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O método de Rietveld (MR) de refinamento de estruturas de amostras policristalinas, com dados de difração de raios X foi implantado. Foram realizados testes com amostras de NaCl, NaCl:KCl (1:1 em massa) e PbTiO3. Nos testes com NaCl, foram refinados a escala e os parâmetros de rede, vibrações térmicas e perfil com várias funções para o ajuste do perfil e &#916 2 &#952 = 0.01, 0.02 e 0.04&#176. A análise quantitativa com as amostras de NaCl:KCl (1:1 em massa) preparadas para esse fim mostraram que o MR fornece bons resultados. Foi observado que a proporção de NaCl aumentou ligeiramente com a relação à de KCl em cada conjunto de dados sucessivamente medido. Nos testes com PbTiO3, os resultados mostraram uma boa concordância com os resultados obtidos com difração de nêutrons. A seguir, o método foi aplicado no estudo das cerâmicas piezoelétricas (Pb1-3/2yLay)TiO3 (PLT) e Pb(Zr1-xTix)O3 (PZT). Para o PLT o MR foi aplicado para a determinação precisa do deslocamento dos cátions relativamente ao centro dos respectivos poliedros de coordenação (CQPb para o Pb/La e CQTi para o Ti) tendo sido encontrado: Pb/La - CQPb = 0.68(2)&#197 (y=0.025), 0.43(2)&#197 (y=0.10), 0.25(2)&#197 (y=0.20) e Ti - CQTi = 0.66(2)&#197 (y=0.025), 0.36(4)&#197 (y=0.10) e 0.18(7)&#197 (y= 0.20). No caso do PZT duas amostras foram estudadas. Com a primeira, preparada pela técnica de co-precipitação, o MR foi aplicado para a determinação da fórmula química, tendo sido encontrado PbZr0.30Ti0.70O3. Com a segunda, preparada por mistura convencional de óxidos, o MR foi aplicado para a determinação da proporção das fases tetragonal e romboédrica coexistentes na amostra, fornecendo 79% de tetragonal e 21% de romboédrica / The Rietveld method (RM) of structura refinement of polycrystalline samples with X-ray diffraction data was implemented. Tests were performed with samples of NaCl, NaCl:KCl (1:1 in weight) and PbTiO3. for NaCl, the scale factor, lattice, thermal vibrations and profile parameters were refined with several profile functions and step lenght of 0.01, 0.02 and 0.04&#176. The quantitative alanysis test with the NaCl:KCl (1:1 in weight) sample prepared for this purpose, showed that the RM gives good results. It was observed that the relative proportion of NaCl had a slight increase for each successive data collection. In the tests with PbTiO3, the results showed good agreement with that of nêutron diffraction. The method was applied in the analysis of the piezoelectrics ceramics (Pb1-3/2yLay)TiO3 (PLT) and Pb(Zr1-xTix)O3 (PZT). In the PLT cases the RM was applied for the precise determination of the cátions shifts from their coordination polyedra centre (CQPb for Pb/La and CQTi for Ti) and it was found that Pb/La - CQPb = 0.68(2)&#197 (y=0.025), 0.43(2)&#197 (y=0.10), 0.25(2)&#197 (y=0.20) and Ti - CQTi = 0.66(2)&#197 (y=0.025), 0.36(4)&#197 (y=0.10) and 0.18(7)&#197 (y= 0.20). For the PZT two samples were studied. With the first, prepared by co-precipitation technique, the RM was applied for the determination of the chemical formula, and it was found to be PbZr0.30Ti0.70O3. For the second, prepared by conventional technique of mixture of oxides, the RM was applied for the quantitative analysis of the coexisting phases in the sample, and it was found to be 79% tetragonal and 21% rhombohedra

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A nonlinear active vibration absorber to control the vibrations of plates is investigated. The absorber is based on the saturation phenomenon associated with dynamical systems with quadratic nonlinearities and a two-to-one internal resonance. The technique is implemented by coupling a second-order controller with the plate's response through a sensor and an actuator. Energy is exchanged between the primary structure and the controller and, near resonance, the plate's response saturates to a small value. Numerical as well as experimental results are presented for a cantilever rectangular plate. For numerical studies, finite-element methods as well as modal analysis are implemented. The commercially available software ABAQUS is used in the finite-element analysis together with a user-provided subroutine to model the controller. For the experimental studies, the plate is excited using a dynamic shaker. Strain gages are used as sensors, while piezoelectric ceramic patches are used as actuators. The control technique is implemented using a dSPACE digital signal processing board and a modeling software (SIMULINK). Both numerical and experimental results show that the control strategy is very efficient. A numerical study is conducted to optimize the location of the actuators on the structure to maximize its controllability. In this regard, the control gain is maximized for the PZT actuators. Furthermore, a more general method is introduced that is based on a global measure of controllability for linear systems. Finally, the control strategy is made adaptive by incorporating an efficient frequency-measurement technique. This is validated by successfully testing the control strategy for a non-conventional problem, where nonlinear effects hinder the application of the non-adaptive controller. / Ph. D.

Les systèmes de récupération d’énergies basées sur les vibrations mécaniques environnantes suscitent l’intérêt depuis de nombreuses années. Augmenter l’efficacité de la conversion d'énergie est primordial, mais celle-ci pour être bien maitrisée, passe par la mise au point de modèles précis et notamment par la prise en compte des lois régissant les matériaux piézoélectriques. En effet, ces matériaux sont à la base des couplages mécano/électriques et il est capital de comprendre comment ils fonctionnent quelque soit l'excitation externe. Un modèle précis du matériau ferroélectrique est indispensable pour établir des critères de conception des prototypes et leur optimisation. Dans cette thèse, un modèle précis, temporel, large bande tenant compte de l’ensemble des non-linéarités d’une céramique piézoélectrique a été développé. L’utilisation d’opérateurs fractionnaires a permis d’augmenter fortement la bande de fréquence de validité du modèle. Le modèle permet notamment de prévoir l’évolution de la polarisation diélectrique ainsi que le déplacement mécanique de l’échantillon testé et ceci quelque soit le type de stimulation (contrainte mécanique pure, champ électrique et même excitation hybride électriques/mécaniques). La dérivé fractionnaire a dans un premier temps été utilisée pour l’hystérésis sous excitation électrique pour décrire le comportement dynamique de la polarisation diélectrique. En effet, au delà d’un seuil de fréquence, lorsque l’état du matériau n’est plus quasi-statique, une contribution dynamique apparaît. Cette contribution joue un rôle primordial lorsque les niveaux de fréquence et d’amplitude sont élevés. La même étude a ensuite été menée sous contrainte mécanique, et le même opérateur fractionnaire a été utilisé avec succès. Nous avons entre autre constaté que sur un même échantillon les paramètres de simulation établis sous champ électrique étaient conservés sous contrainte mécanique. Ensuite, un modèle inverse permettant d’imposer la forme d’onde de la polarisation ou du déplacement a été proposé. Pour une polarisation ou un déplacement donné, le modèle inverse permet de déterminer avec précision l’effort mécanique à appliquer sur la céramique piézo-électrique. Ces modèles sont nécessaires pour optimiser une forme d’onde de contrainte mécanique ou électrique et obtenir un rendement supérieur des systèmes récupérateurs d’énergie. En effet, une nouvelle technique couplée champ électrique/contrainte mécanique de récupération d’énergie est présentée à la fin de la thèse, technique qui nous a permis de valider l’utilisation du modèle. L’utilisation du modèle permet d’optimiser la mise au point d’un prototype mais également d’obtenir la valeur exacte du rendement de la méthode en rendant compte notamment des pertes diélectriques. Dans la thèse, le modèle sous ses différentes variantes est décrit de manière exhaustive. / Energy harvesting based on mechanical vibration has been a long time research topic for the last few decades. In addition to enhancing the energy conversion amount, another objective is to master and give a precise model with consideration of the disciplines of piezoelectric material behavior. A precise model for the ferroelectric material is mighty needed in the energy harvesting process, so as to give an instruction to the prototype designing and modelling optimizing. In this thesis, a model working on wide bandwidth considering the nonlinearity of the piezoceramic has been developed. The employment of the fractional derivative has broadened the usage of this model on expanded bandwidth. The model permit to predict the evolution of the dielectric polarization as well as the mechanical displacement, which has been tested on different samples under different kinds of stimulation (pure mechanical, pure electrical and hybrid of electrical and mechanical excitations). This fractional derivative factor has been first developed under electrical excitations to describe the dynamic behavior. In the development of this model to mechanical field, the fractional derivative factor was found available as well under the mechanical excitation in the same value. In the following study, an inverse of mechanical model has been developed as well. In the end, we stimulate the piezoceramic using both electrical and mechanical excitation to augment the energy harvesting amount which could become a promising method in energy harvesting field. Every model has been exhaustively demonstrated and specific measuring benches have been established to validate these models. Experiments results and simulations in different kinds of excitations (amplitudes, frequencies) for every kind of the above models have been compared. Good approximation has been acquired indicating the model has a good accuracy in describing the material property and dynamic behavior.

