Parametric excitation of the DWSC (Deep Water Stable Craneship) is studied in this thesis. It occurs for a system without any external forcing, when one of the coefficients in the equation of motion (EOM) modeling the system varies with time. Parametric instability might be triggered for certain values of the parameters describing the time-varying coefficient. The DWSC, basically a stepped classic spar with a catamaran as its deck, because of certain unique features, may be susceptible to parametric excitation. This thesis examines the phenomenon of parametric excitation with respect to roll motion in head seas, using time-domain simulation and stability analysis. It examines the DWSC's susceptibility to parametric instability using the same methods of analysis and the effect of damping (especially viscous drag) on parametric excitation and instability. The thesis uses Mathieu's equation as the basis for stability analysis and time-simulates the coupled heave-sway-roll EOM. Time-domain simulation is done for two reasons: firstly for determining the variation in roll stiffness because of a regular wave (the variation in roll stiffness is an input to the stability analysis) and secondly for simulating the coupled heave-sway-roll EOM. Both time-domain analysis and stability analysis are done for sea states of interest and for examining interesting phenomena like roll resonance (due to body-wave interaction) and parametric instability. Results highlight: 1) a "cancellation frequency" in the heave wave exciting force; 2) the effect of viscous drag on coupled heave-sway-roll motions; 3) time-simulations validating the stability analysis; 4) the trend of stability with increasing sea states, wave periods and amplitudes; 5) characteristics of parametric instability; 6) the methodology used to predict or detect parametric instability and 7) the effect of viscous drag on parametric instability.

The Variable Inertia System Wave Energy Converter (VISWEC) is a self-reacting point absorber (SRPA) type wave energy converter (WEC) capable of changing its mechanical impedance using an internal reaction mass system. The reaction mass is coupled to a rotating assembly capable of varying its inertia and this changing inertia has the effect of creating an added inertial resistance, or effective mass, to oscillations of the reaction mass. An SRPA has two main bodies, designated Float and Spar, capable of utilizing the relative motion between the two bodies to create power through a power take-off (PTO). The implementation of the reaction mass, a 3rd body, and the variable inertial system (VIS) is designed to change the response of the Spar in order to create larger relative velocities between the two bodies and thus more power. It is also possible to lock the VIS within the Spar, and when this is done the system is reduced to a conventional 2-body SRPA configuration. To better understand the effects of the implementation of the VIS on the overall stability of the VISWEC and the power conversion performance, a numerical model simulation within ProteusDS, a time-domain modelling software, was created. Power production and parametric excitation are the metrics of comparison between the two systems. Parametric excitation is a phenomenon that correlates wave excitation frequency to roll stability and has been shown to negatively affect power production in SRPAs. Simulations of the 2 and 3-body provide a basis of comparison between the two systems and allow the assessment of parametric excitation prohibited or exacerbated by the implementation of the VIS as well as power production. The simulation executed within the commercial software ProteusDS incorporates articulated bodies defined with physical parameters connected through connections allowing kinematic constraints and relations and hydrodynamics of the hull geometries as they are exposed to regular waves. ProteusDS also has the ability to apply kinematic constrains on the entire system allowing the analysis of isolated modes of motion. The implementation of the VIS demonstrates a generally higher power production and stabilization of the system with regards to parametric excitation. While the 3-body system is more stable, the bandwidth at which rolling motion is induced increased in comparison to the 2-body system. Rolling motions in both the 2 and 3-body systems are characteristic of parametric excitation and show a direct correlation to reduced power production. Overall the 3-body VISWEC outperforms the typical 2-body SRPA representation but more research is required to refine the settings of the geometric and PTO control. / Graduate

