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The dynamic properties of several rectangular and V-shaped microcantilevers were investigated. Particular attention was paid to the higher flexural eigenmodes of oscillation. The potential of the higher flexural modes was demonstrated through the use of cantilevers as standalone sensors for adsorbed mass. The mass adsorbed on the surface of a cantilever was in the form of a homogeneous water layer measured as a function of relative humidity. The minimum detectable water layer thicknesses were 13.7 Å, 3.2 Å, 1.1 Å, and 0.7 Å for the first four modes of a rectangular cantilever, clearly demonstrating enhanced accuracy for the higher eigenmodes of oscillation. These thicknesses correspond to minimum detectable masses of 33.5 pg, 7.8 pg, 2.7 pg and 1.7 pg for the first four modes. For quantitative applications the spring constants of each cantilever must be determined. Many methods exist but only a small number can calibrate the higher flexural eigenmodes. A method was developed to simultaneously calibrate all flexural modes of microcantilever sensors. The method was demonstrated for the first four eigenmodes of several rectangular and V-shaped cantilevers with nominal fundamental spring constants in the range of 0.03 to 1.75 N/m. The spring constants were determined with accuracies of 5-10 %. Spring constants of the fundamental mode were generally in agreement with those determined using the Sader method. The method is compatible with existing AFM systems. It relies on a flow of gas from a microchannel and as such poses no risk of damage to the cantilever beam, its tip, or any coating. A related method was developed for the torsional modes of oscillation. Preliminary results are shown for the fundamental mode of a rectangular cantilever. The method can be easily extended to the higher torsional modes, V-shaped cantilevers, and potentially, the flapping modes of the legs of V-shaped microcantilevers.

The tokamak is so far the most promising magnetic configuration for achieving a net production of fusion energy. The D-T fusion reactions result in 3.5 MeV alpha-particles, which may destabilize Alfvén eigenmodes through wave-particle interaction. These instabilities redistribute the alpha-particles from the central region of the plasma towards the edge, where they are thermalized, and hence result in a reduced heating efficiency. The high-energy alpha-particles may even be thrown out of the plasma and may damage the wall. To investigate the destabilization of Alfvén eigenmodes by high-energy ions, ion cyclotron resonance heating (ICRH) and neutral beam injection (NBI) are often used to create a high-energy tail on the distribution function. The ICRH does not only produce high-energy anisotropic tails, it also decorrelates the wave-particle interaction with the Alfvén eigenmodes. Without decorrelation of the wave-particle interaction an ion will undergo a superadiabatic oscillation in phase space and there will be no net transfer of energy to the mode. For the thermal ions the decorrelation from collisions dominates while for the high-energy ions the decorrelation from ICRH dominates. As the unstable modes grow up, the gradients in phase space, which drive the mode, are reduced, resulting in a weaker drive. The dynamics of the system becomes non-linear due to a continuous restoration of the gradients by D-T reactions and ICRH. In this thesis the non-linear dynamics of toroidal Alfvén eigenmodes (TAEs) during ICRH has been investigated using the SELFO code. The SELFO code, which calculates the distribution function during ICRH self-consistently using a Monte-Carlo metod, has been upgraded to include interactions with TAEs. The fast decay of the mode amplitude as the ICRH is switched off, which is seen in experiments, as well as the oscillation of the mode amplitude as the distribution function is repetetively built up by the ICRH and flattened by the TAE has been reproduced using numerical simulations. In the presence of several unstable modes the dynamics become more complicated. The redistribution of an alpha-particle slowing down distribution function as well as the reduced heating efficiency in the presence of several modes has also been investigated. / QC 20100628

Previously, we proposed and experimentally demonstrated enhanced recording speeds by using a resonant optical cavity to semi-passively increase the reference beam power while recording image bearing holograms. In addition to enhancing the reference beam power the cavity supports the orthogonal reference beam families of its eigenmodes, which can be used as a degree of freedom to multiplex data pages and increase storage densities for volume Holographic Data Storage Systems (HDSS). While keeping the increased recording speed of a cavity enhanced reference arm, image bearing holograms are multiplexed by orthogonal phase code multiplexing via Hermite-Gaussian eigenmodes in a Fe: LiNbO3 medium with a 532 nm laser at two Bragg angles for expedited recording of four multiplexed holograms. We experimentally confirmed write rates are enhanced by an average factor of 1.1, and page crosstalk is about 2.5%. This hybrid multiplexing opens up a pathway to increase storage density while minimizing modifications to current angular multiplexing HDSS.

