Vibration control is a large branch in control research, because all moving systems may induce desired or undesired vibration. Due to the limitation of passive system's adaptability and changing excitation input, vibration control brings the solution to change system dynamic with desired behavior to fulfill control targets. According to preference, vibration control can be separated into two categories: vibration reduction and vibration amplification. Lots of research papers only examine one aspect in vibration control. The thesis investigates the control development for both control targets with two different control applications: vehicle suspension and ocean wave energy converter. It develops control methods for both systems with simplified modeling setup, then followed by the application of a novel mechanical motion rectifier (MMR) gearbox that uses mechanical one-way clutches in both systems. The flow is from the control for common system to the control design for a specifically designed system. In the thesis, active (model predictive control: MPC), semi-active (Skyhook, skyhook-power driven damper: SH-PDD, hybrid model predictive control: HMPC), and passive control (Latching Control) methods are developed for different applications or control performance comparison on single system. The thesis also studies about new type of system with switching mechanism, in which other papers do not talk too much and possible control research direction to deal with such complicated system in vibration control. The state-space modeling for both systems are provided in the thesis with detailed model of the MMR gearbox. From the simulation, it can be shown that in the vehicle suspension application, the controlled MMR gearbox can be effective in improving vehicle ride comfort by 29.2% compared to that of the traditional hydraulic suspension. In the ocean wave energy converter, the controlled MMR WEC with simple latching control can improve the power generation by 57% compared to the passive MMR WEC. Besides, the passive MMR WEC also shows its advantage on the passive direct drive WEC in power generation improvement. From the control development flow for the MMR system, the limitation of the MMR gearbox is also identified, which introduces the future work in developing active-MMR gearbox by using an electromagnetic clutch. Some possible control development directions on the active-MMR is also mentioned at the end of the thesis to provide reference for future works. / Master of Science / Vibration happens in our daily life in almost all cases. It is a regular or irregular back and forth motion of particles. For example, when we start a vehicle, the engine will do circular motion to drive the wheel, which causes vibration and we feel wave pulses on our body when we sit in the car. However, this kind of vibration is undesirable, since it makes us uncomfortable. The car manufacture designs cushion seats to absorb vibration. This is a way to use hardware to control vibration. However, this is not enough. When vehicle goes through bumps, we do have suspension to absorb vibration transferred from road to our body. The car still experiences a big shock that makes us feel dizzy. On the opposite direction, in some cases when vibration becomes the motion source for energy harvesting, we would like to enhance it. Hardware can be helpful, since by tuning some parameters of an energy harvesting device, it can match with the vibration source to maximize vibration. However, it is still not enough due to low adaptability of a fixed parameter system. To overcome the limitation of hardware, researches begin to think about the way to control vibration, which is the method to change system behavior by using real-time adjustable hardware. By introducing vibration control, the theory behind that started to be investigated. This thesis investigates the vibration control theory application in both cases: vibration reduction and vibration enhancement, which are mentioned above due to opposite application preferences. There are two major applications of vibration control: vehicle suspension control and ocean wave energy converter (WEC) control. The thesis starts from the control development for both fields with general modeling criteria, then followed by control development with specific hardware design-mechanical motion rectifier (MMR) gearbox-applied on both systems. The MMR gearbox is the researcher designed hardware that targets on vibration adjustment with hardware capability, which is similar as the cushion seats mentioned at the beginning of the abstract. However, the MMR cannot have capability to furtherly optimize system vibration, which introduces the necessity of control development based on the existing hardware. In the suspension control application, the control strategy introduced successfully improve the vehicle ride comfort by 29.2%, which means the vehicle body acceleration has been reduced furtherly to let passenger feel less vibration. In the WEC application, the power absorbed from wave has been improved by 57% by applying suitable control strategy. The performance of improvement on vibration control has proved the effect on further vibration optimization beyond hardware limitation.

