In recent years, the study of metamaterials has been a subject of much interest, with acoustic metamaterials being applied to a wide range of applications. This utility is in part due to the incorporation of various elements in their design. The addition of local resonators provides greater versatility in controlling vibrations. Nonlinear elements introduce features such as discrete breathers and frequency shift. Electromechanical metamaterials have been established to have great potential for use in simultaneous energy harvesting in addition to vibration control. Furthermore, metamaterials with quasiperiodic patterning have been shown to possess useful properties such as edge-localized modes. However, no works investigate the interaction between all these elements, especially in the nonlinear regime. In this work, we investigate a unique metamaterial with local resonators, nonlinearity, electromechanical elements, and quasiperiodicity. The proposed metamaterial is examined using both analytical and numerical techniques in order to firmly establish the effects of each element. First, a nonlinear metamaterial with electromechanical local resonators is studied using the perturbation method of multiple scales, wavepacket excitation and direct integration, and specto-spatial processing techniques. The effect of the electromechanical local resonators is established for both the linear and nonlinear regimes, notably including the addition of new bandgaps and pass bands. The influence of electrical parameters on the system dynamics is explored through parametric analysis, demonstrating their use in tuning the system response. It is also shown that nonlinear phenomena such as localized solitons and frequency shift are present in the voltage response of the electromechanical metamaterial. Next, a nonlinear metamaterial with local resonators and quasiperiodicity is investigated using the method of multiple scales as well as numerical solution of the method of harmonic balance. Topological features stemming from quasiperiodicity are observed in the linear and nonlinear regimes. The presence of local resonators is shown to result in an additional, topologically trivial bandgap. The influence of quasiperiodic parameters and the source of quasiperiodicity on the system's band structure and mode shapes are established in both the linear and nonlinear regimes. Nonlinearity is also shown to affect topological features such as edge modes, resulting in amplitude dependence that can affect the localization of these modes in the nonlinear regime. Finally, a metamaterial with nonlinearity, electromechanical local resonators, and quasiperiodic patterning is modeled and investigated. Multiple configurations are examined, including different shunt circuits coupled to the electromechanical resonators and different sources of quasiperiodic patterning. It is shown that electromechanical local resonators produce two topologically trivial bandgaps, compared to the single trivial bandgap of the purely mechanical resonator. The influence of mechanical, electrical, and quasiperiodic parameters is explored to establish the effects of these parameters on bandgap formation in the linear regime. The behavior of the metamaterial in the nonlinear regime was found to be consistent with a purely mechanical system, with no adverse effects from the presence of electromechanical elements. The impact of nonlinear and quasiperiodic phenomena on energy harvesting is also investigated. Through exploration of this unique metamaterial, it is shown that beneficial features from all elements can be present at once, resulting in a versatile metamaterial with great potential for numerous applications. / Doctor of Philosophy / In recent years, the study of metamaterials has been a subject of much interest. Despite their name, metamaterials are not homogenous materials, but engineered structures designed to possess properties not found in naturally occurring materials. Many elements can be incorporated into metamaterial design, each with its own benefits. These can range from nonlinear springs, which allow the metamaterial to behave differently as its deformation increases, to electromechanical components, which convert the motion of the metamaterial into electrical voltage. While these elements have been examined individually and in certain combinations, no works examine the combination of elements proposed in this dissertation. In this work, we investigate the impact of nonlinearity, electromechanical components, and two other beneficial elements on the system's vibration response. Combinations of these elements are examined using various analysis techniques, which are used to establish the effects of each element individually as well as their interaction when combined. Multiple variations are examined for each element, such as different types of nonlinearity or different circuits attached to the electromechanical elements. This allows us to confirm the presence of valuable features exclusive to the elements incorporated into the metamaterial. Through exploration of multiple combinations of these metamaterial elements, it is shown that beneficial features from all elements can be present at once, resulting in a versatile metamaterial with great potential for numerous applications.

