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.

Absorvedores de vibração são comumente usados em aplicações com intuito de reduzir indesejadas amplitudes de vibração de estruturas e maquinas vibrantes. O conceito de um absorvedor de vibração linear consiste na ideia de projetar um subsistema com frequência de ressonância coincidente com uma dada frequência de interesse, tal que a amplitude de vibração do sistema primário e significativamente reduzida quando comparada a situação original, sem o absorvedor de vibração. Porem, uma deficiência dos absorvedores de vibração lineares típicos e sua estreita faixa de frequência de operação. Para superar essa deficiência, muitas tentativas de solução usando subsistemas não lineares tem sido propostas na literatura, ja que se apropriadamente projetados, eles podem aumentar a faixa de frequência de absorção de vibração e/ou melhorar a redução das amplitudes de vibração do sistema primário. Contudo, a síntese e o projeto de tais absorvedores não lineares não e tão simples e direta como no caso linear. Baseado na geometria de uma topologia proposta e encontrada na literatura, que compreende a inclusão de uma montagem do tipo snap through truss no lugar da mola linear do absorvedor de vibração, este trabalho tem intenção de apresentar um estudo sobre o projeto e otimização de um absorvedor dinâmico de vibrações não linear. Portanto, o efeito dos parâmetros do absorvedor e analisado quanto as perspectivas de redução das amplitudes de vibração do sistema principal como também de aumento da faixa de frequência de operação. A analise paramétrica do absorvedor foi promovida para responder questões sobre as variáveis de projeto, tanto físicas como geométricas. Realizou-se otimização do absorvedor com objetivo de sintoniza-lo a frequência de trabalho desejada, através de busca extensiva e algoritmos genéticos. Os resultados mostram que o absorvedor não linear proposto pode ser mais efetivo que seu correspondente linear em ambos os aspectos, na redução da máxima amplitude de vibração e no aumento da faixa de frequência de absorção. Portanto, apesar da dificuldade inicial de projeto, esse tipo de absorvedor representa uma alternativa interessante na atenuação das amplitudes de vibração ao longo de uma extensa faixa de frequência. / Dynamic vibration absorbers are commonly used in several applications in order to reduce undesired vibration amplitudes of vibrating machinery and structures. The concept of a linear vibration absorber is based on the idea of designing a subsystem with a resonance frequency coincident with a given frequency of interest such that the vibration amplitude of the primary system is significantly reduced when compared to the original situation (without the vibration absorber). But one of the known handicaps of typical linear vibration absorbers is their narrow frequency range of operation. To overcome this handicap, a number of tentative solutions have been proposed in the literature using nonlinear subsystems. If properly designed, they could enlarge the frequency range of vibration absorption and/or improve vibration reduction of the primary system. However, the synthesis and design of such nonlinear absorbers are not as straightforward as for their linear counterpart. A proposed design found in the open literature consists of replacing the linear spring of the vibration absorber by a nonlinear snap-through truss. This work aims to present a study on the design and optimization of a nonlinear dynamic vibration absorber based on snap-through absorber geometry. The effect of the absorber parameters was analyzed on both, the primary system vibration amplitude reduction and the frequency range of operation. Parametric analyses of the absorber were carried out to answer questions about the physical and geometric design variables. The absorber optimization was performed in two different ways, by extensive search and genetic algorithms, in order to tune it in the desired working frequency. The results show that the proposed nonlinear vibration absorber may be more effective than its linear counterpart both in terms of maximum vibration amplitude reduction and absorption frequency-range. Therefore, despite the increased design complexities such an absorber is an interesting alterna- tive in attenuating vibration amplitudes over a wide frequency range.

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequency occurrence in engineering applications. Therefore, the present thesis focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on optimization and sensitivity analysis procedures, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this thesis sets the emphasis on a tuning procedure of nonlinear vibration absorbers that can be computationally tractable and treat strongly nonlinear regimes of motion. The proposed methodology is a two-step procedure relying on a frequency-energy based approach followed by a bifurcation analysis. The first step, carried out in the free vibration case, imposes the absorber to possess a qualitatively similar dependence on energy as the primary system. This gives rise to an optimal nonlinear functional form and an initial set of absorber parameters. Based upon these initial results, the second step, carried out in the forced vibration case, exploits the relevant information contained within the nonlinear frequency response functions, namely, the bifurcation points. Their tracking in parameter space enables the adjustment of the design parameter values to reach a suitable tuning of the absorber. The use of the resulting integrated tuning methodology on nonlinear vibration absorbers coupled to systems with nonlinear damping is then investigated. The objective lies in determining an appropriate functional form for the absorber so that the limit cycle oscillation suppression is maximized. Finally, the proposed tuning methodology of nonlinear vibration absorbers may impose the use of complicated nonlinear functional forms whose practical realization, using mechanical elements, may be difficult. In this context, an electro-mechanical nonlinear vibration absorber relying on piezoelectric shunting possesses attractive features as various functional forms for the absorber nonlinearity can be achieved through proper circuit design. The foundation of this new approach are laid down and the perspectives are discussed.

Liquid sloshing in a 2D tank applied on a wave energy capture system and reducing the oscillation of an offshore platform are discussed in this study. A fully nonlinear time-independent finite difference method and the forth-order Runge-Kutta method are implemented to solve the coupled motions of liquid sloshing in a 2D tank with a floating platform. When the external forcing frequency of the Dynamic Vibration Absorber System composed by a tuned liquid damper and a tuned mass damper is identical to the fundamental frequency of the tank, the external force can be effectively diminished by the sloshing-induced force. In the meantime, the maximum effect of tuned mass damper on reducing the amplitude of the floating platform appears. When the frequency of external forcing is close to the first natural frequency of the liquid tank, the coupled effect between the motions of both the tank and the platform can effectively reduce the vibration of the platform and the total energy of the whole system. The Eigenfrequency of a wave capture system is formed by the coupled effect of a liquid tank and a wave capture system. When the excitation frequency of the wave capture system is near its Eigenfrequency, the sloshing-induced force is much larger than that of external and the maximum displacement of the wave energy capture system occurs. As a result, the wave energy capacity of the wave capture system can be averagely increased to 150% by the influence of liquid sloshing in the tank.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / This work is dedicated to the design of a vibrating blade dynamic vibration absorber (ADVLV), which is composed by a blade that is subjected to an initial traction T , and contains a concentrated mass m that is fixed at a given position d along the blade. These three parameters can be adjusted so that the ADVLV is tuned. For this aim, a finite element model of the system was built, leading to a design methodology for the absorber. Also, design of experiment techniques were performed to obtain the most interesting configurations for the system, both for the computational and experimental models. Special care was taken with respect to the boundary conditions for the finite element model, so that the dynamic responses could correspond to the physical aspects of the problem, accordingly. Besides, an experimental prototype was constructed and tested under laboratory conditions. The experimental results were compared with those obtained from mathematical simulation. From this comparison, it was concluded that the finite element model had to be updated in such a way that experimental results could match. A vibrating string dynamic vibration absorber (ADVCV) was also studied. However, this DVA configuration presented two anti-resonant frequencies due to the coupling of the first vibration mode along the horizontal and vertical directions with a concentrated mass. Another phenomenon that was observed is the tridimensional motion of the vibrating string around its equilibrium position, leading to an ellipsoid-shape movement when a harmonic excitation whose frequency coincides with the primary system resonance frequency is applied to the system. This way, the ADVCV is not able to attenuate the vibration amplitude of the primary system satisfactorily. It is worth mentioning that the proposed ADVLV presents a good dynamic behavior besides a wide frequency range along which the DVA can be tuned. Besides, the present vibration absorbing device is simple and can be easily connected to the primary system both to mechanical and civil engineering structures. / Este trabalho aborda o projeto de um absorvedor dinâmico de vibrações do tipo lâmina vibrante (ADVLV), sendo este constituído por uma lâmina sujeita a uma tração inicial T com uma massa concentrada m que pode ser fixada em uma posição d da lâmina. Este três parâmetros podem ser alterados a fim de se obter a sintonia do ADVLV. Para realizar o estudo deste, foi elaborado um modelo de elementos finitos do sistema, permitindo assim obter a metodologia para seu projeto. Também foram usadas técnicas de planejamento de experimento para obter as melhores configurações, tanto para os ensaios computacionais como experimentais. Foram tomados cuidados na criação das condições de contorno do modelo de elementos finitos, a fim de se obter respostas que representem adequadamente os aspectos físicos do problema. Também foi construído um protótipo e este foi ensaiado no laboratório. Os resultados obtidos foram comparados com os obtidos através da simulação computacional. A partir desta comparação verificou-se a importância de realizar ajustes no modelo de elementos finitos para adequar este à realidade. Também foi estudado o absorvedor dinâmico de vibração do tipo corda vibrante. Entretanto este ultimo ADV apresentou duas freqüências de anti-ressonância devido ao acoplamento do primeiro modo de vibrar nas direções horizontal e vertical da corda vibrante com uma massa concentrada. Outro fenômeno observado foi o movimento tridimensional da corda vibrante em torno da sua posição de equilíbrio, resultando uma forma semelhante a um elipsóide de revolução quando uma excitação harmônica com freqüência igual à freqüência de ressonância do sistema primário é aplicada sobre o sistema. Desta forma, o ADVCV não consegue cumprir a sua função de atenuar a amplitude de vibração da estrutura primária, sendo, portanto, completamente ineficiente neste caso. O ADVLV, proposto neste trabalho, apresentou comportamento dinâmico satisfatório, além de uma grande faixa de freqüências na qual o ADV pode ser sintonizado. Este dispositivo é de fácil construção e acoplamento, tanto a sistemas mecânicos, como a estruturas de construção civil. / Mestre em Engenharia Mecânica

Absorvedores de vibração são comumente usados em aplicações com intuito de reduzir indesejadas amplitudes de vibração de estruturas e maquinas vibrantes. O conceito de um absorvedor de vibração linear consiste na ideia de projetar um subsistema com frequência de ressonância coincidente com uma dada frequência de interesse, tal que a amplitude de vibração do sistema primário e significativamente reduzida quando comparada a situação original, sem o absorvedor de vibração. Porem, uma deficiência dos absorvedores de vibração lineares típicos e sua estreita faixa de frequência de operação. Para superar essa deficiência, muitas tentativas de solução usando subsistemas não lineares tem sido propostas na literatura, ja que se apropriadamente projetados, eles podem aumentar a faixa de frequência de absorção de vibração e/ou melhorar a redução das amplitudes de vibração do sistema primário. Contudo, a síntese e o projeto de tais absorvedores não lineares não e tão simples e direta como no caso linear. Baseado na geometria de uma topologia proposta e encontrada na literatura, que compreende a inclusão de uma montagem do tipo snap through truss no lugar da mola linear do absorvedor de vibração, este trabalho tem intenção de apresentar um estudo sobre o projeto e otimização de um absorvedor dinâmico de vibrações não linear. Portanto, o efeito dos parâmetros do absorvedor e analisado quanto as perspectivas de redução das amplitudes de vibração do sistema principal como também de aumento da faixa de frequência de operação. A analise paramétrica do absorvedor foi promovida para responder questões sobre as variáveis de projeto, tanto físicas como geométricas. Realizou-se otimização do absorvedor com objetivo de sintoniza-lo a frequência de trabalho desejada, através de busca extensiva e algoritmos genéticos. Os resultados mostram que o absorvedor não linear proposto pode ser mais efetivo que seu correspondente linear em ambos os aspectos, na redução da máxima amplitude de vibração e no aumento da faixa de frequência de absorção. Portanto, apesar da dificuldade inicial de projeto, esse tipo de absorvedor representa uma alternativa interessante na atenuação das amplitudes de vibração ao longo de uma extensa faixa de frequência. / Dynamic vibration absorbers are commonly used in several applications in order to reduce undesired vibration amplitudes of vibrating machinery and structures. The concept of a linear vibration absorber is based on the idea of designing a subsystem with a resonance frequency coincident with a given frequency of interest such that the vibration amplitude of the primary system is significantly reduced when compared to the original situation (without the vibration absorber). But one of the known handicaps of typical linear vibration absorbers is their narrow frequency range of operation. To overcome this handicap, a number of tentative solutions have been proposed in the literature using nonlinear subsystems. If properly designed, they could enlarge the frequency range of vibration absorption and/or improve vibration reduction of the primary system. However, the synthesis and design of such nonlinear absorbers are not as straightforward as for their linear counterpart. A proposed design found in the open literature consists of replacing the linear spring of the vibration absorber by a nonlinear snap-through truss. This work aims to present a study on the design and optimization of a nonlinear dynamic vibration absorber based on snap-through absorber geometry. The effect of the absorber parameters was analyzed on both, the primary system vibration amplitude reduction and the frequency range of operation. Parametric analyses of the absorber were carried out to answer questions about the physical and geometric design variables. The absorber optimization was performed in two different ways, by extensive search and genetic algorithms, in order to tune it in the desired working frequency. The results show that the proposed nonlinear vibration absorber may be more effective than its linear counterpart both in terms of maximum vibration amplitude reduction and absorption frequency-range. Therefore, despite the increased design complexities such an absorber is an interesting alterna- tive in attenuating vibration amplitudes over a wide frequency range.

