Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Mnoho aplikací přijímá, odesílá a zpracovává data v textové podobě. Správné a bezpečné zpracování těchto dat je typicky zajištěno tzv. ošetřením řetězců (string sanitization). Pomocí metod formální verifikace je možné analyzovat takovéto operace s řetězci a prověřit, zda jsou správně navržené či implementované.  Naším cílem je vytvořit obecný nástroj pro analýzu systémů jejichž konfigurace lze kódovat pomocí slov z vhodné abecedy, a také jeho specializaci pro analýzu programů pracujících s řetězci. Nejprve jsou popsaný konečné automaty a převodníky a poté různé třídy a podtřídy symbolických převodníků, zejména pak jejich omezení. Na základě těchto informací je pak pro použití v analýze programů navržen nový typ symbolických převodníků. Dále je popsán regulární model checking, speciálně pak jeho variantu založenou na abstrakci automatů, tzv. ARMC, u kterého je známo že dokáže velmi úspěšně překonat problém stavové exploze u automatů a umožňuje nám tzv. dosáhnout pevného bodu v analýze. Poté je navržena vlastní analýza programů psaných v imperativním paradigmatu, a to zejména programů manipulujících s řetězci, založená na principech ARMC. Následuje popis vlastní implementace nástroje s důrazem na jeho praktické vlastnosti. Rovněž jsou popsaný důležité části knihovny AutomataDotNet, na které nástroj staví. Práci je uzavřena diskuzí experimentů s nástrojem provedených na příkladech z knihovny LibStranger.

A sobreposição de frequências ultrassônicas a uma ferramenta em operações de perfuração, utilizando transdutores piezelétricos, resulta em melhorias na usinagem de metais, garantindo melhor acabamento (ausência de rebarba), redução do tamanho do cavaco e menor desgaste ferramental. A utilização desse tipo de técnica na perfuração de rochas reduz a carga axial e aumenta a velocidade do processo, possibilitando maior profundidade de perfuração, podendo vir a ser muito útil em pesquisas aplicadas à perfuração de reservas petrolíferas e exploração mineral. Este trabalho teve como objetivo simular e aplicar um transdutor piezelétrico ultrassônico de potência para perfuração de rochas e metais. Para as simulações numéricas duas técnicas foram utilizadas: o método dos elementos finitos (MEF) e o método das matrizes em cadeia (MMC). O MEF permitiu análises harmônicas e modais de forma rápida e precisa enquanto o MMC resultou em expressão analítica, possibilitando melhor compreensão dos parâmetros físicos e geométricos envolvidos na performance do transdutor. Ambos os métodos nortearam o projeto do protótipo a ser usado em ensaios de perfuração. Para a construção do protótipo, foi projetado um mandril para a fixação da broca, que foi adaptado a um transdutor de potência de 20 kHz. Ensaios de perfuração de rochas e de discos de alumínio foram realizados com o protótipo. A aplicação do protótipo à perfuração de rochas carbonáticas demonstrou redução no tempo de furação, quando comparada ao método convencional (sem aplicação de ultrassom). Na furação de discos de alumínio, a redução de rebarbas, quebra do cavaco durante a operação e melhor acabamento da peça, são conclusões evidentes das melhorias proporcionadas pela sobreposição de frequências ultrassônicas à broca. / Superposition of high frequency vibration in the tool, driven by a piezoelectric actuator, in a drilling machining process of metals results in some improvements such as finishing quality (without burr), reduction of tool wear and chip dimensions. Similar techniques applied in rock perforation reduce the axial load in the tool, which enhances the process velocity, resulting in deeper perforation. This might be useful in oil and mineral exploration, opening the feasibility of researches in this field. The aim of this work is to simulate and implement an ultrasonic piezoelectric transducer to perforate rocks and metals. Concerning numerical simulation, two techniques were performed: finite element method (FEM) and chain matrix method (CMM). FEM simulations provide fast and effective modal and harmonic analysis. CMM provide mathematical expressions, analytically exposing geometrical and physical parameters involved in the transducer performance. Both methods were the guide and basement for the prototype project, able to perform perforation experiments. For the construction of the prototype, a drill chuck were designed and adapted for a 20 kHz power ultrasonic transducer. Aluminum drilling and rock perforation experiments were carried out with this prototype. A lower perforation time was achieved in carbonate rocks when the ultrasound-aided method was used as opposed to the conventional method. Results in aluminum disks presented burr reduction, better part finishing and breakage of chips during operation. Those results evidently appoint some improvements due to the power ultrasonic superposition in the drilling process.

No final da década de 90, foi observado que filmes de espumas poliméricas carregadas eletricamente poderiam apresentar elevados coeficientes piezoelétricos quando eletricamente carregados. Isso devido a macro dipolos elétricos, formados por cargas elétrica opostas aprisionadas nas superfícies internas das cavidades do material. Esses filmes porosos, receberam os nomes de piezoeletretos ou ferroeletretos. Inicialmente produzidos por microextrusão aerada a partir de polipropileno, esses piezoeletretos estimularam as pesquisas devido aos elevados coeficientes piezoelétricos apresentados. No entanto, à baixa estabilidade térmica desse material, limitou sua aplicação em temperaturas mais elevadas. Isso direcionou as pesquisas para técnicas de produção de espumas com outros materiais. Recentemente, uma nova abordagem com dois filme de Teflon FEP moldados e colados por fusão, mostrou-se viável na produção de estruturas com cavidades fechadas. Por meio desse processo termo-moldado, não só estruturas termicamente mais estáveis foram produzidas mas também com elevados coeficientes piezoelétricos. Porém a principal vantagens desse processo foi a possibilidade de produzir estruturas com cavidades bem definidas, o que permite um carregamento mais uniforme e controle na freqüência de ressonância. Contudo, todos os processos de produção de piezoeletretos apresentados, possuem algumas limitações, como, por exemplo, o controle efetivo das cavidades e limites quanto ao número de camadas, o que tem se observado aumenta a resposta elétrica. Neste trabalho, é apresentada uma nova técnica para a produção de piezoeletretos, baseada em um sistema de laminação. Este possibilita elaborar estruturas com total controle das cavidades, através da fusão de dois poliméricos juntamente com um molde pré-fabricado. Os coeficientes piezoelétricos obtidos com essas estruturas foram similares aos encontrados nas espumas e termicamente mais estáveis quando produzidas com fluoropolímeros. Ainda neste trabalho foram analisadas a influência da altura e largura das cavidades no coeficiente piezoelétrico, o comportamento de estruturas formadas com diferentes polímeros, e também a versatilidade de estruturas com múltiplas camadas. / At the end of 90´s, it was observed that electrically charged foams made from polymers films could exhibit very high piezoelectric coefficients, due to macro-dipoles formed by trapped charges in the inner surfaces of the internal voids of the film. This films with small cavities after has been electrically charged received the names of piezoelectrets or ferroelectrects. They were initially prepared from polypropylene grains extruded into films in a physical blow process. However, the low thermal stability of the piezoelectric coefficient presentec by this voided films, motivated researches to explore different materials which were thermically more stables. Recently a new approach, were two Teflon FEP films were molded and fused to produce cavities with bubbles shapes was presented. These thermo-fused structures reveal also to present very high piezoelectric coefficients, after received properly charging. One of the major advantages of this molded structures piezoelectrets is the possibility to create piezoelectrets with well defined voids, which is supposed to provide a more homogeneous charging and a broadband frequency control. Nevertheless, the methods to produce homogenic structures developed so far are still facing problems to control the cavities and to create multi-layer structures. In this work a new process to produce piezoelectrets is presented. The method based on the lamination of two polymer films with a pre-fabricated template provides full control of the air cavities. After the template is removed, a well defined open channel structures is formed. Later when electrodes are deposited on both sides of the fused films the structure is electrically chargec and a piezoelectret with piezoelectric coefficients similar to the foams is formed. With this new controlled process to prepare piezoeletrets several parameters of the cavities were investigated, including the comparison of ferroelectretcs made from different materials and multi-layers samples.

