Práce je věnována generování náhodných struktur dvousložkových vláknových kompozitních materiálů a statistickým metodám analýzy náhodnosti těchto struktur. Byly vyvinuty čtyři algoritmy a vygenerované struktury byly statisticky porovnány s reálnými daty.

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Attention has been focused on electromagnetic chirality and its potential applications to microwave, millimeter wave and optical wave devices. In this work, wave propagation through a chiral periodic structure with arbitrary shape is investigated. Although perturbation theory and coupled-mode theory have been used to analyze chiral periodic structure, those are approximate methods and can only be used for low frequency applications. In this work, the rigorous mode-matching method is used to solve the problem. Staircase approximation is introduced to change the curved structure to a multilayer structure. The field solutions in the uniform air regions and unbounded air-chiral periodic array have been derived. Finite element method is used to solve the eigenvalues and eigenfunctions in the periodic chiral slabs. Mode-matching method is used at the boundaries to calculate the scattering characteristics. Numerical results are displayed to explain the underlying physical properties of the chiral periodic structure. The Wood's anomalies at high frequencies have been investigated and explained by the excitation of leaky waves guided along the periodic layer. The influence of frequency, chirality parameter, incident angle, curve shape and period are discussed. It has been found that the chiral periodic structure can be used as both a frequency selective device and a mode conversion device. First, the derivation and numeric calculation were done with the principal plane incidence. Then, the discussion was extended to the more general case of oblique incidence by the coordinate transformation.

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The concept of photonic crystals was born in the late 1980's when two important letters were published that showed the possibility to control light propagation by a periodic structure. A photonic crystals consists of two or more materials with different dielectric functions periodically arranged on the length scale of light. If the conditions are favorable, a gap will open in the dispersion relation, often called photonic band structure, and electromagnetic waves with frequency in the gap range cannot propagate through the photonic crystal. In this thesis, mainly two types of structures and their properties have been numerically investigated: two-dimensional structures that are either square or triangular. In the calculations, both dielectric and polaritonic materials have been used. Polaritonic materials have an interval of high reflectance in the IR range, due to strong lattice resonances. Within such an interval, the real part of the dielectric function is negative, which causes a metal-like behavior. A polaritonic material, BeO has been introduced in photonic crystals to study the coexistence of structure and polaritonic gaps. Band structures and for some cases transmission spectra have been calculated to study the existence of complete gaps, i.e. energy intervals in which an incoming electromagnetic wave is totally reflected regardless of polarization and angle of incidence. A brief discussion on signature management and thermal emission, and calculations for low-emittance coatings is included. It is shown that a 50-60µm layer of a 3D photonic crystal can be sufficient to achieve a thermal emittance of 20%.

In the first part of the thesis, the 2-D structures in stratified media are analyzed using an efficient MoM technique. The method is used to optimize transmitted or reflected electric fields from the 2-D structures. The genetic algorithm is used in the optimization process. In the second part a 3-D MoM technique is implemented to analyze multilayered structures with periodically implanted material blocks. Using the method, the dispersion and reflection characteristics of the structure are calculated for different configurations. The results are compared with the results found in the literature and it is seen that they are in good agreement. Asymptotic Waveform Evaluation (AWE) technique is utilized to obtain the Pade approximation of the solution in terms of frequency. The high order derivatives that are required by the AWE technique are calculated through Automatic Differentiation technique. Using the AWE method, the dispersion diagram and reflection characteristics of the periodic structures are obtained in a shorter time. The results are compared with the ones obtained through direct calculation and it is seen that they are in perfect agreement. The reflection coefficients that are obtained from the 3-D MoM procedure are used to calculate Green&rsquo / s functions that approximate electric field of an infinitesimal dipole on the periodically implanted substrate. Using the calculated Green&rsquo / s functions and the spectral domain MoM procedure, dispersion characteristics of a microstrip line on the periodically implanted substrate are obtained.

Numerical analysis of periodic structures in layered media is usually accomplished by using Method of Moments which requires the formation of the impedance matrix of the structure. The construction of this impedance matrix requires the evaluation of the periodic Green&rsquo / s function in layered media which is expressed as an infinite series in terms of the spectral domain Green&rsquo / s function. The slow converging nature of this series make these kinds of analysis computationally expensive. Although some papers have proposed methods to accelerate the computation of these series successfully for a single frequency point, it is still very computation intensive to obtain the frequency response of the structure over a band of frequencies. In this thesis, Discrete Complex Image Method (DCIM) is utilized for the efficient computation of the periodic Green&rsquo / s function. First, the spectral domain Green&rsquo / s function in layered media is approximated by complex exponentials through the use of DCIM. During the application of the DCIM, three-level approximation scheme is employed to improve accuracy. Then, Ewald&rsquo / s transformation is applied to accelerate the computation of the infinite series involved in the periodic Green&rsquo / s functions. The accuracy and the efficiency of the method is demonstrated through numerical examples.