<p> This thesis describes the analytical study of the stability of the structural system under circulatory loading and/or parametric excitation. The model is a double pendulum, composed of two rigid weightless bars of equal length and two concentrated masses at the ends of each bar, on an oscillating base. The vertical oscillation of the base produces parametric excitation to the system. A circulatory force is applied at the free end. At the joints the restoring moments are produced by spring and damping. The damping coefficients are taken as positive, and the gravitational effects are included. </p> <p> The combined effect of the circulatory loading and parametric excitation on stability of the system is investigated. The problem is so formulated that the stability of the system is represented by coupled Mathieu equations. The effect of damping on the boundary of stability is also determined. </p> / Thesis / Master of Engineering (ME)

Au moyen d'une expérience d'excitation paramétrique d'onde de surface, nous mettons en évidence l'existence de nouveaux types d'ondes solitaires et stationnaires à la surface de l'eau. Ces ondes de grande amplitude sont très non-linéaires et l'étude théorique réalisée ne permet pas de rendre compte de la forme des vagues mais permet de comprendre l'origine du phénomène d'hystérésis observé qui est nécessaire à la compréhension des phénomènes observés. En effet, l'existence de ces ondes (dans notre configuration expérimentale) est conditionnée par la présence d'un domaine de bistabilité dans le plan amplitude d'excitation - amplitude des vagues au coeur duquel nous avons montré qu'il était possible d'avoir coexistence de deux solutions, une d'amplitude nulle et une d'amplitude non nulle. Ces expériences en géométrie Hele-Shaw ont aussi permis de mettre en évidence des ondes enveloppes qui ne sont encore décrit par aucun modèle existant. Il s'agit à notre connaissance de la première onde enveloppe stationnaire observé à la surface de l'eau. Nous mettons aussi en évidence des ondes de gravité de très grande amplitude, qui sont formées alternativement d'étoiles et de polygones. Nous montrons que la symétrie du motif (nombre de branche de l'étoile) est indépendante de la taille et de la forme du récipient vibré. Nous montrons qu'un mécanisme de couplage non-linéaire résonant à trois ondes peut expliquer cette géométrie, bien que cette possibilité fut rejetée pour des ondes purement gravitaire. / By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are respectively of odd and even symmetries. Both solitary waves oscillate subharmonically with the forcing frequency. They are highly nonlinear, and dier strongly from the other types of localized patterns. Moreover, to our knowledge, such a solitary waves of odd symmetry has never been reported hitherto. We report a new type of standing gravity waves of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vibrating vertically a tank. The symmetry of the star (i.e. the number of branches) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration. We show that this wave geometry results from nonlinear resonant couplings between three waves, although this possibility has been denied for pure gravity waves up to now.

Neste trabalho apresentamos o estudo da variação da temperatura cinética de átomos aprisionados magneticamente bombeados por campos eletromagnéticos externos. Aprisionamos átomos de Sódio em uma armadilha magnética de quadrupolo e submetemos esses átomos a um campo magnético externo oscilante. Medimos a temperatura e o número dos átomos remanescentes na armadilha a partir de imagens de tempo de vôo. O processo de medida consiste em desligar a armadilha, deixando a nuvem atômica expandir balisticamente e então fazer uma imagem da fluorescência desses átomos gerada por um pulso de luz próximo da ressonância atômica. Do tamanho da nuvem e do número de fótons capturados podemos obter a temperatura e o número de átomos da amostra. Observamos um significativo resfriamento para algumas freqüências de oscilação do campo externo e posterior aquecimento para freqüências um pouco maiores. Observamos ainda simultaneamente ao resfriamento uma grande perda de átomos da armadilha. Por fim, apresentamos algumas simulações numéricas que reproduzem o fenômeno observado, bem como um modelo que explica os experimentos baseado em excitação seletiva dos átomos confinados pelo campo magnético externo. / In this work we present a study of the shift of the kinetic temperature of magnetically trapped atoms, excited by external electromagnetic fields. We trapped Sodium atoms in a quadrupole magnetic trap and applied an oscilating magnetic field to these atoms. We mesured the temperature and the number of the remaining atoms from time of flight images. The measure is done turning off the trap, leaving the cloud of atoms in a ballistic expansion and making an image of the fluorescence of these atoms after the shot of a near ressonant light. From the size of the cloud and the number of photons captured we can measure the temperature and number of atoms in the sample. We observed cooling of the atoms for some frequencies of the external field and heating for frequencies a bit larger. We observed that a high number of atoms were lost from the trap simultaneously with the cooling. Finally, we present numerical simulations that reproduce the observed phenomena and a model that explains the experiments\' results based on selective excitation of the trapped atoms by the external field.