Orientador: Jozué Vieira Filho / Banca: Vicente Lopes Junior / Banca: Carlos Antonio. Barros Alves / Banca: Carlos de Marqui Junior / Banca: Washington Luiz de Melo / Resumo: A técnica da impedância eletromecânica (E/M) tem sido amplamente pesquisada para o desenvolvimento de sistemas de SHM (Structural Health Monitoring - monitoramento de integridade estrutural) em diversas aplicações. Embora existam muitos trabalhos que indiquem a eficiência e a viabilidade dessa técnica, alguns problemas práticos em aplicações reais ainda precisam ser investigados. A medição da impedância elétrica, etapa básica da técnica, geralmente é realizada por instrumentos comerciais volumosos, pesados e de alto custo, características proibitivas para muitas aplicações. A seleção da faixa de frequência em que a impedância deve ser medida para assegurar boa sensibilidade ao dano é feita por métodos de tentativa e erro ou por metodologias que utilizam dados medidos em uma quantidade considerável de testes. Além disso, o dimensionamento dos transdutores é feito sem um embasamento teórico, independentemente das características da estrutura monitorada. Neste trabalho é proposto um sistema de medição de impedância elétrica rápido, versátil e de baixo custo que substitui com eficiência os instrumentos comerciais. A partir de um circuito eletromecânico equivalente, o efeito de carregamento do transdutor devido à estrutura monitorada foi analisado. A análise do efeito de carregamento permite dimensionar corretamente o transdutor de acordo com a estrutura monitorada e assegurar um bom desempenho do sistema. O circuito eletromecânico também foi utilizado para determinar, teoricamente, as faixas de frequência em que o transdutor tem boa sensibilidade e auxiliar na seleção da faixa de frequência adequada para a detecção de danos estruturais. Todas as metodologias propostas foram verificadas através de experimentos em estruturas de alumínio e houve uma boa concordância entre os resultados teóricos e experimentais / Abstract: The electromechanical (E/M) impedance technique has been widely studied for the development of Structural Health Monitoring (SHM) systems in various applications. Although there are many studies indicating the effectiveness and feasibility of this technique, some practical issues in real applications yet should be investigated. The electrical impedance measurement, basic stage of the technique, is usually performed by bulky, heavy and expensive instruments; these features are prohibitive for many applications. The selection of the frequency range in which the electrical impedance must be measured to ensure good sensitivity for damage detection is performed by trial and error methods or by methodologies that use measured data in a considerable amount of tests. Furthermore, the design of the transducer is done without theoretical basis, regardless the characteristics of the host structure. In this work, a fast, versatile and low-cost electrical impedance measurement system was developed; the proposed system successfully replaces the conventional instruments. From an equivalent electromechanical circuit, the transducer loading effect due to the host structure was analyzed. The analysis of the loading effect allows the correct design of the transducer according to the host structure for ensure a good performance of the system. The electromechanical circuit was also used to theoretically determine the frequency ranges in which the transducer has good sensitivity and assist in the selection of the suitable frequency range for structural damage detection. All proposed methodologies were validated by experimental tests on aluminum structures and there was a good match between the theoretical and practical results / Doutor

A l’opposé de l’approche consistant à concevoir aucas par cas des contraintes et des algorithmes leur étant dédiés, l’objet de cette thèse concerne d’une part la description de familles de contraintes en termes de composition de fonctions, et d’autre part la synthèse d’objets combinatoires pour de telles contraintes. Les objets concernés sont des bornes précises, des coupes linéaires, des invariants non-linéaires et des automates finis ; leur but principal est de prendre en compte l’aspect combinatoire d’une seule contrainte ou d’une conjonction de contraintes. Ces objets sont obtenus d’une façon systématique et sont paramétrés par une ou plusieurs contraintes, par le nombre de variables dans une séquence, et par les domaines initiaux de ces variables. Cela nous permet d’obtenir des objets indépendants d’une instance considérée. Afin de synthétiser des objets combinatoires nous tirons partie de la vue déclarative de telles contraintes, basée sur les expressions régulières, ainsi que la vue opérationnelle, basée sur les automates à registres et les transducteurs finis. Il y a plusieurs avantages à synthétiser des objets combinatoires par rapport à la conception d’algorithmes dédiés : 1) on peut utiliser ces formules paramétrées dans plusieurs contextes, y compris la programmation par contraintes et la programmation linéaire, ce qui est beaucoup plus difficile avec des algorithmes ; 2) la synergie entre des objets combinatoires nous donne une meilleure performance en pratique ; 3) les quantités calculées par certaines des formules peuvent être utilisées non seulement dans le contexte de l’optimisation mais aussi pour la fouille de données. / Contrary to the standard approach consisting in introducing ad hoc constraints and designing dedicated algorithms for handling their combinatorial aspect, this thesis takes another point of view. On the one hand, it focusses on describing a family of sequence constraints in a compositional way by multiple layers of functions. On the other hand, it addresses the combinatorial aspect of both a single constraint and a conjunction of such constraints by synthesising compositional combinatorial objects, namely bounds, linear inequalities, non-linear constraints and finite automata. These objects are obtained in a systematic way and are not instance-specific: they are parameterised by one or several constraints, by the number of variables in a considered sequence of variables, and by the initial domains of the variables. When synthesising such objects we draw full benefit both from the declarative view of such constraints, based on regular expressions, and from the operational view, based on finite transducers and register automata.There are many advantages of synthesising combinatorial objects rather than designing dedicated algorithms: 1) parameterised formulae can be applied in the context of several resolution techniques such as constraint programming or linear programming, whereas algorithms are typically tailored to a specific technique; 2) combinatorial objects can be combined together to provide better performance in practice; 3) finally, the quantities computed by some formulae cannot just be used in an optimisation setting, but also in the context of data mining.

No final da década de 90, foi observado que filmes de espumas poliméricas carregadas eletricamente poderiam apresentar elevados coeficientes piezoelétricos quando eletricamente carregados. Isso devido a macro dipolos elétricos, formados por cargas elétrica opostas aprisionadas nas superfícies internas das cavidades do material. Esses filmes porosos, receberam os nomes de piezoeletretos ou ferroeletretos. Inicialmente produzidos por microextrusão aerada a partir de polipropileno, esses piezoeletretos estimularam as pesquisas devido aos elevados coeficientes piezoelétricos apresentados. No entanto, à baixa estabilidade térmica desse material, limitou sua aplicação em temperaturas mais elevadas. Isso direcionou as pesquisas para técnicas de produção de espumas com outros materiais. Recentemente, uma nova abordagem com dois filme de Teflon FEP moldados e colados por fusão, mostrou-se viável na produção de estruturas com cavidades fechadas. Por meio desse processo termo-moldado, não só estruturas termicamente mais estáveis foram produzidas mas também com elevados coeficientes piezoelétricos. Porém a principal vantagens desse processo foi a possibilidade de produzir estruturas com cavidades bem definidas, o que permite um carregamento mais uniforme e controle na freqüência de ressonância. Contudo, todos os processos de produção de piezoeletretos apresentados, possuem algumas limitações, como, por exemplo, o controle efetivo das cavidades e limites quanto ao número de camadas, o que tem se observado aumenta a resposta elétrica. Neste trabalho, é apresentada uma nova técnica para a produção de piezoeletretos, baseada em um sistema de laminação. Este possibilita elaborar estruturas com total controle das cavidades, através da fusão de dois poliméricos juntamente com um molde pré-fabricado. Os coeficientes piezoelétricos obtidos com essas estruturas foram similares aos encontrados nas espumas e termicamente mais estáveis quando produzidas com fluoropolímeros. Ainda neste trabalho foram analisadas a influência da altura e largura das cavidades no coeficiente piezoelétrico, o comportamento de estruturas formadas com diferentes polímeros, e também a versatilidade de estruturas com múltiplas camadas. / At the end of 90´s, it was observed that electrically charged foams made from polymers films could exhibit very high piezoelectric coefficients, due to macro-dipoles formed by trapped charges in the inner surfaces of the internal voids of the film. This films with small cavities after has been electrically charged received the names of piezoelectrets or ferroelectrects. They were initially prepared from polypropylene grains extruded into films in a physical blow process. However, the low thermal stability of the piezoelectric coefficient presentec by this voided films, motivated researches to explore different materials which were thermically more stables. Recently a new approach, were two Teflon FEP films were molded and fused to produce cavities with bubbles shapes was presented. These thermo-fused structures reveal also to present very high piezoelectric coefficients, after received properly charging. One of the major advantages of this molded structures piezoelectrets is the possibility to create piezoelectrets with well defined voids, which is supposed to provide a more homogeneous charging and a broadband frequency control. Nevertheless, the methods to produce homogenic structures developed so far are still facing problems to control the cavities and to create multi-layer structures. In this work a new process to produce piezoelectrets is presented. The method based on the lamination of two polymer films with a pre-fabricated template provides full control of the air cavities. After the template is removed, a well defined open channel structures is formed. Later when electrodes are deposited on both sides of the fused films the structure is electrically chargec and a piezoelectret with piezoelectric coefficients similar to the foams is formed. With this new controlled process to prepare piezoeletrets several parameters of the cavities were investigated, including the comparison of ferroelectretcs made from different materials and multi-layers samples.