Submitted by Lara Oliveira (lara@ufersa.edu.br) on 2017-07-18T21:43:56Z No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-25T14:46:31Z (GMT) No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-25T14:46:56Z (GMT) No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Made available in DSpace on 2017-07-25T14:47:21Z (GMT). No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) Previous issue date: 2013-11-22 / The microstrip antennas are in constant evidence in current research due to its numerous advantages. Fractal geometry proposed by Mandelbrot(1975 ) combined with the performance and convenience of planar structures are an excellent combination used in the design of antennas in order to reduce the dimensions and enhance its bandwidth, and allows the emergence of best bands frequency by virtue of ownership of high -similarity. Compared with the conventional microstrip antennas, patch antennas with fractal type substrates have lower resonance frequency, enabling the manufacture of even more compact antennas. The aim of this work consists of the design of patch antennas with dielectric substrates organized almost periodic basis through the use of fractal geometry sequence Cantor applied to a circular patch antenna fed by microstrip line, designed for a resonant frequency of 10 GHz. Analysis of this microstrip antenna is made in various types of dielectric substrates by simulation through software commercial Ansoft HFSS - Designer, used for accurate analysis of the electromagnetic behavior of the antennas by the finite element method by presenting results from resonant frequency and radiation pattern, making comparisons with other results in the literature. This dissertation also presents a bibliographic study on theories of antennas while also addressing about fractal geometry, emphasizing its characteristics and properties as well as its applicability. This paper also presents a study of almost periodic structures and their mathematical formalism considered throughout this work / As antenas de microfita estão em constante evidência nas pesquisas atuais, devido às suas inúmeras vantagens. A geometria fractal proposta por Mandelbrot (1975) aliada ao bom desempenho e comodidade das estruturas planares são uma excelente combinação utilizada no projeto de antenas com o intuito de reduzir suas dimensões e realçar sua largura de banda, além de permitir o surgimento de melhores bandas de frequência em consequência da propriedade da alto-similaridade. Em comparação com as antenas em microfita convencionais, as antenas tipo patch com substratos fractais apresentam frequência de ressonância inferiores, possibilitando a fabricação de antenas ainda mais compactas. O objetivo desse trabalho consiste no projeto de antenas patch com substrato dielétrico organizado de forma quase periódica por meio da utilização da geometria fractal da sequência de Cantor aplicada a uma antena de patch circular alimentada por linha de microfita, projetada para uma frequência ressonância de 10 GHz. É feita análise dessa antena de microfita em vários tipos de substratos dielétricos por simulação através do software comercial Ansoft Designer-HFSS, usado para análise precisa do comportamento eletromagnético das antenas através do método dos elementos finitos apresentando resultados de frequência de ressonância, diagrama de radiação, carta de Smith e de campos elétricos e magnéticos fazendo-se comparações com outros resultados obtidos na literatura. Esta dissertação ainda apresenta um estudo bibliográfico em teorias de antenas, abordando também a respeito da geometria fractal, dando ênfase a suas características e propriedades como também a sua aplicabilidade. Este trabalho ainda apresenta um estudo sobre as estruturas quase periódicas e seu formalismo matemático / 2017-07-18

