Dizertační práce pojednává o návrhu a optimalizaci periodických struktur s elektromagnetickým zádržným pásmem (EBG – electromagnetic band gap) pro potlačení povrchových vln šířících se na elektricky tlustých dielektrických substrátech. Nepředvídatelné chování elektromagnetických vlastností těchto struktur v závislosti na parametrech elementární buňky činí jejích syntézi značně komplikovanou. Bez patřičného postupu je návrh EBG struktur metodou pokusu a omylu. V první části práce jsou shrnuty základní poznatky o šíření elektromagnetických vln v tzv. metamateriálech. Následně je diskutován správný způsob výpočtu disperzního diagramu ve vybraných komerčních programech. Jádrem dizertace je automatizovaný návrh a optimalizace EBG struktur využitím různých globálních optimalizačních algoritmů. Praktický význam vypracované metodiky je předveden na návrhových příkladech periodických struktur s redukovanými rozměry, dvoupásmovými EBG vlastnostmi, simultánním EBG a AMC (artificial magnetic conductor – umělý magnetický vodič) chováním a tzv. superstrátu. Poslední kapitola je věnována experimentálnímu ověření počítačových modelů.

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Ce travail est consacré à la description macroscopique de deux types de plaques structurées contrastées dont le comportement dynamique est atypique : le premier cas correspond à une plaque raidie dans une direction par des raidisseurs régulièrement espacés, le second correspond au cas d’une plaque bi-raidie dans les deux directions par un treillis périodique de poutres. Les différents régimes de comportement sont spécifiés en fonction des paramètres mécaniques et géométriques des raidisseurs et de la plaque. Le comportement dynamique de ces plaques est établi en faisant émerger, par homogénéisation asymptotique, la description locale et globale. Le modèle est construit à partir des équations élasto-dynamiques tri-dimensionnelles du matériau combinées à des développements asymptotiques. Le travail se concentre sur des situations de résonance interne qui correspondent à des contrastes spécifiques entre les paramètres de la plaque et du raidisseur. L’analyse met clairement en évidence les cinématiques enrichies de la plaque et aboutit à un modèle analytique macroscopique qui inclut les mécanismes de torsion et de flexion. Dans le cas de la plaque mono-raidie, un modèle hybride fait intervenir des paramètres effectifs dont les expressions analytiques sont précisées. Ce modèle est analogue à un modèle de poutre et permet d’appréhender le comportement de la plaque en incluant la résonance interne. Ce modèle non conventionnel montre la coexistence de deux régimes dynamiques. Les caractéristiques de dispersion atypique associées aux ondes de flexion et de torsion proviennent de paramètres effectifs dépendants de la fréquence, comme la masse effective, l’inertie de rotation effective, et la rigidité de torsion effective associées à la plaque. Cette théorie est ensuite étendue au cas de la plaque bi-raidie, et conduit à un opérateur de type plaque non conventionnel incluant des paramètres effectifs. Ces résultats permettent d’examiner des courbes de dispersion atypiques en fonction des contrastes géométriques et mécaniques entre les différents composants. La validité des modèles et leur robustesse sont vérifiées en comparant les résultats analytiques à des simulations numériques de type éléments finis WFEM. Les comparaisons montrent que les mécanismes observables numériquement sont bien décrits par le modèle analytique proposé. Enfin, deux maquettes sont utilisées pour la validation expérimentale : une correspondant à une plaque mono-raidie comportant un contraste géométrique, et l’autre correspondant à la plaque bi-raidie impliquant des contrastes géométrique et mécanique. Les réponses mesurées par vibromètre laser sont traitées par corrélation d’onde IWC. Les mesures sont reproduites pour plusieurs conditions limites de plaques internes et différentes valeurs de masse ajoutées pour montrer la performance du modèle homogénéisé. Une très bonne corrélation apparaît entre les mesures expérimentales et les prédictions issues du modèle. Cette approche peut être utilisée pour décrire le comportement de panneaux raidis industriels et pour concevoir des structures ayant des propriétés spécifiques à certaines fréquences. / This work is devoted to the modeling of two types of contrasted structured plates that exhibit non-conventional dynamic behavior : the first one corresponds to periodic unidirectionally stiffened plates and the second one corresponds to orthogonally stiffened plates. The different regimes of behavior are specified, according to the mechanical and geometrical parameters of the beam and the plate. The dynamic behavior of such stiffened plates is established by up-scaling, through multi-scale asymptotic method, the linear local description of the plate and the stiffening beams coupled together. The behavior is derived from the three-dimensional elastodynamic laws of the materials combined with asymptotic expansions formulation. The study focuses on situations of inner resonance that corresponds to specific mechanical contrasts between the beam and plate parameters. The analysis clearly evidences the enriched kinematics of such plate and yields to a synthetic and analytic macroscopic representation that encompasses the flexural and torsional mechanisms, as well as guided waves. In the case of unidirectionally ribbed plates, an effective hybrid beam/plate model is obtained and the analytical expressions of effective parameters are specified. It results in a beam-like operator that provides a simple understanding of the behavior taking into account inner resonance. This atypical model accounts from the coexistence of two types of dynamic regimes. The unusual dispersion features of flexural and torsional waves arise from frequency dependent parameters, namely, the effective mass, the effective rotational inertia and the effective torsional spring rigidity associated with the plate. The theory is then extended to an orthogonally ribbed plate, and yields a non-conventional plate model with frequency dependent parameters. These results allow investigating the atypical dispersion equation with respect to the geometrical and mechanical contrasts of the structural components. The validity and robustness of the model are also verified by comparing theoretical predictions with finite element based computations, namely the WFEM (Wave Finite Element Method). Comparisons show that mechanisms identified numerically are correctly predicted by the proposed homogenized model. Finally, two mock-ups are considered experimentally, corresponding to uni-directionally ribbed plate with geometrical contrast and orthogonally ribbed plates involving geometrical and mechanical contrasts. The out-of-plane displacement field under random excitation is measured using a scanning laser vibrometer, then post-processed using the IWC (Inhomogeneous Wave Correlation) method. This is performed for various internal boundary conditions and added mass to highlight the ability of the homogenized model to describe different configurations. A good agreement is found between the experimental measurements and the analytical predictions. The presented approach can be used to describe the motion of ribbed panels of industrial interest and/or to design structures having specific atypical features in a given frequency range.

L’amélioration du confort des usagers ainsi que l’augmentation du niveau de sécurité des structures requièrent le développement de techniques permettant de limiter efficacement les vibrations. Dans cette optique, les travaux exposés ici proposent le développement et l’analyse de méthodes de contrôle vibratoire pour des structures de faibles dimensions et utilisant peu d’énergie. Afin de satisfaire à ces deux critères, il est ici proposé d’utiliser des éléments piézoélectriques électriquement interfacés de manière non-linéaire et périodiquement distribués sur la structure-cible à contrôler. Ainsi, l’approche proposée permet de bénéficier à la fois des avantages des techniques de contrôle non-linéaires appliquées aux matériaux intelligents de type piézoélectrique, offrant des performances remarquables tout en étant peu consommatrices d’énergie, avec ceux des structures périodiques exhibant des bandes fréquentielles interdites présentant de fortes atténuations de la propagation d’onde. Plus particulièrement, ce mémoire s’intéresse à différentes architectures d’interconnexion des interfaces électriques non-linéaires permettant un bon compromis entre la bande fréquentielle contrôlée et les performances en termes d’atténuation des vibrations. Ainsi, trois architectures principales sont proposées, allant de structures totalement périodiques, tant au niveau mécanique qu’électrique (interconnexions), à des structures présentant un certain degré d’apériodicité sur le plan électrique (entrelacement), impactant ainsi la propagation de l’onde acoustique en élargissant la bande de contrôle, pour enfin proposer une architecture hybride entre interconnexion et entrelacement conduisant à des systèmes large bande performants. / For ameliorating vibration reduction systems in engineering applications, miscellaneous vibration control methods, including vibration damping systems, have been developed in recent years. As one of intelligent vibration damping systems, nonlinear electronic damping system using smart materials (e.g., piezoelectric materials), is more likely to achieve multimodal vibration control. With the development of meta-structures (a structure based upon metamaterial concepts), electronic vibration damping shunts, such as linear resonant damping or negative capacitance shunts, have been introduced and integrated abundantly in the electromechanical meta-structure design for wave attenuation and vibration reduction control. Herein, semi-passive Synchronized Switch Damping on the Inductor (SSDI) technique (which belongs to nonlinear electronic damping techniques), is combined with smart meta-structure (also called smart periodic structure) concept for broadband wave attenuation and vibration reduction control, especially for low frequency applications. More precisely, smart periodic structure with nonlinear SSDI electrical networks is investigated from the following four aspects, including three new techniques for limiting vibrations: First, in order to dispose of a tool allowing the evaluation of the proposed approaches, previous finite element (FE) modeling methods for piezoelectric beam structures are summarized and a new voltage-based FE modeling method, based on Timoshenko beam theory, is proposed for investigating smart beam structure with complex interconnected electrical networks; then, the first developed technique lies in smart periodic structure with nonlinear SSDI interconnected electrical networks, which involves wave propagation interaction between continuous mechanical and continuous nonlinear electrical media; the second proposed topology lies in smart periodic structures with nonlinear SSDI interleaved / Tri-interleaved electrical networks involving wave propagation interaction between the continuous mechanical medium and the discrete nonlinear electrical medium. Due to unique electrical interleaved configuration and nonlinear SSDI electrical features, electrical irregularities are induced and simultaneously mechanical irregularities are also generated within an investigated periodic cell; the last architecture consists in smart periodic structures with SSDI multilevel interleaved-interconnected electrical networks, involving wave propagation interaction between the continuous mechanical medium and the multilevel continuous nonlinear electrical medium. Compared with the SSDI interconnected case, more resonant-type band gaps in the primitive pass bands of purely mechanical periodic structures can be induced, and the number of such band-gaps are closely related to the interconnection / interleaved level. Finally, the main works and perspectives of the thesis are summarized in the last chapter.

Made available in DSpace on 2017-07-21T19:25:45Z (GMT). No. of bitstreams: 1 VagnerI.pdf: 11138375 bytes, checksum: d9bd7c0fe3aba2949fbf229e29e527e4 (MD5) Previous issue date: 2015-03-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we investigated the parameter space of a system consisting of two oscillators coupled in a master-slave configuration. In order to do so we employed Lyapunov exponent's diagrams in the parameter space, the distribution of the finite-time Lyapunov exponents and its positive fraction. We were able to show that, when the slave system is coupled to the master, the shrimp-shaped periodic structures that previously existed begins to be eroded from the outside, and that the erosion progresses with the increase in the intensity of the coupling. We also showed that in the region where the erosion takes place the second Lyapunov exponent exhibits a bimodal distribution with a maximum close to zero and the other close to 0:1. By plotting the points in the phase space that belong to each maximum we were able to identify two kinds of attractors, a limit cicle and a chaotic attractor, in which the slave system intermittently moves. / Neste trabalho foi investigado o espaço de parâmetros de um sistema formado por dois osciladores acoplados em uma configuração mestre-escravo. Como ferramenta de análise utilizamos diagramas de expoente de Lyapunov no espaço de parâmetros, a distribuição a tempo finito do expoente de Lyapunov e sua fração positiva. Mostramos que quando o sistema escravo é acoplado ao mestre as estruturas periódicas em formato de camarão existentes anteriormente começam a ser erodidas de fora para dentro, e que essa erosão aumenta com o aumento da intensidade do acoplamento. Mostramos também que na região em que ocorre a erosão o segundo expoente de Lyapunov apresenta uma distribuição bimodal com um máximo próximo a zero e outro próximo a 0; 1. Plotando os pontos no espaço de fase pertencentes a cada um dos máximos encontramos dois tipos de atratores, um ciclo limite e um atrator caótico, nos quais o sistema escravo transita de forma intermitente.

This thesis investigates topology optimization techniques for periodic continuum structures at the macroscopic level. Periodic structures are increasingly used in the design of structural systems and sub-systems of buildings, vehicles, aircrafts, etc. The duplication of identical or similar modules significantly reduces the manufacturing cost and greatly simplifies the assembly process. Optimization of periodic structures in the micro level has been extensively researched in the context of material design, while research on topology optimization for macrostructures is very limited and has great potential both economically and intellectually. In the present thesis, numerical algorithms based on the bi-directional evolutionary structural optimization method (BESO) are developed for topology optimization for various objectives and constraints. Soft-kill (replacing void elements with soft elements) formulations of topology optimization problems for solid-void solutions are developed through appropriate material interpolation schemes. Incorporating the optimality criteria and algorithms for mesh-independence and solution-convergence, the present BESO becomes a reliable gradient based technique for topology optimization. Additionally, a new combination of genetic algorithms (GAs) with BESO is developed in order to stochastically search for the global optima. These enhanced BESO algorithms are applied to various optimization problems with the periodicity requirement as an extra constraint aiming at producing periodicity in the layout. For structures under static loading, the present thesis addresses minimization of the mean compliance and explores the applications of conventional stiffness optimization for periodic structures. Furthermore, this thesis develops a volume minimization formulation where the maximum deflection is constrained. For the design of structures subject to dynamic loading, this thesis develops two different approaches (hard-kill and soft-kill) to resolving the problem of localized or artificial modes. In the hard-kill (completely removing void elements) approach, extra control measures are taken in order to eliminate the localized modes in an explicit manner. In the soft-kill approach, a modified power low material model is presented to prevent the occurrence of artificial and localized modes. Periodic stress and strain fields cannot be assumed in structures under arbitrary loadings and boundaries at the macroscopic level. Therefore being different from material design, no natural base cell can be directly extracted from macrostructures. In this thesis, the concept of an imaginary representative unit cell (RUC) is presented. For situations when the structure cannot be discretized into equally-sized elements, the concept of sensitivity density is developed in order for mesh-independent robust solutions to be produced. The RUC and sensitivity density based approach is incorporated into various topology optimization problems to obtain absolute or scaled periodicities in structure layouts. The influence of this extra constraint on the final optima is investigated based on a large number of numerical experiments. The findings shown in this thesis have established appropriate techniques for designing and optimizing periodic structures. The work has provided a solid foundation for creating a practical design tool in the form of a user-friendly computer program suitable for the conceptual design of a wide range of structures.

Le domaine des matériaux intelligents et des structures adaptatives constitue un domaine de recherche consacré à la conception de structures architecturées ayant la faculté de modifier leur comportement en réponse à un stimulus externe. Le travail proposé dans cette thèse porte sur l’analyse et la conception d’un système pour le contrôle vibroacoustique adaptatif. Il s’attache à la conception d’une interface active faite de transducteurs piézo-électriques disposés en réseau bidimensionnel. Chaque transducteur est shunté individuellement par un circuit électronique externe synthétisant une capacité négative. Cette stratégie de contrôle se base sur le couplage multipysique entre la plaque et les circuit électroniques mis en communication et permet de contrôler les ondes se propageant au sein de la structure. Le dispositif ainsi créé est qualifié de métacomposite. La performance du metacomposite a été évaluée par le biais de nombreux essais numériques et expérimentales. Du point de vue modélisation, l’analyse a été réalisée à l’aide du théorème de Bloch adapté aux systèmes piézo-élastiques à deux dimensions. Par la suite, une procédure d’optimisation a été utilisée dans le but de sélectionner les paramètres de shunt électrique les plus appropriés.Un prototype du guide d’ondes a été fabriqué et testé. Les résultats montrent clairement que ce dispositif permet de modifier les propriétés vibratoires de la structure porteuse, que ce soit en terme d’atténuation ou de trasmission. Enfin, un modèle éléments finis de la plaque a été utiliser afin d’évaluer la robustesse de la stratégie de contrôle proposée vis-à-vis d’une modification des paramètres du circuit, de la topologie del’interface active ou des propriétés de la plaque contrôlée. / Smart materials is an active research area devoted to the design of structured materials showingphysical properties that can be modified in response to an external stimulus.This study focuses on the analysis and design of adaptive system for vibroacoustic control. Theresearch investigates the design of a active interface made of piezoelectric transducers arranged ina two-dimensional lattice. Each transducer is individually shunted to an external electric circuitsynthesizing a negative capacitance effect. It allows to control waves propagating inside a structuretaking advantage of the multi-field coupling between the structural plate and the electrical circuitsshunting the piezoelectric patches.The performance of the metacomposite has been evaluated through numerous numerical andexperimental tests. The smart wave-guide has been analyzed by using the Bloch theorem appliedto two-dimensional piezo-elastic systems. Subsequently an optimization procedure has been usedwith the purpose to select the most appropriate set of circuit’s parameters.A prototype of the smart waveguide has been manufactured and tested. The results results clearlyshow the filtering and attenuating capabilities of this device.Finally a finite element model of the finite extent smart plate has been considered in order toasses the robustness of the proposed control strategy respect to a modification of the circuit’sparameters, the topology of the active interface and the properties of the controlled plate.A brief review conclude the work delineating which aspects of the design should be modified inorder to obtain a device suitable for industrial applications.

Orientadores: José Roberto de França Arruda, Jean-Mathieu Mencik / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-28T14:24:53Z (GMT). No. of bitstreams: 1 Silva_PriscillaBrandao_D.pdf: 13049086 bytes, checksum: 2f821e196dd604384d15489bda2360cb (MD5) Previous issue date: 2015 / Resumo: Nesta tese de doutorado, o método dos elementos finitos ondulatórios é utilizado para cálculo da resposta harmônica de sistemas mecânicos envolvendo estruturas com periodicidade unidimensional, i.e., estruturas compostas por subestruturas idênticas arranjadas ao longo de uma direção. Tais sistemas mecânicos podem ser complexos e são comumente encontrados em aplicações de engenharia como, por exemplo, nas fuselagens de aviões. A primeira parte da tese é dedicada ao cálculo das ondas que se propagam ao longo dessas estruturas. Uma breve revisão da literatura sobre as formulações disponíveis para o problema de autovalor associado ao método dos elementos finitos ondulatórios é apresentada, assim como um estudo dos erros numéricos induzidos por estes problemas de autovalor no caso de um guia de ondas sólido. Na segunda parte desta tese, modelagens de superelementos para estruturas periódicas são propostas. Neste contexto, matrizes de rigidez dinâmica e de receptância ou flexibilidade de estruturas periódicas são expressas a partir dos modos de onda. Comparadas às matrizes de rigidez dinâmica e receptância obtidas pelo método dos elementos finitos convencional, as matrizes baseadas no método dos elementos finitos ondulatórios são calculadas de forma bastante rápida e sem perda de acuracidade. Ademais, uma estratégia eficiente de redução de ordem de modelo é apresentada. Comparada às formulações que utilizam a base completa de ondas, esta estratégia proporciona redução do tempo computacional requerido para cálculo da resposta forçada de estruturas periódicas. De fato, é mostrado que elementos espectrais numéricos de alta ordem podem ser construídos a partir do método dos elementos finitos ondulatórios. Isto constitui uma alternativa ao método dos elementos espectrais convencional, cuja utilização está limitada a estruturas simples para as quais soluções analíticas por ondas existam. A motivação por trás das formulações de matrizes de superelementos a partir do método dos elementos finitos ondulatórios está na utilização do conceito de ondas numéricas para calcular a resposta harmônica de sistemas mecânicos acoplados que envolvam estruturas com periodicidade unidimensional e junções elásticas a partir de procedimentos de montagem clássicos de elementos finitos ou técnicas de decomposição de domínio. Este assunto é tratado na terceira parte desta tese. Nesse caso, o método de Craig-Bampton é usado para expressar as matrizes de superelementos de junções por meio de modos estáticos e de interface fixa. Um critério baseado no método dos elementos finitos ondulatórios é considerado para a seleção dos modos da junção que mais contribuem para a resposta forçada do sistema. Isto também contribui para o aumento da eficiência da simulação numérica de sistemas acoplados. Finalmente, na quarta parte desta tese, o método dos elementos finitos ondulatórios é utilizado para mostrar que é possível projetar estruturas periódicas com potencial para funcionar como filtros de vibração em bandas de frequência específicas. Com o intuito de destacar a relevância dos desenvolvimentos propostos nessa tese, ensaios numéricos envolvendo guias de onda sólidos, pórticos planos e estruturas tridimensionais do tipo fuselagem aeronáutica são realizados / Abstract: In this thesis, the wave finite element (WFE) method is used for assessing the harmonic forced response of mechanical systems that involve structures with one-dimensional periodicity, i.e., structures which are made up of several identical substructures along one direction. Such mechanical systems can be quite complex and are commonly encountered in engineering applications, e.g., aircraft fuselages. The first part of the thesis is concerned with the computation of wave modes traveling along these structures. A brief literature review is presented regarding the available formulations for the WFE eigenproblem, which need to be solved for expressing the wave modes, as well as a study of the numerical errors induced by these eigenproblems in the case of a solid waveguide. In the second part of the thesis, the WFE-based superelement modeling of periodic structures is proposed. In this context, the dynamic stiffness matrices and receptance matrices of periodic structures are expressed in terms of wave modes. Compared to the conventional FE-based dynamic stiffness and receptance matrices, the WFE-based matrices can be computed in a very fast way without loss of accuracy. In addition, an accurate strategy for WFE-based model order reduction is presented. It provides significant computational time savings for the forced response analysis of periodic structures compared to WFE-based superelement modeling, which makes use of the full wave basis. Indeed, it is shown that higher-order numerical spectral elements can be built by means of the WFE method. This is an alternative to the conventional spectral element method, which is limited to simple structures for which closed-form wave solutions exist. The motivation behind the formulation of WFE-based superelement matrices is the use of the concept of numerical wave modes to assess the forced response of coupled mechanical systems that involve structures with one-dimensional periodicity and coupling elastic junctions through classic finite element assembly procedures or domain decomposition techniques. This issue is addressed in the third part of this thesis. In this case, the Craig-Bampton method is used to express superelement matrices of coupling junctions by means of static and fixed-interface modes. A WFE-based criterion is considered to select among junction modes those that contribute most to the system forced response. This also contributes to enhancing the efficiency of the numerical simulation of coupled systems. Finally, in the fourth part of this thesis, the WFE method is used to show the potential of designing periodic structures which work as vibration filters within specific frequency bands. In order to highlight the relevance of the developments proposed in this thesis, numerical experiments which involve solid waveguides, two-dimensional frame structures, and three-dimensional aircraft fuselage-like structures are carried out / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutora em Engenharia Mecânica / 2010/17317-9 / FAPESP

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The sight of work is study form high frequency electromagnetic wave in inhomogeneous materials. The main are refractions and reflection on boundary of materials with different properties and form electromagnetic wave in periodic structure. The work contain analytic and numeric solution. The numeric solution was realized in program COMSOL.