Ce travail porte sur l’étude de matériaux micro/nano structurés permettant l’ingénierie des structures de bande dans le domaine des ondes élastiques. Nous nous sommes intéressés en particulier à l’intégration de ces matériaux dans les dispositifs électro-acoustiques et l’étude de l’interaction avec les ondes acoustiques de surface.La démarche consiste à mener des simulations par la méthode des éléments finis, pour calculer les structures de bande et les spectres de transmission. Nous avons étudié l’effet des paramètres géométriques et élastiques des micro-plots sur les branches acoustiques représentant les modes de surface. Nous avons ensuite discuté l’effet de la symétrie de l’arrangement sur la polarisation des modes de surface. Nous avons également étudié l’effet de la symétrie sur la sensibilité des modes de surface à une variation de température.Sur le plan expérimental, Nous avons élaboré des transducteurs inter-digités sur un substrat piézoélectrique de LiNbO3. Nous avons intégré divers cristaux phononiques composés de micro-plots de Ni, obtenues par électrodéposition. Les spectres de transmission ont été mesurés à l’aide d’un analyseur de réseau et comparés aux résultats theoriques.En dehors des cristaux phononiques basés sur des plots du nickel, d’autres structures ont également été présentées dans ce travail, incluant des matériaux bidimensionnels à base de nanoparticules magnétiques auto-assemblées et des nanofils du nickel électrodéposés à travers des membranes nano-poreuses d’alumine. / This work concerns the study of micro/nano structured materials for the engineering of band structures in the field of elastic waves. We were interested in particular to the integration of these materials in electro-acoustic devices and the study of the interaction with the surface acoustic waves.The approach is to carry out the simulation using the finite element method to calculate the band structures and the transmission spectra. We studied the effect of geometrical and elastic parameters of micro-pillars on acoustic branches representing surface modes. Then we discussed the effect of the symmetry of the arrangement on the polarization of the surface modes. We also investigated the effect of the symmetry on the sensitivity of surface modes with the variation of temperature.Experimentally, we have developed interdigital transducers on a piezoelectric substrate of LiNbO3. We have fabricated various phononic crystals composed of nickel micro-pillars, obtained by electrodeposition. The transmission spectra were measured by a network analyzer and compared with the theoretical results.Besides the phononic crystals based on nickel pillars, some other periodic micro/nano structures were also involved in this work, such as two dimensional materials based on self-assembled magnetic nanoparticles and nickel nanowires electroplated through nano-porous alumina membranes.

Récemment, les actionneurs ioniques ultra-minces à base de poly (3,4-éthylènedioxythiophène) (PEDOT) ont surmonté certains obstacles initiaux pour augmenter le potentiel d'applications dans les dispositifs microfabriqués. Bien que la microfabrication d’actionneurs à trois couches, n’impliquant aucune manipulation manuelle, ait été démontrée, leurs performances mécaniques restent limitées pour des applications pratiques. Le but de cette thèse est d'optimiser les transducteurs dans la phase de fabrication des couches minces en utilisant des micro technologies, de caractériser complètement les propriétés électrochimiques des transducteurs ainsi obtenus, et de développer un modèle pour simuler leurs capacités électromécaniques bidirectionnelles (actionnement et détection). Tout d'abord, les actionneurs à trois couches ultra-minces à base de PEDOT sont fabriqués par polymérisation en phase vapeur de 3,4-éthylènedioxythiophène en réalisant un procédé de synthèse couche par couche. Le travail présenté constitue la première caractérisation complète de microactionneurs ioniques à base de PEDOT fonctionnant dans l’air d’une si faible épaisseur (17 μm) présentant une déformation en flexion et une génération de force de 1% et 12 μN respectivement. En effet, les propriétés électriques, électrochimiques et mécaniques des microactionneurs ont été minutieusement étudiées. La caractérisation non linéaire a été étendue à la dépendance de la capacité volumétrique sur une fenêtre de tension. Le coefficient d'amortissement a été caractérisé pour la première fois. Par ailleurs, un modèle multi-physique non linéaire a été proposé comme méthode de simulation des réponses en mode actionneur et capteur dans des couches multiples, représenté à l'aide d'un formalisme Bond Graph, et a été capable de mettre en œuvre tous les paramètres caractérisés. La concordance entre les simulations et les mesures a confirmé l'exactitude du modèle pour prédire le comportement dynamique non linéaire des actionneurs. En outre, les informations extraites du modèle ont également permis de mieux comprendre les paramètres critiques des actionneurs et leur incidence sur l'efficacité de l'actionneur et sur la distribution de l'énergie. Enfin, un nouveau modèle linéaire électromécanique bidirectionnel a été introduit pour simuler la capacité de détection du transducteur à trois couches et a été confirmé par des résultats expérimentaux dans les domaines fréquentiel et temporel d'un déplacement d'entrée sinusoïdal. Les actionneurs résultants et les modèles proposés sont prometteurs pour la conception, l'optimisation et le contrôle des futurs dispositifs de microsystèmes souples dans lesquels l'utilisation d'actionneurs en polymère devrait être essentielle. / Recently, ultrathin poly (3,4-ethylenedioxythiophene) (PEDOT) – based ionic actuators have overcome some initial obstacles to increase the potential for applications in microfabricateddevices. While microfabrication processing of trilayer actuators that involve no manual handling has been demonstrated, their mechanical performances remain limited for practical applications. The goal of this thesis is to optimize the transducers in thin films fabrication by micro technologies, fully characterize the electrochemomechanical properties of the resulting trilayers, and develop a model to simulate their bidirectional electromechanical ability (actuation and sensing). At first, ultrathin PEDOT-based trilayer actuators are fabricated via the vapor phase polymerization of 3,4-ethylenedioxythiophene combining with the layer by layer synthesis process. This constitutes the first full characterization of ionic PEDOT-based microactuators operating in air of such a small thickness (17 μm) having bending deformation and output force generation of 1% and 12 μN respectively. Secondly, electrical, electrochemical and mechanical properties of the resulting microactuators have been thoroughly studied. Non-linear characterization was extended to volumetric capacitance dependence on voltage window. Damping coefficient was characterized for the first time. Thirdly, a nonlinear multi-physics model was proposed as a method of simulating actuator and sensor responses in trilayers, represented using a Bond Graph formalism, and was able to implement all of the characterized parameters. The concordance between the simulations and the measurements confirmed the accuracy of the model in predicting the non-linear dynamic behavior of the actuators. In addition, the information extracted from the model also provided an insight into the critical parameters of the actuators and how they affect the actuator efficiency, as well as the energy distribution. Finally, a nouveau bidirectional electromechanical linear model was introduced to simulate the sensing ability of the trilayer transducer and was confirmed via experimental results in both frequency and time domains of a sinusoidal input displacement. The resulting actuators and the proposed models are promising for designing, optimizing, and controlling of the future soft microsystem devices where the use of polymer actuators should be essential.

In this work passive piezoelectric devices for vibration damping are studied. It is developed the basic idea of synthesizing electrical wave guides to obtain an optimal electro-mechanical energy exchange and therefore to dissipate the mechanical vibrational energy in the electric form. Modular PiezoElectroMechanical (PEM) structures are constituted by continuous elastic beams (or bars) coupled, by means of an array of PZT transducers, to lumped dissipative electric networks. Both refined and homogenized models of those periodic systems are derived by an energetic approach based on the principle of virtual powers. Weak and strong formulation of the dynamical problem are presented having in mind future studies involving the determination of numerical solutions. In this framework the effectiveness of the proposed devices for the suppression of mechanical vibrations is investigated by a wave approach, considering both the extensional and flexural oscillations. The optimal values of the electric parameters for a fixed network topology are derived analytically by a pole placement technique. Their sensitivities on the dimensions of the basic cell of the periodic system and on the design frequency are studied. Moreover the dependence of damping performances on the frequency is analyzed. Comparing the performances of different network topological configurations, the advantages of controlling a mechanical structure with an electric analog are shown. As a consequence of those results, new interconnections of PZT transducers are proposed. An experimental setup for the validation of the analytical and numerical results is proposed and tested. A classical experience on resonant shunted PZT is reproduced. Future experimental work is programmed.