. Then, the computational code is modified to be coupled with a Lagrangean structures dynamical code by using the arbitrary Lagrangean – Eulerian description (ALE). At the end, the coupling is made with a positional nonlinear geometrical structural dynamics code based on the finite element method.

Apresentam-se as bases teóricas do Método de Elementos Finitos (MEF) piezoelétrico, e a sua aplicação na modelagem de transdutores de ultra-som piezoelétricos, que consiste na determinação das características vibracionais (frequências de ressonância e anti-ressonância, modos de vibrar e coeficiente de acoplamento eletromecânico), obtenção da curva de admitancia, análise transiente da estrutura piezoelétrica sujeita a uma excitação pulsada e análise da influência da variação das constantes piezoelétricas do transdutor com o raio. Utilizando-se o MEF aplicado a acústica obteve-se o campo acústico gerado pelo transdutor operando em onda contínua, bem como iniciou-se o estudo da propagação de ondas num líquido, analisando-se as ondas geradas pela excitação pulsada de um pistão plano em contato com o fluido. Os modos de vibrar e os valores de frequências de ressonância obtidos para um transdutor, foram comparados com os resultados experimentais. / The theoretical basis of piezoelectric finite element method (FEM), and its application in piezoelectric ultrasonic transducer modelling is presented. Among these applications we have the calculation of resonance and antiresonance frequencies, vibration modes, piezoelectric coupling coefficient, admittance curve and transient analysis of piezoelectric structure excited by a short pulse. By means of piezoelectric FEM the influence of variation of piezoelectric constant with radius is analysed. It is discussed three kind of functions (linear, cosinoidal and Gaussian). This technique is called apodization. The acoustic filed generated by the transducer operating in continuous wave (CW) was calculated by using FEM applied to acoustic, considering the fluid-structure coupling. The study of wave propagation in liquids is started by using FEM, analyzing the waves generated by a plane piston in contact with the fluid, excited by a short pulse. For each case discussed above, all boundary conditions and hypothesis assumed in the construction of finite element models are discussed. Although the models considered are circular transducers, the concepts acquired can be expanded to other geometries. The vibrational modes were visualized by means of a laser interferometry technique (ESPI), and the admittance curves were measured by using an impedometer. These results were compared with the FEM results, and the models precision was discussed.