No description available.

Neste trabalho apresentamos o estudo da variação da temperatura cinética de átomos aprisionados magneticamente bombeados por campos eletromagnéticos externos. Aprisionamos átomos de Sódio em uma armadilha magnética de quadrupolo e submetemos esses átomos a um campo magnético externo oscilante. Medimos a temperatura e o número dos átomos remanescentes na armadilha a partir de imagens de tempo de vôo. O processo de medida consiste em desligar a armadilha, deixando a nuvem atômica expandir balisticamente e então fazer uma imagem da fluorescência desses átomos gerada por um pulso de luz próximo da ressonância atômica. Do tamanho da nuvem e do número de fótons capturados podemos obter a temperatura e o número de átomos da amostra. Observamos um significativo resfriamento para algumas freqüências de oscilação do campo externo e posterior aquecimento para freqüências um pouco maiores. Observamos ainda simultaneamente ao resfriamento uma grande perda de átomos da armadilha. Por fim, apresentamos algumas simulações numéricas que reproduzem o fenômeno observado, bem como um modelo que explica os experimentos baseado em excitação seletiva dos átomos confinados pelo campo magnético externo. / In this work we present a study of the shift of the kinetic temperature of magnetically trapped atoms, excited by external electromagnetic fields. We trapped Sodium atoms in a quadrupole magnetic trap and applied an oscilating magnetic field to these atoms. We mesured the temperature and the number of the remaining atoms from time of flight images. The measure is done turning off the trap, leaving the cloud of atoms in a ballistic expansion and making an image of the fluorescence of these atoms after the shot of a near ressonant light. From the size of the cloud and the number of photons captured we can measure the temperature and number of atoms in the sample. We observed cooling of the atoms for some frequencies of the external field and heating for frequencies a bit larger. We observed that a high number of atoms were lost from the trap simultaneously with the cooling. Finally, we present numerical simulations that reproduce the observed phenomena and a model that explains the experiments\' results based on selective excitation of the trapped atoms by the external field.