To deal with a rapid development of high-speed trains and high-speed railways, constant improvement of the railway infrastructure is necessary and engineers are continuously facing challenges in order to design efficient and optimized structures. Nowadays, more and more railway bridges are built and thus, they require the engineers’ attention both regarding their design and their maintenance. A comprehensive knowledge of the infrastructures and the trains is crucial: their behaviours need to be well known. However, today, the ballast - the granular material disposed on the track and on which the rails lie – is not well known and its effect in dynamic analyses are rarely accounted for. Engineers are still investigating the role played by the ballast in the dynamic behaviour of bridges.  This master thesis aims at quantifying the influence of the ballast on the dynamic properties of a bridge. Is the ballast just an additional mass on the structure or does it introduce any additional stiffness? Thus, this project investigates different alternatives and parameters to propose a realistic and reliable model for the ballast superstructure and the track. For the purpose of this study, a simply supported steel truss bridge located in Poland is studied. The bridge was excited by a harmonic force and the interesting point regarding the experiments is that acceleration measurements were collected before and after the ballasted track setting up on the bridge deck. Then, these data are processed through MATLAB in order to obtain the natural frequencies of the bridge at two different times during its construction. The determined natural frequencies for the un-ballasted case are then compared with analytical values obtained with a 3D finite element model implemented in the software LUSAS. This step aims at calibrating the un-ballasted finite element model so that the bridge is represented as realistically as possible. Once it has been done, a model both for the ballast and the track is proposed using solid elements for the ballast superstructure and beam elements for the rails, the guard rails and the sleepers. Different parameters influencing the natural frequencies and modes shapes of the bridge are testing and it appears that the ballast introduces an additional stiffness through a bending stiffness in the ballast and a change in the support conditions. Finally, the contribution of these parameters is assessed and discussed: the stiffness of the ballast increases the stiffness of the bridge by more than 20% for the 2nd vertical bending vibration mode and the support conditions increase the bridge’s stiffness by more than 15% and 30% respectively for the 1stvertical bending the 1st torsional vibration modes.

Le présent mémoire a pour objet d’étudier la relation entre les modes propres de vibration avec les mesures de saut temporel ultrasonore. La méthode de saut temporel est une technique de l’acoustique non linéaire qui s’intéresse à l’évaluation des dommages internes dans le béton notamment à un jeune âge. Elle est basée sur le décalage temporel dans le temps d’arrivée des ondes ultrasonores après que le milieu de propagation ait été soumis à une excitation mécanique par laquelle le réseau de microfissuration interne est perturbé. Son application in situ avait été testée, mais il y avait un consensus général que l’amplitude du saut temporel pouvait dépendre de la nature du mode propre excité de la structure. La méthode a donc été appliquée au laboratoire sur des poutres en béton armé (non endommagé) afin d’étudier cette influence. Les ondes de surface ont été étudiées à cause de leur sensibilité aux variations de propriétés mécaniques du béton. Les résultats obtenus montrent que les valeurs de saut temporel dépendent fortement du mode excité, les modes ayant manifesté d’une façon notable et énergétique dans le spectre de Fourrier d’accélération sont ceux ayant provoqué un décalage temporel significatif. De plus, l’excitation de deux modes par une même amplitude ne produit pas le même effet. Par ailleurs, les résultats indiquent que le choix du mode à exciter est important, car l’excitation d’un mode inapproprié ne révèle pas l’état réel du béton/de l’ouvrage ausculté. Enfin, la présente étude conclut qu’il y a une dépendance entre les modes propres des structures sur les mesures de saut temporel ; la prise en compte de telle dépendance améliore l’efficacité de la technique de saut temporel, et tout dans une configuration simple et optimale. / Abstract : The purpose of this project is to study the relationship between of eigenmodes of vibration and ultrasonic time shift measurements. Indeed, the method of time shift is a technique of nonlinear acoustics which is interested in the evaluation of the internal damage in the concrete especially at early age. It is based on the time shift in the arrival time of the ultrasonic waves after the medium has subjected a mechanical excitation by which the internal microcracking network is disturbed. Its application in situ was recently experienced, but there was a consensus that the amplitude of the time shift could depend on the nature of the excited eigenmode of the structure. The method was applied in the laboratory on reinforced concrete beams (undamaged) to assess their influence. The surface waves were thus investigated in this experiment because of their sensitivity to the variation of the mechanical properties of concrete. The results show that the time shift values depend strongly on the excited mode; the modes which have manifested in a notable and energetic manner in the acceleration spectrum are tho se which have caused a significant time shift. Moreover, the excitation of two modes by the same amplitude does not produce the same effect. Also, the results indicate that the choice of the mode to be excited is important, because the excitation of an ina ppropriate mode does not reveal the actual condition of the concrete or examined structure. Finally, the present study concludes that there is dependence between the eigenmodes of the structures on the time shift measurements; the taking into account of such dependence improves the efficiency of the time shift technique, all in a simple and optimal configuration.