Les travaux de cette thèse ont pour but de développer un prototype d’éco-pilote, nommé EcoNav, permettant d’optimiser la vitesse d’un bateau afin de réduire sa consommation de carburant. EcoNav est composé de plusieurs modules dont : un modèle hydraulique 2D simulant l’écoulement hydrodynamique (vitesse du courant et hauteur d’eau) le long du trajet du bateau; - un modèle de résistance à l’avancement servant à alimenter un modèle de prédiction de la consommation de carburant; - un algorithme d’optimisation permettant de trouver le profil optimal de vitesse. Afin de pouvoir estimer la consommation de carburant, un modèle numérique de la résistance à l’avancement en milieu confiné a été développé durant la première partie de cette thèse. Ce modèle numérique 3D simule l’écoulement du fluide autour du bateau et permet de calculer les forces agissant sur sa coque. La résolution des équations RANS est couplée avec un algorithme de quasi-Newton afin de trouver la position d’équilibre du bateau et calculer son enfoncement. Cette méthode est validée en comparant les résultats numériques avec des résultats expérimentaux issus d’essais en bassin de traction. L’influence de l’enfoncement sur la résistance à l’avancement et la précision de la méthode est étudiée en comparant les résultats numériques obtenus avec et sans enfoncement. La précision des modèles empiriques de prédiction de la résistance à l’avancement est également comparée à celle du modèle numérique. Enfin, le modèle numérique est utilisé afin de déterminer si le confinement en largeur ou en profondeur ont une influence identique sur l’augmentation de résistance à l’avancement. Les résultats de cette étude permettent d’établir si le confinement de la voie d’eau peut être caractérisé à l’aide d’un paramètre unique (coefficient de blocage par exemple) ou bien deux paramètres permettant de distinguer le confinement latéral et vertical. Dans la seconde partie de cette thèse, les méthodes numériques utilisées pour le modèle d’éco-pilote sont décrites et comparées afin de sélectionner celles qui sont le plus adaptées à chaque module. EcoNav est ensuite utilisé afin de modéliser un cas réel : celui du bateau automoteur Oural navigant sur la Seine entre Chatou et Poses (153 km). La consommation optimisée est comparée à la consommation non optimisée, calculée à partir des vitesses AIS observées sur le tronçon étudié. L’influence de la trajectoire du bateau et de son temps de parcours sur sa consommation sont également étudiés. Les résultats de ces investigations ont montré qu’optimiser la vitesse du bateau permet d’obtenir une réduction de la consommation de carburant de l’ordre de 8 % et qu’optimiser la trajectoire du bateau ainsi que prendre en compte des informations en temps réel (disponibilité des écluses, trafic sur le fleuve) peuvent permettre de réaliser des économies de carburant supplémentaires. / An eco-driving prototype, named EcoNav, is developed with the aim of optimizing a vessel speed in order to reduce fuel consumption for a given itinerary. EcoNav is organized in several modules : - a 2D hydraulic model simulating the flow conditions (current speed and water depth) along the itinerary; - a ship resistance model calculating the thrust necessary to counteract the hydrodynamic forces ; - a fuel consumption model calculating the fuel consumption corresponding to the thrust input; - a non linear optimization algorithm calculating the optimal speed profile. In order to evaluate the fuel consumption of an inland vessel, a ship resistance numerical model is developed in the first part of this PhD. This 3D numerical model simulates the flow around an inland self-propelled vessel and evaluates the hydrodynamic forces acting on the hull. A RANS solver is coupled with a quasi-Newton approach to find the equilibrium position and calculate ship sinkage. This method is validated by comparing the results of numerical simulations to towing tank tests. The numerical results with and without sinkage are also compared to study the influence of sinkage on ship resistance and on the accuracy of the method. Additionally, some empirical models are investigated and compared with the accuracy of the numerical method. Finally, the numerical model is used to determine if channel with and water depth restriction contribute to the same amount of ship resistance increase for the same level of restriction. The results of that investigation give insight to whether channel restriction can be characterized by a unique parameter (for instance the blockage ratio) or two parameters to distinguish water depth and channel with effects. In the second part of this PhD, the numerical methods used in the speed optimization model are described and validated. The speed optimization model is then used to simulate a real case: the itinerary of the self-propelled ship Oural on river Seine, between Chatou and Poses (153 km). The optimized fuel consumption is compared with the non-optimized fuel consumption, based on AIS speed profile retrieved on this itinerary. The effects of the ship trajectory and travel duration on fuel consumption are also investigated. The results of those investigations showed that optimizing the ship speed lead to an average fuel saving of 8 % and that using an optimal track and including real time information such as lock availability and river traffic can lead to additional fuel savings.

The marine current turbine (MCT) is an exciting proposition for the extraction of renewable tidal and marine current power. However, the numerical prediction of the performance of the MCT is difficult due to its complex geometry, the surrounding turbulent flow and the free surface. The main purpose of this research is to develop a computational tool for the simulation of a MCT in turbulent flow and in this thesis, the author has modified a 3D Large Eddy Simulation (LES) numerical code to simulate a three blade MCT under a variety of operating conditions based on the Immersed Boundary Method (IBM) and the Conservative Level Set Method (CLS). The interaction between the solid structure and surrounding fluid is modelled by the immersed boundary method, which the author modified to handle the complex geometrical conditions. The conservative free surface (CLS) scheme was implemented in the original Cgles code to capture the free surface effect. A series of simulations of turbulent flow in an open channel with different slope conditions were conducted using the modified free surface code. Supercritical flow with Froude number up to 1.94 was simulated and a decrease of the integral constant in the law of the wall has been noticed which matches well with the experimental data. Further simulations of the marine current turbine in turbulent flow have been carried out for different operating conditions and good match with experimental data was observed for all flow conditions. The effect of waves on the performance of the turbine was also investigated and it has been noticed that this existence will increase the power performance of the turbine due to the increase of free stream velocity.