A mechatronic system of actuators, sensors, and analog circuits is demonstrated to control the self-excited oscillations known as chatter that occur when single-point turning a rigid workpiece with a flexible tool. The nature of this manufacturing process, its complex geometry, harsh operating environment, and poorly understood physics, present considerable challenges to the control system designer. The actuators and sensors must be rugged and of exceptionally high bandwidth and the control must be robust in the presence of unmodeled dynamics. In this regard, the qualitative characterization of the chatter instability itself becomes important. Chatter vibrations are finite and recognized as limit cycles, yet modeling and control efforts have routinely focused only on the linearized problem. The question naturally arises as to whether the nonlinear stability is characterized by a jump phenomenon. If so, what does this imply for the "robustness" of linear control solutions? To answer our question, we present an advanced hardware and control system design for a boring bar application. Initially, we treat the cutting forces merely as an unknown disturbance to the structure which is essentially a cantilevered beam. We then approximate the structure as a linear single-degree-of-freedom damped oscillator in each of the two principal modal coordinates and seek a control strategy that reduces the system response to general disturbances. Modal-based control strategies originally developed for the control of large flexible space structures are employed; they use second-order compensators to enhance selectively the damping of the modes identified for control. To attack the problem of the nonlinear stability, we seek a model that captures some of the behavior observed in experiments. We design this model based on observations and intuition because theoretical expressions for the complex dynamic forces generated during cutting are lacking. We begin by assuming a regenerative chatter mechanism, as is common practice, and presume that it has a nonlinear form, which is approximated using a cubic polynomial. Experiments demonstrate that the cutting forces couple the two principal modal coordinates. To obtain the jump phenomena observed experimentally, we find it necessary to account for structural nonlinearies. Gradually, using experimental observation as a guide, we arrive at a two-degree-of-freedom chatter model for the boring process. We analyze the stability of this model using the modern methods of nonlinear dynamics. We apply the method of multiple scales to determine the local nonlinear normal form of the bifurcation from static to dynamic cutting. We then find the subsequent periodic motions by employing the method of harmonic balance. The stability of these periodic motions is analysed using Floquet theory. Working from a model that captures the essential nonlinear behavior, we develop a new post-bifurcation control strategy based on quench control. We observe that nonlinear state feedback can be used to control the amplitude of post-bifurcation limit cycles. Judicious selection of this nonlinear state feedback makes a supplementary open-loop control strategy possible. By injecting a harmonic force with a frequency incommensurate with the chatter frequency, we find that the self-excited chatter can be exchanged for a forced vibratory response, thereby reducing tool motions. / Ph. D.

Conventional isolation models deal with massless isolators, which tend to overestimate the isolator performance because they neglect the internal resonances (IRs) due to the inertia of the isolator. Previous researches on the IR problem is not adequate because they only discussed this problem in terms of vibration based on single degree-of-freedom (SDOF) models. These studies did not reveal the importance of the IRs, especially from the perspective of the noise radiation. This dissertation is novel compared to previous studies in the following ways: (a) a three-DOF (3DOF) model, which better represents practical vibration systems, is employed to investigate the importance of the IRs; (b) the IR problem is studied considering both vibration and noise radiation; and (c) passive and hybrid control approaches using dynamic vibration absorbers (DVAs) to suppress the IRs are investigated and their potential demonstrated. The 3DOF analytical model consists of a rigid primary mass connected to a flexible foundation through three isolators. To include the IRs, the isolator is modeled as a continuous rod with longitudinal motion. The force transmissibility through each isolator and the radiated sound power of the foundation are two criteria used to show the effects and significance of the IRs on isolator performance. Passive and hybrid DVAs embedded in the isolator are investigated to suppress the IRs. In the passive approach, two DVAs are implemented and their parameters are selected so that the IRs can be effectively attenuated without significantly degrading the isolator performance at some other frequencies that are also of interest. It is demonstrated that the passive DVA enhanced isolator performs much better than the conventional isolator in the high frequency range where the IRs occur. The isolator performance is further enhanced by inserting an active force pair between the two passive DVA masses, forming the hybrid control approach. The effectiveness and the practical potential of the hybrid system are demonstrated using a feedforward control algorithm. It is shown that this hybrid control approach not only is able to maintain the performance of the passive approach, but also significantly improve the isolator performance at low frequencies. / Ph. D.