L’étude présentée dans cette thèse se situe dans le domaine de l’acoustique modale des conduits avec des parois absorbantes et un écoulement moyen. Nous considérons une source de bruit en amont avec une fréquence fixe. Avec cela, nous étudions les modes propres acoustiques du conduit en terme de nombre d’onde qui sont présents.Avec cette étude, nous contribuons à la meilleure compréhension de la propagation du sondans ce type de configuration. Parmi les applications, il y a la réduction du bruit des moteurs des aéronefs.Une analyse numérique par la méthode pseudospectrale de collocation, sur la base de polynômes de Chebyshev, a été mise en ouvre pour obtenir le spectre des modes, dans un domaine transversal.Pour cela, deux programmes ont été utilisés : le programme FiEStA, qui a été développé dans le cadre de cette thèse, et qui résout les équations d’Euler linéarisées, en considérant un problème à une ou deux une ou deux dimensions. D’autre part, le programme MAMOUT, a été utilisé pour résoudre les équations de Navier-Stokes linéarisées, pour étudier plus spécifiquement les effets de la viscosité.Avec ces outils, on a constaté les effets de trois paramètres : lorsque le rapport d’aspect augmente, la densité des modes, en particulier des modes propagatifs, se développe également.Quand le nombre de Mach de l’écoulement moyen augmente, on observe les effets suivants sur les valeurs propres : un déplacement vers la partie réelle négative, une amplification de leur valeur absolue et un déplacement vers les modes d’indice inférieur. Le profil d’écoulement moyen induit aussi un déplacement dans les valeur propres, pas facilement prévisible. Il modifie également la forme des fonctions propres ; ce qui est notamment visible pour le mode d’onde plane. Les changements d’impédance induisent un échange cyclique de valeurs propres entre les valeurs de parois rigides des modes consécutifs. Avec certaines valeurs d’impédance, les modes acoustiques de paroi apparaissent. Ils sont caractérisés par la forme exponentielle de leurs fonctions propres.En plus des modes acoustiques, il existe des modes hydrodynamiques de surface qui se sont révélés avec quelques valeurs d’impédance et forme et nombre de Mach de l’écoulement moyen. Pour un ensemble de données de référence, ces modes ont été étudiés. L’impédance a été considérée avec un modèle basé sur des données de la littérature, tout comme le profil d’écoulement moyen.Un mode hydrodynamique a été trouvé. Avec certaines valeurs de la fréquence, l’ensemble des paramètres donne lieu à une instabilité. En utilisant le critère Briggs Bres pour la stabilité,l’instabilité a été jugée absolue.À partir du comportement des modes avec différentes valeurs de l’impédance, et conformément aux résultats publiés, nous avons défini la condition que le spectre doit remplir pour réduire autant que possible le bruit. C’est cela qu’on appelle l’impédance optimale. Nous avons calculé cette valeur pour différents fréquences et écoulements moyens. / The study presented in this thesis is within the domain of modal acoustics of lined ducts withgrazing flow. We consider an upstream source of noise with a fixed frequency, within a lined duct.From this, we study the eigenmodes in terms of wavenumber that are present in this system.With this study, we contribute to the better understanding of sound propagation in thedescribed configuration. Within its main applications, we can find the noise reduction fromaeroengines.A numerical analysis with the pseudospectral collocation method, based on Chebyshevpolynomials was used to obtain the spectrum of modes within the duct, in a domain transversalto the mean flow. For this, two programs were used: On one hand, within the frame of this thesis,the program FiEStA was developed. It solves the linearized Euler Equations, considering eitherone or two dimensions of the transversal plane. On the other hand, the already existing programMAMOUT was used for verification and to solve also the linearized Navier-Stokes Equations toobserve the effects of viscosity.With these tools, the first result was to notice the effects of three parameters: When theaspect ratio grows, the density of modes in the spectrum grows also. In particular, we havemore propagative modes. As the mean flow Mach number grows, we observe these effects on theeigenvalues: a displacement to the negative real part, a slight amplification of their absolute valueand a displacement towards the modes of lower index. The difference in mean flow profile inducesanother displacement