The velocity field in the wake of a small scale flexible parachute canopy was measured using two-dimensional particle image velocimetry. The experiments were performed in a water tunnel with the Reynolds number ranging from 3.0-6.0 x 104. Both a fully inflated canopy and the inflation phase were investigated in a constant freestream (i.e. an infinite mass condition). The fully inflated canopy experienced a cyclic“breathing" which corresponded to the shedding of a vortex ring from the canopy. The normalized breathing frequency had a value of 0.56 +/- 0.03. The investigation of the canopy inflation showed that during the early stages of the inflation, the boundary layer on the canopy surface remains attached to the canopy while the canopy diameter increases substantially. The boundary layer begins to separate near the apex region when the diameter is ~68% of the fully inflated diameter. The separation point then progresses upstream from the canopy apex region toward the canopy skirt. During this time period, the force rapidly increases to its maximum value while the separation point of the boundary layer moves upstream towards the skirt. The force then declines rapidly and the separated boundary layer rolls-up into a large vortex ring near the canopy skirt. At the same time, the canopy is drawn into an over-expanded state after which the cyclic breathing initiates. The unsteady potential force was estimated from the rate of change of the canopy volume. It contributed no more than 10% of the peak opening force and was only significant during the early stages of inflation. The majority of the opening force was the result of the time rate of change of the fluid impulse. It accounts for approximately 60% of the peak opening force. This result shows that the formation of the viscous wake is the primary factor in the peak drag force of the canopy.

La maîtrise du bruit et des vibrations est un objectif fréquemment rencontré dans le domaine industriel. Qu’il s’agisse de questions de confort ou de sécurité, les domaines d’applications sont nombreux et variés : transport, BTP, ingénierie civile et militaire… Dans cette thèse, un problème de vibroacoustique interne avec couplage fluide-structure est étudié. Il s’agit d’une cavité remplie de fluide dont les parois sont constituées d’une structure sandwich viscoélastique. Les difficultés numériques associées à ce modèle portent sur la non linéarité du matériau et sur les propriétés des opérateurs matriciels manipulés (conditionnement, non symétrie). Le calcul des vibrations du système dissipatif couplé nécessite une valeur initiale, choisie comme la solution du problème conservatif. Cette solution n’étant pas aisée à déterminer, deux solveurs aux valeurs propres basés sur la Méthode Asymptotique Numérique (MAN) sont proposés pour résoudre le problème des vibrations libres du système conservatif. Associant des techniques de perturbation d'ordre élevé et de continuation, la MAN permet de transformer le problème non linéaire de départ en une suite de problèmes linéaires, plus simples à résoudre. Les solutions obtenues sont ensuite utilisées comme point initial pour déterminer la réponse libre du système dissipatif. Un solveur de Newton d’ordre élevé, basé sur les techniques d’homotopie et de perturbation est développé pour résoudre ce problème. Enfin, le régime forcé est étudié. Pour toutes les configurations envisagées, les résultats obtenus mettent en évidence des performances numériques améliorées par rapport aux méthodes classiquement utilisées (Arpack, Newton…). / Noises and vibrations control is a common objective in the industrial field. Whether it is a question of comfort or safety, the fields of application are numerous and varied: transport, building, civil and military engineering… In this thesis, a vibroacoustics interior problem with fluid-structure coupling is studied. A cavity filled of fluid whose walls are made of a sandwich viscoelastic structure is considered. The numerical difficulties associated with this model relate to the non-linearity of the viscoelastic material and the properties of the matrix operators used (conditioning, non-symmetry). The calculation of the vibrations of the coupled dissipative system requires an initial value, chosen as the solution to the conservative problem. Since this solution is difficult to determine, two eigenvalue algorithms based on the Asymptotic Numerical Method (ANM) are proposed to solve the problem of free vibrations of the conservative system. Combining high order perturbation and continuation techniques, ANM transforms the initial non-linear problem into a set of linear problems that are easier to solve. The solutions obtained are then used as the initial point to determine the free vibrations of the dissipative problem. A high order Newton solver, based on homotopy and perturbation techniques, is developed to solve this problem. Finally, the forced harmonic response of the damped system is computed. For all the configurations tested, the results obtained show improved numerical performance compared to the methods conventionally used (Arpack solver, Newton algorithm…).