Constrained negative stiffness elements in volume concentrations (1% to 2%) embedded within viscoelastic materials have been shown to provide greater energy absorption than conventional materials [Lakes et al., Nature (London) 410, 565–567 (2001)]. This class of composite materials, called meta-materials, could be utilized in a variety of applications including noise reduction, anechoic coatings and transducer backings. The mechanism underlying the meta-material's behavior relies on the ability of the negative stiffness element to locally deform the viscoelastic material, dissipating energy in the process. The work presented here focuses specifically on the design of the negative stiffness elements, which take the form of buckled beams. By constraining the beam in an unstable, S-shaped configuration, the strain energy density of the beam will be at a maximum and the beam will accordingly display negative stiffness. To date, physical realization of these structures has been limited due to geometries that are difficult to construct and refine with conventional manufacturing materials and methods. By utilizing the geometric freedoms allowed by the Selective Laser Sintering (SLS) machines, these structures can be built and tuned for specific dynamic properties. The objective of this research was to investigate the dynamic behavior of SLS-constructed meso-scale negative stiffness elements with the future intention of miniaturizing the elements to create highly absorptive meta-materials. This objective was accomplished first through the development and analysis of a mathematical model of the buckled beam system. A characterization of the Nylon 11 material was performed to obtain the material properties for the parts that were created using SLS. Applying the mathematical model and material properties, a tuned meso-scale negative stiffness structure was fabricated. Transmissibility tests of the meso-scale structure revealed that the constrained negative stiffness system was able to achieve overall higher damping and vibration isolation than an unconstrained system. Quasistatic behavior of the system indicated that these elements would be ideal for implementation within meta-materials. Based on the results of the meso-scale system, a method to test a representative volume element for a negative stiffness meta-material was developed for future completion. / text

<p>Dynamic systems and robotic manipulators designed for time-optimal point-to-point motion are adversely affected by residual vibrations introduced due to the joint flexibility inherent in the system. Over the years, multiple techniques have been employed to improve the efficiency of such systems. While some techniques focus on increasing the system damping to efficiently dissipate the residual energy at the end of the move, several techniques achieve rapid repositioning by developing cleverly shaped input profiles that aim to reduce energy around the natural frequency to avoid exciting the resonant modes altogether. In this work, a numerical framework for constructing shaped inputs using a Versine basis function with peak acceleration constraint has been developed and improvements for the existing numerical framework for the Ramped Sinusoid basis function have been made to extend the range of values of the weighting function and improve the computational time. Performance metrics to evaluate the effectiveness of the numerical framework in minimizing residual vibrations have been developed. The effects of peak input acceleration and weighting function on the residual vibration in the system have been studied. The effectiveness of the method has been tested under multiple conditions in simulations and the results were validated by performing experiments on a two-link flexible joint robotic arm. The simulation and experimental results conclusively show that the inputs developed using the constrained numerical approach result in better residual vibration performance as compared to that of an unshaped input. </p>

L’objet de cette thèse est d’étudier différents dispositifs d’amortissement de vibrations en basses fréquences des aubes de rotor de soufflante ("fan") d’un turboréacteur. Les solutions étudiées utilisent des pastilles piézoélectriques, liées à l’aube et connectées à un circuit électrique passif ou semi-passif. Dans la première partie, il s’agit de mettre en pratique le modèle électromécanique développé dans la thèse de Julien Ducarne, puis de l’étendre au cas tridimensionnel par l’utilisation de la méthode des éléments finis. Ce modèle de comportement prend en compte le couplage entre une structure mécanique quelconque et des pastilles piézoélectriques planes ou courbes. Par la suite, un modèle réduit à faible nombre