Des panneaux sandwichs en nid d'abeilles sont largement utilisés, notamment dans l’industrie aérospatiale et aéronautique, à cause du très bon rapport entre rigidité en flexion et poids. Concernant leur modélisation, ils sont considérés classiquement comme de milieux homogénéisés équivalents afin d'éviter des modèles numériques prohibitifs en coûts de calculs. Cependant, des travaux précédents ont montré que, si le comportement dynamique en membrane des sandwichs peut être correctement représenté par des modèles homogénéisés classiques dans une large gamme de fréquences, ces mêmes modèles ne permettent malheureusement pas de bien décrire le comportement en flexion dans le domaine de hautes fréquences (HF). En effet, la couche centrale en nid d'abeilles joue un rôle important dans le comportement en flexion du sandwich, il est donc indispensable de la modéliser de manière appropriée. Or, lorsque les longueurs d’onde impliquées deviennent aussi petites que les longueurs caractéristiques des cellules du nid d’abeilles, cette microstructure cellulaire interagit fortement avec les ondes et génère des effets d’interaction non négligeables, qui ne sont malheureusement pas pris en compte par des modèles homogénéisés classiques. Dans le cadre de cette thèse, on s’intéresse donc à l'amélioration de l’analyse théorique et numérique de la propagation d’ondes élastiques HF dans ces panneaux composites. On exploite les caractéristiques périodiques du nid d'abeilles en utilisant sur une approche numérique basée sur la théorie des ondes de Bloch. En effet, en décomposant des solutions non périodiques sur une base composée de modes périodiques de Bloch, il est possible de développer des modèles numériques, qui considèrent des phénomènes de propagation des ondes à l’intérieur d’une seule cellule de base et captent toutes les interactions. Ces modèles numériques sont donc de taille raisonnable, par rapport aux dimensions souvent très importantes des structures industrielles. Des analyses théoriques et des outils de modélisation ont été développés pour des milieux périodiques composés de structures minces : poutres ou plaques. Notre approche a été développée et validée pour des structures périodiques uni- puis bi-dimensionnelles composées de poutres. Pour les cas 2D, la forme de la cellule est hexagonale ou rectangulaire. Nous avons aussi considéré des plaques sandwichs en nid d’abeilles. Pour toutes ces structures, en identifiant les valeurs propres et les modes propres de Bloch sur une cellule primitive pour tous les vecteurs d’onde de Bloch situés dans la première zone de Brillouin dans l’espace de phase, la relation de dispersion entre le vecteur d'onde de Bloch et la valeur propre est calculée. En analysant cette relation de dispersion, les résultats importants sont obtenus, tels que les bandes de fréquences passantes et bloquantes et les caractéristiques d'anisotropie et dispersives des structures périodiques, la comparaison quantitative entre les premiers modes de Bloch et ceux des modèles homogénéisés classiques en vue d’une définition précise du domaine validation en fréquence de ceux-derniers et la mise en évidence des modes de Bloch « rétro-propagatifs » munis d’une vitesse de groupe négative. / Honeycomb core sandwich panels are widely used in the aeronautic industry due to their excellent flexural stiffness to weight ratio. Generally, classical homogenized model is used to model honeycomb core sandwiches in order to have an efficient but not expensive numerical modeling. However, previous works have shown that, while the homogenized models could correctly represent the membrane waves’ behavior of sandwiches in a large frequency range, they could not give satisfying simulation results for the flexural waves’ behavior in the high frequency range (HF). In fact, the honeycomb core layer plays an important role in the propagation of the flexural waves, so that when the involved wavelengths become close to the characteristic lengths of honeycomb cells, the cellular microstructure starts interacting strongly with the waves and its effect should no longer be neglected, which is unfortunately not the case of the homogenized models. In the present work, we are interested in improving the theoretical and numerical analysis of HF elastic waves’ propagation in honeycomb core sandwich panels by a numerical approach based on the Bloch wave theorem, which allows taking into account the periodic characteristics of the honeycomb core. In fact, by decomposing non-periodic wave solutions into their periodic Bloch wave basis modes, numerical models are defined on a basic cell and solved in a efficient way, and provide a better description and so a better understanding of the interaction between HF wave propagation phenomena and the periodic structures. Our numerical approach is developed and validated in the cases of one-dimensional periodic beam structures, of two-dimensional periodic hexagonal and rectangular beam structures and of honeycomb core sandwich plates. By solving the eigenvalue problem of the Bloch wave modes in one primitive cell of the periodic structure for all the wave vectors located in the corresponding first Brillouin zone in the phase space, the dispersion relation between the wave vector and the eigenvalue is calculated. The analysis of the dispersion relation provides important results such as: the frequency bandgaps and the anisotropic and dispersive characteristics of periodic structures, the comparison between the first Bloch wave modes to those of the classical equivalent homogenized models and the existence of the retro-propagating Bloch wave modes with a negative group velocity.

Orientador: Renato Pavanello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T17:42:52Z (GMT). No. of bitstreams: 1 Chang_PauloLeeKungCaetano_M.pdf: 2268901 bytes, checksum: 969b1f62e6eb27512023a9dccd41cac6 (MD5) Previous issue date: 2010 / Resumo: Neste trabalho estuda-se a propagação de ondas em meios elásticos periódicos e meios poro-elásticos. Para o estudo da propagação de ondas em meios elásticos periódicos, modelos discretos uni e bidimensionais são gerados - seguindo padrões encontrados na literatura - e simulados para a obtenção da estrutura de banda e da resposta em frequência, com o objetivo de observar-se o fenômeno band gap. Em seguida, estuda-se a propagação de ondas e a absorção em meios poro-elásticos periódicos. As equações diferenciais de movimento acopladas da poro-elasticidade são obtidas da formulação mista (u,p), baseada no modelo de Biot-Allard. A modelagem numérica do problema de propagação de ondas em meios poro-elásticos é feita utilizando-se o método dos elementos finitos. Mostra-se por meio de simulações numéricas como os padrões de periodicidade influenciam na estrutura de banda da matriz elástica do material poro-elástico e no comportamento global da curva de absorção. Finalmente, as principais conclusões são apresentadas e sugestões para trabalhos futuros são propostas / Abstract: In this work, a study of propagation of sound in elastic periodic materials and poroelastic media is made. One and two dimension discreet models are produced - following the literature - for the purpose of studying wave propagation in periodic elastic materials. The band structure and the frequency response of these materials are obtained by simulation of these models with the intention of observing the phenomenon of band gap. The case for periodic porous media is then studied. The wave equations for the poroelastic media are derived from the mixed displacement-pressure formulation based on the Biot-Allard's poroelasticity equations. The numerical solution of the wave propagation in porous media problem is calculated by the finite element method. It is showed how different periodic patterns affect the band structure of the solid phase of the porous materials and its acoustic absorption. Finally, the main conclusions are presented and some suggestions for future work are made / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica