Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / As cerâmicas piesoelétricas estudadas neste trabalho (Pb1,03Zr0,53Ti0,47O3, Pb1,03Zr0,525Nb0,05Ti0,465Fe0,005O3, Pb1,03Zr0,515Nb0,015Ti0,465Fe0,005O3, Pb1,03Zr0,525Nb0,005Ti0,455Fe0,015O3 e Pb1,03Zr0,515Nb0,015Ti0,455Fe0,015O3) foram sinterizadas a 1200oC e 1250oC por 3,5 h a fim de que suas propriedades piesoelétricas fossem investigadas. Nas composições dos PZT obtidas, a matriz e os dopantes empregaram óxidos como matérias primas. As misturas dos óxidos precursores foram calcinadas a 850oC por 3,5 h para obtenção da fase PZT. Os precursores, os pós e os corpos de prova de PZT foram caracterizados quanto às microestruturas, densidades e propriedades físicas. Após a conformação dos pós e a sinterização, os materiais cerâmicos foram polarizados para caracterização de suas propriedades piesoelétricas através de um impedancímetro na faixa de freqüência de 100 KHz a 200 KHz. Os resultados de dispersão de laser dos precursores revelaram aglomeração do óxido de chumbo e óxido de zircônio. As composições calcinadas apresentaram tamanho de partícula na faixa de 0,44 μm a 0,63 μm. As análises de densidade por método de Arquimedes indicaram uma boa densificação dos corpos de prova sinterizados e pouca influência da temperatura de sinterização com uma escala de valores de 95,73 a 97,65% da densidade teórica. As análises de microscopia eletrônica de varredura revelaram que os sinterizados contendo concentrações diferentes de dopantes exibem uma correlação do tipo e teor de dopante com a natureza da fratura, sendo transgranular, quando dopante ferro for predominante e intergranular, quando o dopante Nb for predominante. Também, o aumento da temperatura de sinterização resultou em fratura transgranular independente do tipo e da concentração de dopante, exceto para baixo teor de dopante da composição equimolar, cujos resultados não foram consistentes com a literatura sobre o material. No que diz respeito às propriedades piesoelétricas, revelou-se que a combinação da variação da composição com a temperatura foi favorável para o aumento dos valores da constante dielétrica da formulação equimolar com maior percentual de dopantes. Já o efeito da temperatura com a composição surtiu um efeito muito negativo para os valores de fator de qualidade mecânica da formulação dopada com mais ferro. Para os valores de constante de freqüência da formulação com maior percentagem de nióbio, o efeito da temperatura com a composição gerou um efeito positivo. / The piezoelectric ceramics studied in this work, Pb1.03Zr0.53Ti0.47O3, Pb1.03Zr0.525Nb0.05Ti0.465Fe0.005O3, Pb1.03Zr0.515Nb0.015Ti0.465Fe0.005O3, Pb1.03Zr0.525Nb0.005Ti0.455Fe0.015O3 and Pb1.03Zr0.515Nb0.015Ti0.455Fe0.015O3, were all of them sintered between 1200oC and 1250oC for 3.5h. After that, their piezoelectric properties were investigated. In the present work, oxides were used as raw material in both, matrices and dopants. The mixture of the precursor oxides were calcinaned at 850oC during 3.5h for obtaining the PZT phase. The precursor oxides, the powders and the PZT samples went through characterization tests in order to have their microstructures, densities and physical properties correctly determined. After the powders had been conformed and performed the sinterization process, the PZT ceramics were polarized and their piezoelectric properties determined by using an impedancemeter working in the frequency from 100 KHz to 200 KHz. The obtained results from laser dispersion had revealed agglomeration of lead and zirconium oxide. The calcined samples presented particle sizes from 0.44 μm to 0.63 μm. The density analyses using the Archimedes method indicated a good densification of the sintered samples and a weak influence of the sintering temperature on the obtained density values, whose values ranged from 95.73 to 97.65 % of the theoretical density value. Analysis performed using the scanning electron microscopy technique (MEV) revealed that the sintered samples had showed a correlation between the type and concentration of the dopant with their fracture mode, which were transgranular when Fe prevails over the Nb as dopant, and intergranular, when is the Nb that prevails over the Fe as dopant. By the other side, from increasing the sintering temperature resulted transgranular fractures, independently of which type and content of dopant had been used, except for the equimolar case with relatively low content of dopant, whose results were not consistent with the literature related to this material. About the piezoelectric properties, the results had showed that the combination of the dopant composition with the sintering temperature had brought better values of dielectric constant for the equimolar formulation with more content of dopant. Relating to the mechanical quality factor, from the combination of the dopant composition with the sintering temperature had decreased the factor when Fe prevails over Nb and increased the frequency factor when is the Nb that prevails over the Fe.

O uso de materiais piezelétricos no desenvolvimento de dispositivos para o aproveitamento de energia provinda de vibrações mecânicas, Energy Harvesting, tem sido largamente estudado na última década. Materiais piezelétricos podem ser encontrados na forma de finas camadas ou pastilhas, sendo facilmente integradas a estruturas sem aumento significativo de massa. A conversão de energia mecânica em energia elétrica se dá graças ao acoplamento eletromecânico dos materiais piezelétricos. A maioria das publicações encontradas na literatura exploram o uso de dispositivos eletromecânicos ressonantes, sintonizados na frequência de operação da estrutura, maximizando assim, a energia elétrica de saída dada uma certa condição de operação. O desempenho desses dispositivos ressonantes para coletar e armazenar energia é altamente dependente da adequada sintonização da sua frequência de ressonância com a frequência de operação do sistema/estrutura. Este trabalho apresenta o projeto, otimização e análise de incertezas de um dispositivo coletor/armazenador de energia que consiste em uma placa sob duas condições de contorno, engastada-livre (EL) e deslizante-livre (DL), com massa sísmica e materiais piezelétricos conectados a um circuito shunt. Um modelo em elementos finitos de placa laminada piezelétrica conectada a circuitos R e RL é utilizado combinando as teorias de camada equivalente e deformação de cisalhamento de primeira ordem. A disposição/quantidade de material piezelétrico bem como a massa sísmica acoplados à estrutura foram otimizadas utilizando-se um Algoritmo Genético, levando em conta análises mecânica (modelo mecânico, geometria, peso) e elétrica (modelo elétrico, circuito armazenador). Além disso, o efeito de incertezas dos parâmetros dielétrico e piezelétrico do transdutor, e da indutância elétrica ligada em série ao circuito coletor/armazenador de energia foi estudado. Os resultados indicam que a inclusão de uma indutância sintética ao circuito pode melhorar a coleta de energia em uma banda de frequência e, ainda, que a otimização geométrica pode reduzir a quantidade de material piezelétrico sem no entanto diminuir significativamente a energia gerada. / The use of piezoelectric materials in the development of devices to harvest energy from mechanical vibrations (Energy Harvesting) has been widely studied in the last decade. Piezoelectric materials can be found in the form of thin layers or patches easily integrated into structures without significant mass increase. The conversion of mechanical energy into electric power is provided by the electromechanical coupling of piezoelectric materials. Most publications in the literature explore the use of resonant electromechanical devices, tuned to the operating frequency of the host structure, thus maximizing the power output given a certain operating condition. The performance of these resonant devices to harvest and store energy is highly dependent on the proper tuning of its resonance frequency with the operation frequency of the system/structure. This work presents a design, optimization and uncertainty analysis of energy harvester device consisting of a plate with tip mass and piezoelectric materials connected to shunt circuits. Two boundary conditions are used for the plate, cantilever (EL) and sliding-free (DL). A coupled finite element model with R and RL circuits, combining equivalent single layer and first order shear deformation theories, was used. The distribution and volume of piezoelectric material and the tip mass coupled to the structure were optimized using a Genetic Algorithm, accounting for both mechanical (mechanical model, geometry, weight) and electric (electric model, storer circuit) analyses. Furthermore, the effect of uncertainties of transducer dielectric and piezoelectric constants and electric inductance connected in series with harvesting circuit was studied. The results indicate that the inclusion of a synthetic inductance can improve energy harvesting performance over a frequency range and also that the geometric optimization may reduce the piezoelectric material volume without diminishing significantly the harvested energy.

Esta tese apresenta uma análise numérica do controle de vibrações estruturais através de cerâmicas piezelétricas em extensão conectadas a circuitos ativo-passivos compostos por resistência, indutância e fonte de tensão. Para tal, um modelo de elementos finitos de vigas sanduíche com três camadas elásticas e/ou piezelétricas foi desenvolvido. Realizou-se também uma modelagem dos componentes do circuito elétrico e seu acoplamento à estrutura gerando assim uma equação de movimento acoplada para a estrutura com elementos piezelétricos conectados aos circuitos elétricos. Uma análise harmônica das equações obtidas foi realizada para se obter uma avaliação preliminar dos efeitos causados pelos componentes elétricos do circuito na estrutura. Observou-se que os elementos passivos do circuito, resistência e indutância, tem não somente um efeito de absorvedor dinâmico de vibrações mas, também, promovem uma amplificação da autoridade de controle no caso de se atuar através da fonte de tensão. Usando a metodologia tradicional de projeto de absorvedores dinâmicos de vibrações, derivou-se expressões para os valores de resistência e indutância de modo a maximizar o desempenho passivo do sistema. Uma análise do efeito de incertezas das constantes piezelétricas e dielétricas da cerâmica piezelétrica considerada e dos componentes de resistência e indutância do circuito elétrico no desempenho do controle passivo e ativo-passivo de estrutura tipo viga cantilever foi realizada. O objetivo desta análise foi quantificar robustez e sensibilidade do controle proposto. Em sequida, um estudo de otimização dos valores de resistência e indutância do circuito elétrico em função da tensão elétrica de controle máxima a ser aplicada em uma placa com diversos atuadores piezelétricos foi realizado. Finalmente e também para a estrutura tipo placa, uma análise de incertezas da rigidez da cola na interface entre estrutura e atuadores piezelétricos e seus efeitos no desempenho do controle passivo e ativo-passivo foi realizada. / This work presents a numerical analysis of the structural vibration control using piezoelectric materials in extension mode connected to active-passive electric circuits composed of resistance, inductance and voltage source. For that, a finite element model for sandwich beams with three elastic or piezoelectric layers was developed. A modeling of the electric circuit dynamics and its coupling to the structure with piezoelectric elements was also done. A harmonic analysis of the resulting equations was performed to yield a preliminary evaluation of the effects caused by the electric circuit components on the structure. It was observed that the passive circuit components not only lead to a dynamic vibration absorber effect but also to an amplification of the control authority in case of actuation using the voltage source. Using the standard methodology for the design of dynamic vibration absorbers, expressions were derived for the resistance and inductance values that optimize the passive vibration control performance of the system. An analysis of the effect of uncertainties of piezoelectric and dielectric constants of piezoelectric ceramic and resistance and inductance components of the shunt circuit on the passive and active-passive control performance for a cantilever beam structure was performed. The objective of this analysis was to quantify robustness and sensitivity of the proposed control. Then, an optimization study of the values of resistance and inductance of the shunt circuit as a function of the maximum control voltage to be applied on a plate with several piezoelectric actuators was performed. Finally and also for the plate structure, an analysis of uncertainties in the stiffness of the adhesive interface between structure and piezoelectric actuators and their effects on the performance of passive control and active-passive was performed.

Les matériaux à gradient d'indice de réfraction (GRIN) présentent des propriétés mécaniques variant en temps ou/et en espace. Ils ont été testés pour des applications prometteuses dans de nombreuses applications d'ingénierie, comme pour le contrôle santé structurale ou la surveillance de structure (SHM), le contrôle des vibrations et bruit, la récupération d'énergie, etc. D'un autre côté, les matériaux piézoélectriques offrent la possibilité de réaliser des cellules composites dont les propriétés mécaniques peuvent être contrôlées en ligne. Motivé par ces deux approches, cette thèse étudie la mise en œuvre de structures GRIN adaptatifs pour le contrôle des ondes élastiques. Deux types de structures GRIN adaptatifs sont étudiés dans ce travail. Le premier exemple concerne la mise en œuvre d'une lentille piézoélectrique dans une plaque. Il est composé de patchs piézoélectriques shuntés, collés périodiquement en surface du guide d'ondes. Les circuits de shunt utilisés permettent d'émuler une capacité négative (NC). En accordant les valeurs de NC on peut ajuster l'indices de réfraction du milieu à l'intérieur de la lentille piézoélectrique et pour satisfaire une fonction sécante hyperbolique. Les résultats numériques montrent que les lentilles piézoélectriques peuvent alors focaliser les ondes de flexion de la plaque sur les points focaux. La lentille piézoélectrique est efficace dans une grande bande de fréquences et efficace dans une grande plage de fonctionnement. Ainsi elle peut focaliser des ondes sur différent points par simple ajustement des valeurs de NC réalisés par le circuit. Cette focalisation adaptative la rend très intéressante pour de nombreuses applications comme la récupération d'énergie ou le SHM. La mise en œuvre de ces techniques pour la récupération d'énergie est discutée dans cette thèse. Le second exemple concerne l'étude d'une structure dont les propriétés mécaniques sont contrôlées en temps et en espace. En particulier, une modulation périodique permet de créer une onde artificielle se propageant dans la structure. L'interaction avec des ondes mécaniques entraîne une rupture de réciprocité visible dans un diagramme de bande non symétrique. De nombreux phénomènes inhabituels sont observés dans ce type de structures variables : fractionnement des fréquences, conversion d'ondes et transmission unidirectionnelles. Deux types de conversion fréquentielle sont démontrés et expliqués. Le premier est induit par la transmission d'énergie entre les différents modes Bloch et le second type est dû à la diffusion de Bragg dans les structures modulées. La transmission unidirectionnelle des ondes pourrait être exploitée pour réaliser des diodes dans des systèmes infinis ou semi-infinis. Cependant, la transmission unidirectionnelle n'existe pas dans les systèmes finis en raison des phénomènes de conversion de fréquence. / GRadient INdex (GRIN) media are those whose properties smoothly vary in space or/and time. They have shown promising effects in many engineering applications, such as Structural Health Monitoring (SHM), vibration and noise control, energy harvesting, etc. On the other hand, piezoelectric materials provide the possibility to build unit cells, whose mechanical properties can be controlled on-line. Motivated by these two facts, adaptive GRIN structures, which can be realized using shunted piezoelectric materials, are explored in this dissertation to control guided elastic waves. Two types of adaptive GRIN structures are studied in this work. The first type is a piezo-lens. It is composed of shunted piezoelectric patches bonded on the surfaces of plates. To control the mechanical properties of the piezoelectric composite, the piezoelectric patches are shunted with Negative Capacitance (NC). By tuning the shunting NC values, refractive indexes inside the piezo-lens are designed to satisfy a hyperbolic secant function in space. Numerical results show that the piezo-lens can focus waves by smoothly bending them toward the designated focal point. The piezo-lens is effective in a large frequency band and is efficient in many different working conditions. Also the same piezo-lens can focus waves at different locations by tuning the shunting NC values. The focusing effect and tunable feature of piezo-lens make it useful in many applications like energy harvesting and SHM. The former application is fully discussed in this thesis. The focusing effect at the focal point results in a known point with high energy density, therefore harvesting at the focal point can yield more energy. Besides, the tunable ability makes the harvesting system adaptive to environment changes. The second type is the time-space modulated structure. Its properties are modulated periodically both in time and space. Particularly, the modulation works like a traveling wave in the structure. Due to the time-varying feature, time-space modulated structures break the reciprocity theorem, i.e., the wave propagation in them is nonreciprocal. Many unusual phenomena are observed during the interaction between waves and time-space modulated structures: frequency splitting, frequency conversion and one-way wave transmission. Two types of frequency conversion are demonstrated and explained. The first type is caused by energy transmission between different orders Bloch modes. The second type is due to the Bragg scattering effect inside the modulated structures. The one-way wave transmission could be exploited to realize one-way energy insulation in equivalent infinite or semi-inffnite systems. However, the one-way energy insulation fails in finite systems due to the frequency conversion phenomenon.

Mechanical vibrations in large structures such as buildings, bridges, dams and critical frequencies in large machinery generally have low frequencies (100Hz-1000Hz). To monitor large areas of such structures we need huge network of low cost, easily manufacturable, self-powered and stand-alone vibration spectrum sensors. The sensors should also consume very little power during their overall operation cycle and have moderately high frequency resoultion. The thesis provides mathematical analysis, design and development of stand-alone, low frequency vibration spectrum analyzer .A mechanically stretched polymer piezoelectric membrane, which has a fixed length and tension, can act as a single frequency detector due to its unique resonant frequency. Stretching multiple ribbons of diffferent lengths and tensions, a vibration spectrum analyzer, which gives the Fourier frequency components present in an arbitrary mechanical input vibration, can be designed. The thesis presents a detailed description of experiments to evaluate a low frequency vibration spectrum analyzer system that accepts an incoming input vibration and directly provides the spectrum as output. Polymer piezoelectric materials being easily manufacturable these sensors can be deployed in wide area sensor networks that monitor large structures. The thesis also shows design of a vibration energy harvesting system based on the concept of harvesting energy at low frequencies. The need for developing such an energy harvesting system arises from the necessity of making the vibration sensor, self-powered. Multiple experimental tests were performed before developing a prototype vibration energy harvesting circuit.

Les matériaux piézoélectriques, comme le titanate-zirconate de plomb Pb(ZrxTi1-x)O3 (PZT), l’oxyde de zinc ZnO, ainsi que la solution solide de Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), sont actuellement l’objet d’études de plus en plus nombreuses à cause de leurs applications innovantes dans les systèmes micro-électromécaniques (MEMS). Afin de les intégrer sur substrat de silicium, certaines précautions doivent être prises en compte concernant par exemple des couches tampon, les électrodes inférieures. Dans cette thèse, des films piézoélectriques (PZT et PMN-PT) ont été épitaxiés avec succès sous forme de monocristaux sur silicium et SOI (silicon-on-insulator) par procédé sol-gel. En effet, des études récentes ont montré que les films piézoélectriques monocristallins semblent posséder des propriétés supérieures à celles des films polycristallins, permettant ainsi une augmentation de la performance des dispositifs MEMS. Le premier objectif de cette thèse était de réaliser l'épitaxie de film monocristallin de matériaux piézoélectriques sur silicium. L'utilisation d’une couche tampon d'oxyde de gadolinium (Gd2O3) ou de titanate de strontium (SrTiO3 ou STO) déposés par la technique d’épitaxie par jets moléculaires (EJM) a été explorée en détail pour favoriser l’épitaxie du PZT et PMN-PT sur silicium. Sur le système Gd2O3/Si(111), l’étude par diffraction des rayons X (XRD) de la croissance du film PZT montre que le film est polyphasé avec la présence de la phase parasite pyrochlore non ferroélectrique. Cependant, le film PZT déposé sur le système STO/Si(001) est parfaitement épitaxié sous forme d’un film monocristallin. Afin de mesurer ses propriétés électriques, une couche de ruthenate de strontium conducteur SrRuO3 (SRO) déposée par ablation laser pulsé (PLD) a été utilisée comme l'électrode inférieure à cause de son excellente conductibilité et de sa structure cristalline pérovskite similaire à celle du PZT. Les caractérisations électriques sur des condensateurs Ru/PZT/SRO démontrent de très bonnes propriétés ferroélectriques avec présence de cycles d'hystérésis. Par ailleurs, le matériau relaxeur PMN-PT a aussi été épitaxié sur STO/Si comme l’a confirmé la diffraction des rayons X ainsi que la microscopie électronique en transmission (TEM). Ce film monocristallin est de la phase de perovskite sans présence de pyrochlore. En outre, une étude en transmission du rayonnement infrarouge au synchrotron a prouvé une transition de phase diffuse sur une large gamme de température, comme attendue dans le cas d’un relaxeur. L'autre intérêt d'avoir des films PZT monocristallins déposés sur silicium et SOI est de pouvoir utiliser les méthodes de structuration du silicium bien standardisées maintenant pour fabriquer les dispositifs MEMS. La mise au point d’un procédé de micro-structuration en salle blanche a permis de réaliser des cantilevers et des membranes afin de caractériser mécaniquement les couches piézoélectriques. Des déplacements par l'application d'une tension électrique ont ainsi pu être détectés par interférométrie. Finalement, cette caractérisation par interférométrie a été combinée avec une modélisation basée sur la méthode des éléments finis. Dans le futur, il sera nécessaire d’optimiser le procédé de microfabrication du dispositif MEMS afin d’en améliorer les performances électromécaniques. Enfin, des caractérisations au niveau du dispositif MEMS lui-même devront être développées en vue de leur utilisation dans de futures applications. / Recently, piezoelectric materials, like lead titanate zirconate Pb(ZrxTi1-x)O3 (PZT), zinc oxide ZnO, and the solid solution Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), increasingly receive intensive studies because of their innovative applications in the microelectromechanical systems (MEMS). In order to integrate them on silicon substrate, several preliminaries must be taken into considerations, e.g. buffer layer, bottom electrode. In this thesis, piezoelectric films (PZT and PMN-PT) have been successfully epitaxially grown on silicon and SOI (silicon-on-insulator) in the form of single crystal by sol-gel process. In fact, recent studies show that single crystalline films seem to possess the superior properties than that of polycrystalline films, leading to an increase of the performance of MEMS devices. The first objective of this thesis was to realize the epitaxial growth of single crystalline film of piezoelectric materials on silicon. The use of a buffer layer of gadolinium oxide(Gd2O3) or strontium titanate (SrTiO3 or STO) deposited by molecular beam epitaxy (MBE) has been studied in detail to integrate epitaxial PZT and PMN-PT films on silicon. For Gd2O3/Si(111) system, the study of X-ray diffraction (XRD) on the growth of PZT film shows that the film is polycrystalline with coexistence of the nonferroelectric parasite phase, i.e. pyrochlore phase. On the other hand, the PZT film deposited on STO/Si(001) substrate is successfully epitaxially grown in the form of single crystalline film. In order to measure the electrical properties, a layer of strontium ruthenate (SrRuO3 or SRO) deposited by pulsed laser deposition (PLD) has been employed for bottom electrode due to its excellent conductivity and perovskite crystalline structure similar to that of PZT. The electrical characterization on Ru/PZT/SRO capacitors demonstrates good ferroelectric properties with the presence of hysteresis loop. Besides, the relaxor ferroelectric PMN-PT has been also epitaxially grown on STO/Si and confirmed by XRD and transmission electrical microscopy (TEM). This single crystalline film has the perovskite phase without the appearance of pyrochlore. Moreover, the study of infrared transmission using synchrotron radiation has proven a diffused phase transition over a large range of temperature, indicating a typical relaxor ferroelectric material. The other interesting in the single crystalline PZT films deposited on silicon and SOI is to employ them in the application of MEMS devices, where the standard silicon techniques are used. The microfabrication process performed in the cleanroom has permitted to realize cantilevers and membranes in order to mechanically characterize the piezoelectric layers. Mechanical deflection under the application of an electric voltage could be detected by interferometry. Eventually, this characterization by interferometry has been studied using the modeling based on finite element method and analytic method. In the future, it will be necessary to optimize the microfabrication process of MEMS devices based on single crystalline piezoelectric films in order to ameliorate the electromechanical performance. Finally, the characterizations at MEMS device level must be developed for their utilization in the future applications.