de degrés de liberté est construit, ce qui permet après résolution de prédire l’efficacité des dispositifs amortissants. Deux techniques, nommées "shunt" et "switch" sont appliquées au cas d’une aube fan. La première consiste à utiliser un circuit électrique résistif ou résonant. La seconde, encore à l’état de recherche, comporte un circuit muni d’un interrupteur synchronisé aux oscillations de la structure, ce qui produit un amortissement analogue à celui d’un frottement sec. La modélisation et l’optimisation électrique de ces circuits, issus de différents travaux antérieurs, ne font l’objet que d’un rappel dans ce mémoire. Une procédure d’optimisation est développée pour pouvoir trouver les géométries et les emplacements des pastilles qui maximisent le couplage électromécanique. Deux algorithmes différents (recuit simulé et recherche avec liste taboue) sont utilisés et mis en interaction avec les outils de calcul éléments finis pour trouver des solutions optimisées. Afin de valider sur un cas industriel l’ensemble des travaux sur les dispositifs piézoélectriques, une campagne d’essai est menée sur une aube fan de CFM56-7b. Les niveaux d’atténuation mesurés et ceux prévus par le modèle sont ensuite comparés. La seconde partie est consacrée à l’évaluation de l’effet des nonlinéarités géométriques sur la dynamique d’une structure tournante. Initialement prévue pour être intégrée à la partie shunt piézoélectrique, ceci afin de pouvoir estimer l’efficacité de ce dernier lorsque la structure tourne et vibre en grande amplitude, l’étude n’a pas été poursuivie et constitue une partie sans lien avec les techniques de réduction de vibrations. Néanmoins, les résultats obtenus en 1D, ainsi que la méthode de prise en compte des nonlinéarités dans le cas 3D viennent compléter et enrichir les différentes études actuelles menées sur le sujet, raison pour laquelle ce chapitre a été ajouté à ce mémoire. La détermination des caractéristiques dynamiques modales et leurs évolutions en fonction de certains paramètres de fonctionnement de l’aube constituent l’objet de cette partie. Plusieurs modèles sont développés et comparés pour pouvoir juger de la présence et de l’importance des divers phénomènes non linéaires dans la réponse forcée d’une poutre en rotation. / Vibration reduction of a turbojet fan blade with piezoelectric patches connected to a passive or semipassive electrical circuit, commonly called "shunt", is addressed in this study. The purpose of this work is to present a method for maximizing the performance of piezoelectric shunts. To validate the model, 2 experiments on a CFM56-7b fan blade are then done. To improve the damping level, a key issue is the optimization of the whole system, in terms of location and size of the piezoelectric patches and electric circuit components choice. It was shown these two optimizations, mechanical and electrical, can be realized separately. Moreover, it is proved the only parameters to maximize are the modal electromechanical coupling factors, which characterize the energy exchanges between the mechanical structure and the piezoelectric patches for a given mode. Since the optimal value of the electric circuit parameters are known as functions of the coupling factors and the system structural characteristics, they can be evaluated in a second step. Thus, the mechanical optimization consists in maximizing the coupling factors by optimizing the patches positions and dimensions, i.e. finding the best design. To fulfill this requirement and in order to manage a complex geometry, a 3D finite element formulation of the coupled electromechanical problem is derived from the one developed by Julien Ducarne during his Ph.D. thesis. A reduced order model of the discretized problem is then obtained by expanding the mechanical displacement unknowns vector onto the short-circuit eigenmodes to get the modal electromechanical coupling factors. However, when the optimization aims to reduce the vibration level with several patches, the main concern arises from the huge number of possible designs to test. For that reason, a method is proposed to cut back simulations time as well as to cope with the many local minima. This method consists in splitting up the optimization procedure in two steps. In the first one, the influence of patches on the structural eigenmodes is neglected. Therefore, an analytic coupling indicator, based on the eigenmodes of the naked host structure, can be defined and gives rise to a first approximate optimization using a simulated annealing algorithm. Then, the solutions of the first step are used as a starting point for a second optimization, working with the tabu search algorithm and where eigenmodes are computed for each new tested design.

Helicopters are versatile vehicles that can vertically take off and land, hover, and perform maneuver at very low forward speeds. These characteristics make them unique for a number of civilian and military applications. However, the radial and azimuthal variation of dynamic pressure causes rotors to experience adverse phenomena such as transonic shocks and 3-D dynamic stall. Adverse interactions such as blade vortex interaction and rotor-airframe interaction may also occur. These phenomena contribute to noise and vibrations. Finally, in the event of an engine failure, rotorcraft tends to descend at high vertical velocities causing structural damage and loss of lives. A variety of techniques have been proposed for reducing the noise and vibrations. These techniques include on-board control (OBC) devices, individual blade control (IBC), and higher harmonic control (HHC). Addition of these devices adds to the weight, cost, and complexity of the rotor system, and reduces the reliability of operations. Simpler OBC concepts will greatly alleviate these drawbacks and enhance the operating envelope of vehicles. In this study, the use of Gurney flaps is explored as an OBC concept using a physics based approach. A three dimensional Navier-Stokes solver developed by the present investigator is coupled to an existing free wake model of the wake structure. The method is further enhanced for modeling of Blade-Vortex-Interactions (BVI). Loose coupling with an existing comprehensive structural dynamics analysis solver (DYMORE) is implemented for the purpose of rotor trim and modeling of aeroelastic effects. Results are presented for Gurney flaps as an OBC concept for improvements in autorotation, rotor vibration reduction, and BVI characteristics. As a representative rotor, the HART-II model rotor is used. It is found that the Gurney flap increases propulsive force in the driving region while the drag force is increased in the driven region. It is concluded that the deployable Gurney flap may improve autorotation characteristics if deployed only over the driving region. Although the net effect of the increased propulsive and drag force results in a faster descent rate when the trim state is maintained for identical thrust, it is found that permanently deployed Gurney flaps with fixed control settings may be useful in flare operations before landing by increasing thrust and lowering the descent rate. The potential of deployable Gurney flap is demonstrated for rotor vibration reduction. The 4P harmonic of the vertical vibratory load is reduced by 80% or more, while maintaining the trim state. The 4P and 8P harmonic loads are successfully suppressed simultaneously using individually controlled multi-segmented flaps. Finally, simulations aimed at BVI avoidance using deployable Gurney flaps are also presented.

[pt] A redução de deslocamentos e acelerações em edifícios é um aspecto de vital importância no projeto de estruturas sob a ação de sismos. Assim, o controle de vibrações de estruturas em regiões sujeitas a eventos sísmicos tem se tornado um importante tema de pesquisa em engenharia. Dentre os mecanismos propostos para a redução de vibrações em estruturas, encontram-se os amortecedores magnetoreológicos (MR). Amortecedores magnetoreológicos são dispositivos passivos ou semiativos que controlam as vibrações com um consumo mínimo de energia. Estes mecanismos são caracterizados por um comportamento histerético não linear que leva em geral a uma grande dissipação de energia. Neste trabalho estuda-se o efeito de um amortecedor MR e de seus parâmetros característicos na redução das vibrações de edifícios e torres esbeltas. Para isto, utiliza-se o modelo de Bouc-Wen. O edifício é descrito como um sistema discreto massa-mola-amortecedor do tipo shear-building e a torre como um pêndulo múltiplo, onde se leva em conta a possibilidade de grandes rotações e deslocamentos. Considera-se o amortecedor localizado na estrutura (primeiro andar) e como um sistema de isolamento de base, com o propósito de verificar a influência da localização do amortecedor na redução das respostas dinâmicas. Quando o dispositivo é usado como isolamento de base, ambos os modelos mostraram uma grande diminuição da resposta dinâmica, em comparação aos resultados com o dispositivo no primeiro andar. Estuda-se também a influência da relação entre as frequências da estrutura e o conteúdo de frequências da excitação na eficiência do amortecedor MR. Os resultados mostram que esta relação tem uma grande influência no grau de redução das vibrações da estrutura controlada. Em todos os casos analisados, observa-se que o amortecedor MR leva a uma redução das vibrações, em particular dos deslocamentos da estrutura. / [en] The reduction of displacements and accelerations in buildings is a vital aspect in the design of structures under an earthquake excitation. Thus, the vibration control of structures in areas subject to seismic events has become an important research topic in engineering. Among the proposed mechanisms to reduce vibrations in structures, are the magneto rheological dampers (MR). Magneto rheological dampers are passive or semi-active devices for vibration control characterized by small energy consumption. These mechanisms are characterized by a nonlinear hysteretic behavior that usually leads to large energy dissipation. In this paper the effect of an MR damper and its characteristic parameters in reducing the vibrations of buildings and slender towers is studied. For this, the Bouc-Wen model is adopted. The building is described as a discrete mass-spring-damper-type shear-building and the tower as a multiple pendulum, which takes into account large displacements and rotations. It is considered that the damper is located in the structure (first floor) or as a base isolation system, in order to verify the influence of the location of the damper in the reduction of dynamic responses. When the device is used as a base isolation, both models show a large decrease of the dynamic response as compared to the results with the device on the first floor. The influence of the relationship between the frequencies of the structure and frequency content of the excitation on the efficiency of MR damper is also investigated. The results show that this relation has a great influence on the degree of reduction of vibrations of the controlled structure. In all cases here analyzed, it is observed that the MR damper leads to a reduction of the vibration response, in particular the displacement of the structure.

<p>Hydraulic systems have many applications in the construction, transportation, and manufacturing sectors. Recent design trends involve systems with higher working pressures and more compact systems, which are advantageous because of power density increase. However, these trends imply higher forces and larger vibration amplitudes while having lesser mass and damping, leading to higher noise levels. Meanwhile, hydraulic machinery started prospecting new applications with tighter noise regulations, a trend which was also pushed by the electrification tendency in several fields of transportation and agriculture. One method to attain noise mitigation is passive-noise canceling techniques have the advantage of not introducing energy to the system. This approach arranges pressure ripple waves in a destructive pattern by projecting a hydraulic circuit's geometry, configuration, and features.</p> <p> </p> <p>This dissertation aims to predict fluid-borne noise sources and investigate passive noise-canceling solutions for multiple operations conditions targeting to impact many hydraulic systems and a broad range of operating conditions. Primarily a coupled system model strategy that includes a one-dimensional line finite element model is developed. The line model predicts pressure wave generation and propagation. The model features versatility since parameters like line diameter and material can be discretized node by node. Simulations are compared to measured data in a realistic novel hydraulic hybrid transmission for validation. </p> <p> </p> <p>Subsequently, an extensive numerical investigation is performed by setting fixed parameters along the hydraulic lines' length and comparing several isolated geometric properties in simulation. The developed line model is also used to study the influence of line features such as diameter and extent of the conduit. Cost-effective and simple passive solution solutions such as Quincke tubes (parallel lines), expansion chambers, and closed branches are selected and investigated on simulation. Four target pressure ripples are chosen as indicators for summarizing passive line elements behavior. The frequency-domain behavior of the pressure ripple peaks regarding the line's length is identified and isolated in simulation at the 50-5000Hz frequency spectrum. An experiment test rig is designed to implement these solutions and the experiments show three developed passive elements as practical and effective solutions for reducing fluid borne noise sources. The selected designs yielded noise source attenuation over most of the frequency spectrum measured with piezoelectric pressure variation sensors and accelerometers in different positions in the hydraulic circuit. Sound pressure measurements detected reductions over 3dB in the best cases. </p> <p> </p> <p>Also, a passive interference approach based on the principle of secondary source flow ripple cancellation was conceptualized, modeled, and implemented in a tandem axial-piston unit. The strategy consists of setting the phase between the two synchronous units to accomplish destructive interference in targeted unit harmonics. Two indexing strategies are investigated first analytically and then on simulation. One of the indexing strategies was implemented in a pre-existent commercial axial-piston tandem unit. Experiment results confirmed effectiveness for the first and third unit’s harmonics, where reductions over 15dB on pressure ripple were measured.