Much recent research has focused on the development lead-free perovskite piezoelectrics as environmentally compatible alternatives to lead zirconate titanate (PZT). Two main categories of lead free perovskite piezoelectric ceramic systems were investigated as potential replacements to lead zirconate titanate (PZT) for actuator devices. First, solid solutions based on Li, Ta, and Sb modified (K���.���Na���.���)NbO��� (KNN) lead-free perovskite systems were created using standard solid state methods. Secondly, Bi-based materials a variety of compositions were explored for (1-x)(Bi���.���Na���.���)TiO���-xBi(Zn���.���Ti���.���)O��� (BNT-BZT) and Bi(Zn���.���Ti���.���)O������(Bi���.���K���.���)TiO������(Bi���.���Na���.���)TiO��� (BZT-BKT-BNT). It was shown that when BNT-BKT is combined with increasing concentrations of Bi(Zn[subscript 1/2]Ti[subscript 1/2])O��� (BZT), a transition from normal ferroelectric behavior to a material with large electric field induced strains was observed. The higher BZT containing compositions are characterized by large hysteretic strains (> 0.3%) with no negative strains that might indicate domain switching. This work summarizes and analyzes the fatigue behavior of the new generation of Pb-free piezoelectric materials. In piezoelectric materials, fatigue is observed as a degradation in the electromechanical properties under the application of a bipolar or unipolar cyclic electrical load. In Pb-based materials such as lead zirconate titanate (PZT), fatigue has been studied in great depth for both bulk and thin film applications. In PZT, fatigue can result from microcracking or electrode effects (especially in thin films). Ultimately, however, it is electronic and ionic point defects that are the most influential mechanism. Therefore, this work also analyzes the fatigue characteristics of bulk polycrystalline ceramics of the modified-KNN and BNT-BKT-BZT compositions developed. The defect chemistry that underpins the fatigue behavior will be examined and the results will be compared to the existing body of work on PZT. It will be demonstrated that while some Pb-free materials show severe property degradation under cyclic loading, other materials such as BNT-BKT-BZT essentially exhibit fatigue-free piezoelectric properties with chemical doping or other modifications. Based on these results, these new Pb-free materials have great potential for use in piezoelectric applications requiring a large number of drive cycles such as MEMS devices or high frequency actuators. / Graduation date: 2013

This thesis presents mathematical modeling and control techniques that can be used to predict and specify performance of biologically inspired actuation systems called cellular actuators. Cellular actuators are modular units designed to be connected in bundles in manner similar to human muscle fibers. They are characterized by inherent compliance and large numbers of on-off discrete control inputs. In this thesis, mathematical tools are developed that connect the performance to the physical manifestation of the device. A camera positioner inspired by the human eye is designed to demonstrate how these tools can be used to create an actuator with a useful force-displacement characteristic. Finally, control architectures are presented that use discrete switching inputs to produce smooth motion of these systems despite an innate tendency toward oscillation. These are demonstrated in simulation and experiment.

High performance twin-tail aircraft, like the F-15 and F/A-18, encounter a condition known as tail buffet. At high angles of attack, vortices are generated at the wing fuselage interface (shoulder) or other leading edge extensions. These vortices are directed toward the twin vertical tails. When the flow interacts with the vertical tail it creates pressure variations that can oscillate the vertical tail assembly. This results in fatigue cracks in the vertical tail assembly that can decrease the fatigue life and increase maintenance costs. For many years, research has been conducted to understand this phenomenon of buffet and to reduce its adverse effects on the fatigue life of aerospace structures. Many proposed solutions to this tail buffet problem have had limited success. These include strengthening the tail, modifying the vortex flow, using an active rudder control, and leading edge extensions. Some of the proposed active controls include piezoelectric actuators. Recently, an offset piezoceramic stack actuator was used on an F-15 wind tunnel model to control buffet induced vibrations at high angles of attack. The controller was based on acceleration feedback control methods. In this thesis a procedure for designing the offset piezoceramic stack actuators is developed. This design procedure includes determining the quantity and type of piezoceramic stacks used in these actuators. The changes of stresses, in the vertical tail caused by these actuators during an active control, are investigated. In many cases, linear controllers are very effective in reducing vibrations. However, during flight, the natural frequencies of the vertical tail structural system changes as the airspeed increases. This in turn, reduces the effectiveness of a linear controller. Other causes such as the unmodeled dynamics and nonlinear effects due to debonds also reduce the effectiveness of linear controllers. In this thesis, an adaptive neural network is used to augment the linear controller to correct these effects.

Magnetoelectric (ME) interactions in matter correspond to the appearance of magnetization by means of an electric field (direct effect) or the appearance of electric polarization by means of a magnetic field (converse effect). The composite laminates which possess large ME coefficient, have attracted much attention in the field of sensors, modulators, switches and phase inverters. In this thesis, we report on the ME performances of the bi- and tri- layered composites. It is shown that their ME couplings can be achieved by combining magnetostrictive and piezoelectric layers. A model based on a driven damped oscillation is established for the piezoelectric/magnetostrictive laminated composite. It is used to simulate the mechanical coupling between the two layers. In addition, we report that the ME coupling can be achieved without magnetic phase but only with eddy current induced Lorentz forces in the metal electrodes of a piezoelectric material induced by ac magnetic field. The models based on the Lorentz effect inducing ME coupling in PZT unimorph bender, polyvinylidene fluoride (PVDF) film and PZT ceramic disc are thus established. The results show the good sensitivity and linear ME response versus dc magnetic field change. Thus, the room temperature magnetic field detection is achievable using the product property between magnetic forces and piezoelectricity. Besides, we report on the electrostrictive performance of cellular polypropylene electret after high-voltage corona poling. We use the Surface Potential test, Thermal Stimulated Depolarization Current experiment and Differential Scanning Calorimetry experiment to analyse its charge storage mechanism. The result show that the electrostrictive coefficient and relative permittivity of the charged samples increase. Last but not least, in order to explain this phenomenon, a mathematic model based on the charged sample has been established.

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