We model different nonlinear systems, analyze their nonlinear aspects and discuss their applications. First, we present a semi-analytical, geometrically-exact, unsteady potential flow model is developed for airfoils undergoing large amplitude maneuvers. Towards this objective, the classical unsteady theory of Theodorsen is revisited by relaxing some of the major assumptions such as (1) flat wake, (2) small angle of attack, (3) small disturbances to the mean flow components, and (4) time-invariant free-stream. The kinematics of the wake vortices is simulated numerically while the wake and bound circulation distribution and, consequently, the associated pressure distribution are determined analytically. The steady and unsteady behaviors of the developed model are validated against experimental and computational results. The model is then used to determine the lift frequency response at different mean angles of attack. Second, we investigate the nonlinear characteristics of an autoparametric vibration system. This system consists of a base structure and a cantilever beam with a tip mass. The dynamic equations for the system are derived using the extended Hamilton's principle. The method of multiple scales is then used to analytically determine the stability and bifurcation of the system. The effects of the amplitude and frequency of the external force, the damping coefficient and frequency of the attached cantilever beam and the tip mass on the nonlinear responses of the system are determined. As an application, the concept of energy harvesting based on the autoparametric vibration system consisting of a base structure subjected to the external force and a cantilever beam with a tip mass is evaluated. Piezoelectric sheets are attached to the cantilever beam to convert the vibrations of the base structure into electrical energy. The coupled nonlinear distributed-parameter model is developed and analyzed. The effects of the electrical load resistance on the global frequency and damping ratio of the cantilever beam are analyzed by linearizion of the governing equations and perturbation method. Nonlinear analysis is performed to investigate the impacts of external force and load resistance on the response of the harvester. Finally, the concept of harvesting energy from ambient and galloping vibrations of a bluff body is investigated. A piezoelectric transducer is attached to the transverse degree of freedom of the body in order to convert the vibration energy to electrical power. A coupled nonlinear distributed-parameter model is developed that takes into consideration the galloping force and moment nonlinearities and the base excitation effects. The aerodynamic loads are modeled using the quasi-steady approximation. Linear analysis is performed to determine the effects of the electrical load resistance and wind speed on the global damping and frequency of the harvester as well as on the onset of instability. Then, nonlinear analysis is performed to investigate the impact of the base acceleration, wind speed, and electrical load resistance on the performance of the harvester and the associated nonlinear phenomena. Short- and open-circuit configurations for different wind speeds and base accelerations are assessed. / Ph. D.

L'usure ondulatoire des rails associée aux vibrations de torsion des essieux de métro a été mise en évidence il y a près d'un demi siècle. L'utilisation d'absorbeurs dynamiques comme solution potentielle à ce problème a été suggérée pour la première fois dans le projet américain du TCRP "Rail Corrugation Mitigation in Transit" en 1998. Cette thèse, réalisée dans le cadre du projet européén "Wheel-rail CORRUGATION in Urban transport", a pour objectif de concevoir un absorbeur dynamique et d'étudier son influence sur la réduction de l'usure ondulatoire liée aux vibrations de torsion. Dans le cadre de ce travail, d'autres types d'usure ondulatoire ont également été traités par des absorbeurs dynamiques. Les trois premiers chapitres de cette thèse sont dédiés à la description des différents types d'usure ondulatoire et à la présentation des méthodes de prédiction. La méthode de dimensionnement des absorbeurs dynamiques est présentée au chapitre 4, ainsi que quelques perspectives de leur efficacité à réduire l'usure ondulatoire. Dans le chapitre 5, un tronçon réel du RER parisien a été étudié. D'une part les prédictions obtenues par différentes méthodes ont été comparées aux mesures sur site. D'autre part, le bénéfice résultant de l'utilisation d'un absorbeur dynamique a été étudié numériquement. Dans le chapitre 6, le cas de l'usure ondulatoire liée aux vibrations de torsion a été étudié spécifiquement. Un absorbeur dynamique a été développé pour réduire ce type d'usure ondulatoire. Son efficacité a été évaluée théoriquement et numériquement, avec un modèle multi-corps flexible du véhicule et de la voie. Dans le chapitre 7, un absorbeur dynamique visant à réduire les vibrations de torsion d'un essieu de métro à échelle réduite a été construit au laboratoire. Son efficacité a été validée expérimentalement en reproduisant les conditions d'apparition des vibrations de torsion de l'essieu sur le banc d'essais du Laboratoire des Technologies Nouvelles de l'INRETS. La correspondance entre les prédictions d'usure à échelle réduite et à échelle réelle a été établie. Une demande de brevet a été déposée par le Laboratoire des Structures Actives pour ce système (N° 06120344.4).