L’objectif principal de cette thèse vise la compréhension et la maitrise des mécanismes physiques menant à l’excitation du mode gyrotropique de vortex magnétique par transfert de spin, et en particulier l’origine des sources de bruit affectant sa dynamique. Ce travail est effectué dans la perspective de parvenir à l’amélioration des propriétés radiofréquences de ces dispositifs appelés Spin Transfer Oscillator.En effet, ces oscillateurs ont l’avantage d’être de taille submicronique (quelques dizaines à quelques centaines de nm), d’être compatibles avec les technologies CMOS et d’être résistants aux radiations. De plus, les mécanismes d’aimantation mis en jeu leur assurent une forte dépendance de la fréquence avec le courant, i.e. une bonne accordabilité, ainsi qu’une réponse dynamique rapide i.e. une agilité élevée. Cependant, différentes questions restent en suspens quant à la possibilité d’améliorer leurs conditions d’oscillations, leur puissance et la cohérence de leurs oscillations.Un premier aspect de mon travail de thèse a été d’étudier l’influence des fluctuations thermiques sur la dynamique entretenue du mode gyrotropique du cœur de vortex. Un des résultats a été de montrer que le bruit de phase du mode gyrotropique résulte majoritairement de fluctuations de phase issues directement des fluctuations thermiques auxquelles s’ajoutent des fluctuations d’amplitude converties en fluctuations de phase. Grâce à un modèle analytique, nous avons pu mettre en évidence le rôle important joué par les non-linéarités des forces agissant sur le vortex. De plus, nous avons pu mesurer les paramètres caractéristiques de l’oscillateur, à savoir, la rapidité à changer sa fréquence mais aussi le facteur de couplage amplitude-phase.La seconde étape de mes travaux a consisté à améliorer les conditions d’obtention de signal rf. Un résultat majeur de ce travail a été l’obtention d’un signal rf puissant en absence de champ magnétique. Les puissances mesurées sont de quelques centaines de µW correspondant à des largeurs de raie faibles allant de quelques centaines de kHz à quelques MHz. Cette spécificité est rendue possible pour une structure complexe de l’oscillateur où la couche magnétique qui polarise en spin le courant a une aimantation perpendiculaire et est différente de la couche de référence pour la magnétorésistance.La troisième étape a été d’optimiser le rendement de l’oscillateur. Un des résultats marquants est que nous avons pu mesurer une puissance rf émise record s’élevant à 3.6 µW, encore jamais obtenue à température ambiante pour les oscillateurs à transfert de spin à base de vortex. Ces fortes puissances résultent du développement de nouvelles jonctions à base de FeB effectués par le groupe de S. Yuasa (AIST, Japon) pour lesquelles l’amélioration de la qualité de la jonction, nous a permis d’obtenir une magnétorésistance atteignant 125% .La faible taille de l’oscillateur a donc un coût qui se paye en termes de bruit de phase. Une solution qui permettrait de résoudre cette limitation et d’améliorer la cohérence des oscillations est la synchronisation mutuelle de plusieurs oscillateurs à transfert de spin au travers des courants rf émis par chacun. Ainsi, la dernière étape de ma thèse a été d’étudier le comportement du mode gyrotropique lorsqu’il est soumis à un courant alternatif. Un résultat important a été de montrer, grâce à une étude expérimentale appuyée sur un modèle analytique, le rôle crucial des non-linéarités et des symétries des forces de synchronisation du mode excité.Ces différents travaux nous ont fournis les outils pour mieux comprendre la dynamique du vortex magnétique et nous ont amené à mettre en place un banc de mesure original pour lequel l’oscillateur se synchronise sur lui-même. En fonction du retard avec lequel le signal émis par l’oscillateur est réinjecté, nous avons pu montrer pour la première fois que la fréquence, la puissance mais aussi la largeur de raie des oscillations peuvent être modulées. / The main goal of this thesis is the understanding of the physical mechanisms and the subsequent control of the properties at the origin of the spin transfer induced magnetic vortex gyrotropic motion in confined systems. In particular the origin of the noise affecting the dynamics has been investigated. This work has been performed with a view to improving the radiofrequency (rf) properties of the so-called Spin Transfer Oscillator (STO).The advantages of such oscillators are their sub-micron size (from few tens to hundreds of nanometres), their compatibility with CMOS technologies and their radiation hardness. Moreover, the magnetization dynamics involved permit a large tunability of frequency as a function of the applied current and a high agility i.e. a fast dynamical response. Nevertheless, several open questions exist regarding the possible optimization of the sustained oscillation conditions and the improvement of the STO power and spectral coherence.The first aspect of my work was to investigate the influence of thermal fluctuations over the sustained vortex core gyrotropic motion. One of the key results of my thesis was to show that the phase noise results from direct phase fluctuations from thermal fluctuations plus amplitude fluctuations converted to phase noise. With an analytical model, we were able to highlight the major role played by the non-linearities of the forces acting on the vortex core. In addition, we were able to measure the characteristic parameters of the oscillator, namely, the speed of frequency response to perturbations as well as the phase-amplitude coupling coefficient.The second important part of my work has been to improve the conditions for obtaining an rf signal. An important result of this work was the measurement of a powerful rf signal in the absence of a magnetic field. The measured powers are a few hundred milliwatts and correspond to low linewidths, ranging from a few hundred kilohertz to a few megahertz. The zero field behaviour was made possible due to the complex structure of the oscillator where the magnetic layer which polarizes the spin current has a perpendicular magnetization, in contrast to the in-plane polarized reference layer.The third step was to optimize the performance of the oscillator. One of the striking results of this thesis is that we measured a record rf output power, up to 3.6 µW, the largest obtained at room temperature for vortex based STOs so far. This high output power results from the development of new FeB based junctions made by the group of Pr. S. Yuasa (AIST, Japan), where the improvement of the quality of the junction allowed us to obtain a magnetoresistance up to 125%.The small size of the oscillator has a cost that is paid in terms of the phase noise. One possible solution that would solve this limitation and enhance the coherence of the oscillations is via mutual synchronization of several STOs through rf currents emitted by each oscillator. Thus, the last stage of my thesis was to study the behaviour of gyrotropic motion when subjected to an alternating current. An important result was to show, through an experimental study in conjunction with an analytical model, the crucial role of the non-linearities and symmetries of the synchronization forces.These various studies have provided us the tools to better understand the dynamics of magnetic vortex and led us to develop an original tester for which the oscillator synchronizes itself with its own rf signal. Depending on the delay at which the oscillator is fed back, we showed for the first time that the frequency, the power and also the linewidth of the oscillations can be modulated.

We tackle the problem of suppressing high-amplitude vibrations of cantilever beams when subjected to either primary external or principal parametric resonances. Guided by results of previous investigations into the nonlinear dynamics of single- and multi-degree-of-freedom structures, we design mechatronic systems of sensors, actuators, and electronic devices and implement nonlinear active feedback control. In the case of external excitation, we devise two vibration absorbers based on either quadratic or cubic feedback. We conduct theoretical analyses and demonstrate that when a two-to-one (one-to-one) internal resonance condition is imposed between the plant and the quadratic (cubic) absorber, there exists a saturation phenomenon. When the plant is forced near its resonant frequency and the forcing amplitude exceeds a certain small threshold, the nonlinear coupling creates an energy-transfer mechanism that limits (saturates) the response of the plant. Our theoretical studies reveal that the cubic absorber creates regimes of high-amplitude quasiperiodic and chaotic responses, thereby limiting its utility. However, we show that superior results can be achieved when the natural frequency of the quadratic absorber is set equal to one-half the excitation frequency. Consequently, we apply the quadratic technique through a variety of linear and nonlinear actuators, sensors, and electronic devices. We design and build second-order analog circuits that emulate the quadratic absorber. Using a DC motor, piezoelectric ceramics, and Terfenol-D struts as actuators and potentiometers, strain gages, and accelerometers as sensors, we demonstrate successful single- and multi-mode vibration control. In order to realize a more versatile implementation of the control strategy, we resort to a digital signal processing (DSP) board. We compose a code in C and design a digital absorber by developing algorithms that, in addition to replacing the analog circuit, automatically detect the amplitude and frequency of oscillation of the plant and fine-tune the absorber parameters. We take advantage of the digital realization, implement a linear absorber, and compare the performance of the quadratic absorber with that of its linear counterpart. In the case of parametric excitation, we investigate two techniques. First, we explore application of the quadratic absorber. We prove theoretically and demonstrate experimentally that this control scheme is not reliable. Then, we propose an alternate approach. We devise a control law based on cubic velocity feedback. We conduct theoretical and experimental investigations and show that the latter strategy leads to effective vibration suppression and bifurcation control. / Ph. D.

This thesis describes the analytical study of a structural system under the combined action of noncirculatory or circulatory loading and oscillating base motion. The model is a double inverted pendulum composed of two rigid weightless bars of equal length with two concentrated masses at the ends of each bar, on an oscillating base. Noncirculatory or circulatory loading is applied at the free end. At the hinges restoring moments are produced by spring and damping forces. Damping coefficients are taken as positive, and gravitational effects are considered. The stability of the system under the combined action of the noncirculatory or circulatory loading and the parametric excitation can be investigated by Hsu's method. This method is applied to solve the coupled Mathieu equations by the given system and determine the unstable resonance, a nonlinear analysis is used to find the steady state response. / Thesis / Master of Engineering (MEngr)