</p> <p> </p> <p>Finally, a fluid-structure interaction based on the poison coupling principle is developed using the method of characteristics. Transfer functions of the pipeline accelerations versus the pressure ripples on lines calculated on simulation and later obtained experimentally to highlight ta critical vibration band from 2000Hz to 3000Hz with high acceleration response.</p> <p> </p><br>

Dans le cadre de la lutte contre les nuisances sonores et vibratoires, cette thèse porte sur la modélisation numérique des structures amorties par dispositifs piézoélectriques shuntés. La première partie du travail concerne la modélisation par éléments finis de structures en vibrations avec des pastilles piézoélectriques shuntées. Dans un premier temps, une formulation éléments finis originale, qui utilise des variables électriques globales (différence de potentiel et charge dans chaque pastille piézoélectrique), est analysée et validée. Dans un second temps, différentes stratégies de réduction de modèle basées sur la méthode de projection modale sont proposées pour résoudre le problème électromécanique discrétisé par éléments finis à moindre coût. La convergence de ces modèles d’ordre réduits est ensuite analysée pour les cas de shunts résistif et résonant. La deuxième partie du travail est consacrée à l’optimisation du système électromécanique, dans le but de maximiser l’amortissement apporté par les dispositifs piézoélectriques shuntés. Pour cela, une procédure d’optimisation topologique, basée sur la méthode SIMP (Solid Isotropic Material with Penalization method), est développée pour déterminer les géométries et les emplacements optimaux des pastilles piézoélectriques. Cette procédure permet de maximiser le coefficient de couplage électromécanique modal entre les éléments piézoélectriques et la structure hôte, ceci de façon indépendante du choix des composants du circuit électrique. Les avantages de l’approche proposée sont mis en avant à travers un exemple de validation et un cas d'application industrielle. Enfin, la dernière partie du travail propose une approche numérique pour modéliser et optimiser la réduction du rayonnement acoustique de plaques minces dans le domaine des basses fréquences avec des éléments piézoélectriques shuntés. Cette approche est valable pour n’importe quelle plaque mince bafflée et non trouée, indépendamment des conditions aux limites. Un exemple d’application concernant l’atténuation du rayonnent acoustique d’une plaque avec renforts est présenté et analysé. / Passive structural vibration and noise reduction by means of shunted piezoelectric patches is addressed in this thesis. The first part of the work concerns the finite element modeling of shunted piezoelectric systems. Firstly, an original finite element formulation, with only a couple of electric variables per piezoelectric patch (the global charge/ voltage), is analyzed and validated. Secondly, several reduced order models based on a normal mode expansion are proposed to solve the electromechanical problem. The convergence of these reduced order models is then analyzed for a resistive and a resonant shunt circuits. In the second part of the work, the concept of topology optimization, based on the Solid Isotropic Material with Penalization method (SIMP), is employed to optimize, in terms of damping efficiency, the geometry of piezoelectric patches as well as their placement on the host elastic structure. The proposed optimization procedure consists of distributing the piezoelectric material in such a way as to maximize the modal electromechanical coupling factor of the mechanical vibration mode to which the shunt is tuned, independently of the choice of electric circuit components. Numerical examples validate and demonstrate the potential of the proposed approach for the design of piezoelectric shunt devices. Finally, the last part of the work concerns the numerical modeling of noise and vibration reduction of thin structures in the low frequency range by using shunted piezoelectric elements. An efficient approach that can be applied to any thin continuous plates in an infinite baffle, independently of the boundary conditions, is proposed. An application example of a thin plate with reinforcements is presented and analyzed.

Dans le cadre de la lutte contre les nuisances sonores et vibratoires, cette thèse porte sur la modélisation numérique des structures amorties par dispositifs piézoélectriques shuntés. La première partie du travail concerne la modélisation par éléments finis de structures en vibrations avec des pastilles piézoélectriques shuntées. Dans un premier temps, une formulation éléments finis originale, qui utilise des variables électriques globales (différence de potentiel et charge dans chaque pastille piézoélectrique), est analysée et validée. Dans un second temps, différentes stratégies de réduction de modèle basées sur la méthode de projection modale sont proposées pour résoudre le problème électromécanique discrétisé par éléments finis à moindre coût. La convergence de ces modèles d’ordre réduits est ensuite analysée pour les cas de shunts résistif et résonant. La deuxième partie du travail est consacrée à l’optimisation du système électromécanique, dans le but de maximiser l’amortissement apporté par les dispositifs piézoélectriques shuntés. Pour cela, une procédure d’optimisation topologique, basée sur la méthode SIMP (Solid Isotropic Material with Penalization method), est développée pour déterminer les géométries et les emplacements optimaux des pastilles piézoélectriques. Cette procédure permet de maximiser le coefficient de couplage électromécanique modal entre les éléments piézoélectriques et la structure hôte, ceci de façon indépendante du choix des composants du circuit électrique. Les avantages de l’approche proposée sont mis en avant à travers un exemple de validation et un cas d'application industrielle. Enfin, la dernière partie du travail propose une approche numérique pour modéliser et optimiser la réduction du rayonnement acoustique de plaques minces dans le domaine des basses fréquences avec des éléments piézoélectriques shuntés. Cette approche est valable pour n’importe quelle plaque mince bafflée et non trouée, indépendamment des conditions aux limites. Un exemple d’application concernant l’atténuation du rayonnent acoustique d’une plaque avec renforts est présenté et analysé. / Passive structural vibration and noise reduction by means of shunted piezoelectric patches is addressed in this thesis. The first part of the work concerns the finite element modeling of shunted piezoelectric systems. Firstly, an original finite element formulation, with only a couple of electric variables per piezoelectric patch (the global charge/ voltage), is analyzed and validated. Secondly, several reduced order models based on a normal mode expansion are proposed to solve the electromechanical problem. The convergence of these reduced order models is then analyzed for a resistive and a resonant shunt circuits. In the second part of the work, the concept of topology optimization, based on the Solid Isotropic Material with Penalization method (SIMP), is employed to optimize, in terms of damping efficiency, the geometry of piezoelectric patches as well as their placement on the host elastic structure. The proposed optimization procedure consists of distributing the piezoelectric material in such a way as to maximize the modal electromechanical coupling factor of the mechanical vibration mode to which the shunt is tuned, independently of the choice of electric circuit components. Numerical examples validate and demonstrate the potential of the proposed approach for the design of piezoelectric shunt devices. Finally, the last part of the work concerns the numerical modeling of noise and vibration reduction of thin structures in the low frequency range by using shunted piezoelectric elements. An efficient approach that can be applied to any thin continuous plates in an infinite baffle, independently of the boundary conditions, is proposed. An application example of a thin plate with reinforcements is presented and analyzed.

La conception des structures assemblées nécessite de disposer d'outils de simulation prédictifs permettant de minimiser les écarts entre les comportements réel et simulé de ces structures. Et ce, d'autant plus que les exigences en terme de performance du système sont élevées et qu'une conception optimale est recherchée. Lors du dimensionnement des structures assemblées, la pratique généralement adoptée en bureau d'étude consiste à définir un coefficient de sécurité permettant de tenir compte de la variabilité du comportement réel de ces structures. L'inconvénient est de conduire nécessairement à un surdimensionnement qui peut aller à l'encontre des objectifs de dimensionnement optimal de ces structures. Les liaisons sont le siège de phénomènes non-linéaires tels que le contact ou le frottement et différentes sources d'incertitude induisent une variabilité sur les caractéristiques dynamiques réelles des liaisons. Malgré les capacités des calculateurs actuels, la prise en compte conjointe des phénomènes non linéaires et des incertitudes lors de la simulation de structures assemblées complexes reste difficilement envisageable par une approche directe. L'objectif de ce travail est de proposer une approche pragmatique de caractérisation du comportement vibratoire des structures légères assemblées en tenant compte de la variabilité des paramètres des liaisons. L'intérêt de cette approche est de pouvoir être intégrée dans une phase de dimensionnement robuste. On peut ainsi envisager de dimensionner une solution d'amortissement des vibrations d'une structure assemblée en tenant compte de la variabilité du comportement réel des liaisons de cette structure. Ce travail étudie d'abord le comportement dynamique d'une structure légère réelle afin d'identifier un modèle nominal «juste suffisant» des liaisons considérées. Une approche non intrusive de caractérisation du comportement vibratoire d'une structure en présence de paramètres incertains est ensuite proposée. Cette approche, intitulée approche SMR (pour Stochastic Model Reduction), exploite le fait que la variabilité des vecteurs propres d'une structure est généralement d'un ordre de grandeur inférieur à la variabilité des fréquences propres associées ce qui permet de réduire considérablement le coût de calcul de l'approche tout en gardant une bonne précision sur l'estimation des fréquences propres aléatoires de la structure. Le principe de l'approche est alors d'adapter la modélisation stochastique à chaque fréquence propre aléatoire en fonction d'une exigence de précision globale sur l'ensemble des fréquences propres aléatoires recherchées. Le point clé de cette approche consiste à identifier le modèle stochastique adapté à chaque configuration de fréquence propre, pour cela un indicateur sans coût de calcul supplémentaire est proposé. Finalement, un modèle stochastique des liaisons de la structure considérée est proposé et l'approche SMR est utilisée dans un processus d'optimisation basé sur le principe du maximum de vraisemblance pour identifier les paramètres de ce modèle. Cette dernière étape de la démarche proposée permet alors de caractériser le comportement vibratoire de structures assemblées constituées de nombreuses liaisons en tenant compte de la variabilité du comportement de chacune des liaisons. La démarche mise en place dans le cadre de cette thèse est alors concrétisée par la proposition d'une stratégie originale de réduction robuste des vibrations d'une structure assemblée légère. / Predictive models are needed to properly design assembled structures. The main issue with this kind of structure is to deal with non-linear phenomena as contact or friction while considering sources of uncertainties mainly responsible for the deviation between the effective behavior of the structure and results from deterministic simulations. This work aims to provide a pragmatic approach to characterize the vibrational behavior of light assembled structures considering the variability of parameters of the joints. This approach would be useful for robust design of solutions, such as solutions for damping vibrations, dedicated to assembled structures and taking into account the variability of the real behavior of each joint.In this work, the dynamical behavior of an actual light structure is studied in order to identify a "just sufficient" nominal model of the considered joints. A non intrusive approach is then proposed to reduce the vibrational stochastic model of a structure with random parameters is then proposed. This approach, referred as the SMR approach (for Stochastic Model Reduction approach), takes advantage of the order of variability of random eigenvectors which is usually lower than the variability of corresponding random eigenfrequencies. It then allows to significantly reduce the computational cost for a given accuracy to estimate the structure random eigenfrequencies. The cornerstone of this approach is to adapt the stochastic modeling to each random eigenfrequency depending on a global accuracy requirement on the whole set of sought random eigenfrequency. The key point is then to identify the stochastic model used for each configuration of random eigenfrequency. A computationally free indicator is then proposed. Finally, a stochastic mechanical model of the joints of the studied structure is proposed. The SMR approach is used in an optimization process based on the maximum likelihood principle to identify the parameters of this stochastic model. This last step allows to characterize the vibrational behavior of assembled structures involving many joints taking into account the variability of each joints. This work is then concluded by applying the proposed approach to the design of an original strategy for robust reduction of vibration of light structures.