in modes, not easily predictable. It changes also the shape of eigenfunctions,which is clearly seen for the planewave mode. The impedance changes induce a cyclic exchange ofeigenvalues from their hard wall value to the hard wall value of a consecutive mode. The changeof eigenfunction is gradually change in wavelength, to obtain the shape of the destination mode.With some impedance values, a pair of modes, called the acoustic surface modes arise. They arecharacterized by the exponential shape of their eigenfunctions.Besides these acoustic surface modes, there are also a pair of hydrodynamic surface modeswhich come to light with some values of impedance and shape and Mach number of the meanflow. With a benchmark data, these modes were studied. The impedance was considered from themodel of a measured liner while the mean flow profile was taken from experimental values. Withthis, the hydrodynamic mode was found. With specific values of frequency, the set of parametersgives rise to an instability. Using the Briggs-Bers criterion for stability, the instability was foundto be absolute for a given frequency.From the comportment of modes with different values of impedance, and in accordance withpublished results, we defined the condition that the spectrum has to fulfill to reduce as much aspossible the upstream noise. This is what we called the optimal impedance. We obtained it forseveral flow profiles and frequencies, in both 1D and 2D domains.

Sensores e atuadores baseados em placas piezelétricas têm apresentado uma crescente demanda no campo denominado Estruturas Inteligentes, incluindo o desenvolvimento de atuadores para aplicações de resfriamento e bombeamento de fluidos, transdutores para novos coletores de energia, e diversas outras aplicações que apresentem requisitos quasi -estáticos e dinâmicos. Esta tese propõe o desenvolvimento de uma formulação de Otimização Topológica (OT) para o projeto de transdutores piezelétricos através da distribuição de material sobre um substrato metálico com o intuito de obter um comportamento quasi -estático e dinâmico desejado com maximização de deslocamentos ou tensão elétrica de saída, especificação de frequências e modos de vibrar, e maximização do Coeficiente de Acoplamento Eletromecânico (CAEM). O Método de Otimização Topológica (MOT) é uma poderosa técnica de otimização estrutural que combina o Método de Elementos Finitos (MEF) com algoritmos de otimização e tem como objetivo a distribuição de material num domínio de projeto para satisfação de objetivos previamente especificados. A modelagem por elementos finitos emprega uma formulação de placa piezelétrica capaz de representar os efeitos piezelétricos direto e inverso. Ela baseia-se na formulação MITC (Mixed Interpolation of Tensorial Components), a qual é confiável, eficiente e evita o problema de travamento por cisalhamento. A formulação de OT é baseada no modelo PEMAP-P (Piezoelectric Material with Penalization and Polarization) combinado ao RAMP (Rational Approximation of Material Properties), no qual variáveis de projeto são as pseudo-densidades que descrevem a quantidade de material piezelétrico em cada elemento finito. Foram definidas funções multiobjetivo para os problemas de otimização quasi -estáticos e dinâmicos. Ao passo que o primeiro maximiza deslocamentos ou tensões elétricas de saída, e evita frequências de ressonância próximas à faixa de trabalho, o segundo projeta os modos de vibrar da estrutura, controla as frequências de ressonância e maximiza o CAEM do transdutor. Este texto apresenta o ciclo de projeto completo para transdutores baseados em placas piezelétricas concebidos através do MOT, apresentando a metodologia utilizada, as formulações dos problemas de otimização, a implementação numérica, os resultados computacionais obtidos, a fabricação e a caracterização de transdutores piezelétricos otimizados para validação experimental dos resultados obtidos pela OT. / Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of the so called Smart Structures, including the development of actuators for cooling and fluid pumping applications, transducers for novel energy harvesting devices, and many other application with quasi -static and dynamic requirements. This thesis proposes the development of a Topology Optimization (TO) formulation to design piezoelectric transducers by distributing piezoelectric material over a metallic plate in order to achieve a desired quasi -static and dynamic behavior with maximization of displacements or output voltages, specified vibration frequencies and modes, and maximization of the Electromechanical Coupling Coefficient (EMCC). The Topology Optimization Method (TOM) is a powerful structural optimization technique which combines the Finite Element Method (FEM) with optimization algorithms and aims at distributing material over a design domain to accomplish with previously set objectives. The finite element employs a piezoelectric plate formulation capable of representing both direct and converse piezoelectric effects. It is based on the MITC (Mixed Interpolation of Tensorial Components) formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model (Piezoelectric Material with Penalization and Polarization) combined with the RAMP model (Rational Approximation of Material Properties), where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element. Multiobjective functions are defined for the quasi -static and dynamic optimization problems. While the former aims at maximizing displacements or output voltages and avoiding resonance frequencies near its working range, the latter aims at designing the vibration mode, controlling the resonance frequency and maximizing the EMCC of the transducer. This text presents the complete design cycle for transducers based on piezoelectric plates designed by using the TOM and shows the applied methodology, optimization problem formulation, numerical implementation, achieved computational results, and the assembly and characterization of optimized piezoelectric transducers for experimental validation of the TO results.

Avec la hausse des niveaux de dimensionnement sismique il est devenu nécessaire de limiter les chargements internes dans les structures, notamment en utilisant des dispositifs glissants. Ces dispositifs plafonnent les efforts internes en déclenchant un glissement de la structure. Il devient cependant nécessaire d'estimer l'amplitude des déplacements de corps rigide, notamment pour les structures stockées dans des réservoirs. Dans ce cas, il est nécessaire de prévenir les impacts entre la structure glissante et les bords du réservoir pour contrôler les risques de fuite. Parmi les structures glissantes immergées, on citera les ponts, les structures côtières en maçonnerie, les râteliers de stockage de combustible nucléaire, etc...Les équations de dynamique associées au comportement de ces structures sont non-linéaires et nécessitent l'utilisation de simulations numériques coûteuses en temps de calcul et ne permettant pas de faire des études de sensibilité rapides. On propose donc une méthode de résolution quasi-analytique de ces équations en traitant dans un premier temps, l'évaluation analytique des matrices de masses ajoutées du couplage fluide-structure, dans un second temps, une méthode de résolution quasi-analytique du glissement d'une structure quelconque immergée dans un fluide avec une actualisation de la géométrie de lames d'eau. Les résultats obtenus présentent une bonne adéquation avec des simulations numériques et offrent un temps de calcul quasiment instantané compatible avec une étude paramétrique ou stochastique de ces structures / As the seismic loadings are increasing in accordance to the recent regulations regarding Earthquake design, the use of sliding devices in structures is becoming more common. These devices limitate the internal forces by creating a rigid body sliding. It is then necessary to estimate the global displacement of the structure, especially concerning structures that are immersed in a reservoir. In this case, the displacement must be well estimated in order to prevent impacts between the sliding structure and the boundaries of the reservoir. We can find such structures in : bridges, costal structures in brick and masonry, or in the nuclear industry with the underwater fuel storage racks, ...The governing equations for the behaviour of these structures are non linear and must be solved using time-consuming computer simulations which are not fit for a stochastic study. Our method consists in, firstly, evaluating analytically the added masses of the fluid-structure interaction, secondly, a semi-analytical solving of the governing equations including the updating of the dimensions of the fluid layers surrounding the sliding structure. The results of this new method are in accordance with the numerical simulations and can be obtained in a short time (1 or 2 seconds) which offers the possibility to make a stochastic analysis of the non linear behaviour

Sensores e atuadores baseados em placas piezelétricas têm apresentado uma crescente demanda no campo denominado Estruturas Inteligentes, incluindo o desenvolvimento de atuadores para aplicações de resfriamento e bombeamento de fluidos, transdutores para novos coletores de energia, e diversas outras aplicações que apresentem requisitos quasi -estáticos e dinâmicos. Esta tese propõe o desenvolvimento de uma formulação de Otimização Topológica (OT) para o projeto de transdutores piezelétricos através da distribuição de material sobre um substrato metálico com o intuito de obter um comportamento quasi -estático e dinâmico desejado com maximização de deslocamentos ou tensão elétrica de saída, especificação de frequências e modos de vibrar, e maximização do Coeficiente de Acoplamento Eletromecânico (CAEM). O Método de Otimização Topológica (MOT) é uma poderosa técnica de otimização estrutural que combina o Método de Elementos Finitos (MEF) com algoritmos de otimização e tem como objetivo a distribuição de material num domínio de projeto para satisfação de objetivos previamente especificados. A modelagem por elementos finitos emprega uma formulação de placa piezelétrica capaz de representar os efeitos piezelétricos direto e inverso. Ela baseia-se na formulação MITC (Mixed Interpolation of Tensorial Components), a qual é confiável, eficiente e evita o problema de travamento por cisalhamento. A formulação de OT é baseada no modelo PEMAP-P (Piezoelectric Material with Penalization and Polarization) combinado ao RAMP (Rational Approximation of Material Properties), no qual variáveis de projeto são as pseudo-densidades que descrevem a quantidade de material piezelétrico em cada elemento finito. Foram definidas funções multiobjetivo para os problemas de otimização quasi -estáticos e dinâmicos. Ao passo que o primeiro maximiza deslocamentos ou tensões elétricas de saída, e evita frequências de ressonância próximas à faixa de trabalho, o segundo projeta os modos de vibrar da estrutura, controla as frequências de ressonância e maximiza o CAEM do transdutor. Este texto apresenta o ciclo de projeto completo para transdutores baseados em placas piezelétricas concebidos através do MOT, apresentando a metodologia utilizada, as formulações dos problemas de otimização, a implementação numérica, os resultados computacionais obtidos, a fabricação e a caracterização de transdutores piezelétricos otimizados para validação experimental dos resultados obtidos pela OT. / Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of the so called Smart Structures, including the development of actuators for cooling and fluid pumping applications, transducers for novel energy harvesting devices, and many other application with quasi -static and dynamic requirements. This thesis proposes the development of a Topology Optimization (TO) formulation to design piezoelectric transducers by distributing piezoelectric material over a metallic plate in order to achieve a desired quasi -static and dynamic behavior with maximization of displacements or output voltages, specified vibration frequencies and modes, and maximization of the Electromechanical Coupling Coefficient (EMCC). The Topology Optimization Method (TOM) is a powerful structural optimization technique which combines the Finite Element Method (FEM) with optimization algorithms and aims at distributing material over a design domain to accomplish with previously set objectives. The finite element employs a piezoelectric plate formulation capable of representing both direct and converse piezoelectric effects. It is based on the MITC (Mixed Interpolation of Tensorial Components) formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model (Piezoelectric Material with Penalization and Polarization) combined with the RAMP model (Rational Approximation of Material Properties), where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element. Multiobjective functions are defined for the quasi -static and dynamic optimization problems. While the former aims at maximizing displacements or output voltages and avoiding resonance frequencies near its working range, the latter aims at designing the vibration mode, controlling the resonance frequency and maximizing the EMCC of the transducer. This text presents the complete design cycle for transducers based on piezoelectric plates designed by using the TOM and shows the applied methodology, optimization problem formulation, numerical implementation, achieved computational results, and the assembly and characterization of optimized piezoelectric transducers for experimental validation of the TO results.