Les métamatériaux sont des composites artificiels présentant des propriétés électromagnétiques qu’on ne trouve pas dans la nature. Malgré des développements spectaculaires durant la dernière décennie, le potentiel de ces structures aux longueurs d’ondes optique n’est pas encore clairement défini en raison de problèmes technologiques et de contraintes physiques telles que les pertes dans les métaux entrant dans la composition des métamatériaux. Dans notre thèse, nous montrons que les métamatériaux ont des propriétés très favorables dans le contexte de l’optique intégrée dans le proche infrarouge. Nous avons développé une stratégie pour incorporer des métamatériaux dans des circuits photoniques qui n’absorbent que très peu d’énergie. Pour cela, nous ne faisons pas directement agir l’ensemble du mode guidé avec les métamatériaux, mais seulement une composante évanescente à l’extérieur du guide. Pour réaliser un tel adaptateur ou d’autres fonctionnalités, il importe de déterminer quelle géométrie de métamatériaux est la plus favorable aux applications infrarouges. Nous proposons d’utiliser des structures à base de fils d’or empilés couche sur couche. A l’aide de simulations numériques et d’expériences en espace libre, nous montrons qu’il est possible d’obtenir toute une gamme de réponses optiques en contrôlant le couplage entre les différents niveaux de fils, c'est-à-dire en ajustant la distance entre les fils ainsi que leur alignement. En particulier, nous avons réussi à contrôler séparément la réponse électrique et magnétique de nos structures, ce qui offre une flexibilité de conception qui ne se rencontre pas dans les métamatériaux proposés jusqu’à présent. / Metamaterials are artificial composites with electromagnetic properties not found in nature. Although the development of metamaterials has experienced a tremendous growth over the past few years, their potential at optical wavelengths is not clearly established due to technological and physical constraints such as high material losses in this spectral range. Here we show that metamaterials have a great potential in the context of integrated optics in the near infrared. We developed a strategy to incorporate metamaterials in photonic circuits with minimal absorption losses. Our approach relies on making the guided modes interact with the metamaterials only through the evanescent tail outside the waveguide. To achieve such an adaptor and other functionalities, it is important to know what is the best geometry for near-infrared applications. We propose to use metamaterials based on multi-layers of Au cut wires. With numerical simulations and experiments, we show that it is possible to create a wide range of optical properties by controlling the interaction between the wires, i.e. by adjusting the distance between the wires and their alignment. In particular we were able to demonstrate

<p dir="ltr">Metamaterials are artificially engineered nanoscale systems with a three-dimensional repetitive arrangement of certain components, and present exceptional optical properties for applications in nanophotonics, solar cells, plasmonic devices, and more. Self-assembled oxide-metal vertically aligned nanocomposites (VANs), with metallic phase as nanopillars embedded in the matrix oxide, have been recently proposed as a promising candidate for metamaterial applications. However, precise microstructural control and the structure-property relationships in VANs are still in high demand. Thus, by employing multiple approaches for structural design, this dissertation attempts to investigate the mechanisms of nanostructure evolutions and the corresponding optical responses.</p><p dir="ltr">In this dissertation, the precise control over the nanostructures has been demonstrated through morphology tuning, nanopillar orderings, and strain engineering. Firstly, Au, a well-known plasmonic mediator, has been selected as the metallic phase that forms nanopillars. Based on the previously proposed strain compensation model which describes the basic formation mechanism of VAN morphology, two oxides were then considered: La_0.7Sr_0.3MnO₃(LSMO) and CeO₂. In the first two chapters of this dissertation, LSMO was considered due to its similar lattice (a_LSMO= 3.87 Å, a_Au= 4.08 Å) and its enormous potential in nanoelectronics and spintronics. Deposited on SrTiO₃ (001) substrate through pulsed laser deposition (PLD), LSMO-Au nanocomposites exhibit ideal VAN morphology as well as promising hyperbolic dispersions in response to the incident illuminations. By substrate surface treatment of annealing at 1000°C, and variation of STO substate orientations from (001), to (111) and (110), the improved and tunable in-plan orderings of Au nanopillars have been successfully achieved. In the third chapter, a new oxide-metal VAN system of <a href="" target="_blank">CeO₂</a>-Au (a_CeO2= 5.411 Å, and a_CeO2/= 3.83 Å) has been deposited. The intriguing 45° rotated in-plan epitaxy presents an unexpected update to the strain compensation model, and tuning of Au morphology from nanopillars, nanoantennas, to nanoparticles also shows an effective modulation of the LSPR responses. COMSOL simulations have been exploited to reveal the relationships between Au morphologies and optical responses. In the last chapter, the two VAN systems of LSMO-Au and CeO₂-Au have been combined to form a complex layered VAN thin film. Investigations into the strain states, the nature of complex interfaces, and the according hybrid properties, show dramatic possibilities for further strain engineering. In summary, this dissertation has provided multiple routes for highly tailorable oxide-metal nanocomposite designs. And the two proposed material systems present great potential in optical metamaterial applications including biosensors, photovoltaics, super lenses, and more.</p>

Metamaterials are typically described as materials with ’unusual’ wave propagation properties. Originally developed for electromagnetic waves, these materials have also spread into the field of acoustic wave guiding and cloaking, with the most relevant of these ’unusual’ properties, being the so called band-gap phenomenon. A band-gap signifies a frequency region where elastic waves cannot propagate through the material, which in principle, could be used to protect buildings from earthquakes. Based on this, two relevant concepts have been proposed in the field of seismic engineering, namely: metabarriers, and metamaterial-based foundations. This thesis deals with the development of the Metafoundation, a metamaterial-based foundation system for the seismic protection of fuel storage tanks against excessive base shear and pipeline rupture. Note that storage tanks have proven to be highly sensitive to earthquakes, can trigger sever economic and environmental consequences in case of failure and were therefore chosen as a superstructure for this study. Furthermore, when tanks are protected with traditional base isolation systems, the resulting horizontal displacements, during seismic action, may become excessively large and subsequently damage connected pipelines. A novel system to protect both, tank and pipeline, could significantly augment the overall safety of industrial plants. With the tank as the primary structure of interest in mind, the Metafoundation was conceived as a locally resonant metamaterial with a band gap encompassing the tanks critical eigenfrequency. The initial design comprised a continuous concrete matrix with embedded resonators and rubber inclusions, which was later reinvented to be a column based structure with steel springs for resonator suspension. After investigating the band-gap phenomenon, a parametric study of the system specifications showed that the horizontal stiffness of the overall foundation is crucial to its functionality, while the superstructure turned out to be non-negligible when tuning the resonators. Furthermore, storage tanks are commonly connected to pipeline system, which can be damaged by the interaction between tank and pipeline during seismic events. Due to the complex and nonlinear response of pipeline systems, the coupled tank-pipeline behaviour becomes increasingly difficult to represent through numerical models, which lead to the experimental study of a foundation-tank-pipeline setup. Under the aid of a hybrid simulation, only the pipeline needed to be represented via a physical substructure, while both tank and Metafoundation were modelled as numerical substrucutres and coupled to the pipeline. The results showed that the foundation can effectively reduce the stresses in the tank and, at the same time, limit the displacements imposed on the pipeline. Leading up on this, an optimization algorithm was developed in the frequency domain, under the consideration of superstructure and ground motion spectrum. The advantages of optimizing in the frequency domain were on the one hand the reduction of computational effort, and on the other hand the consideration of the stochastic nature of the earthquake. Based on this, two different performance indices, investigating interstory drifts and energy dissipation, revealed that neither superstructure nor ground motion can be disregarded when designing a metamaterial-based foundation. Moreover, a 4 m tall optimized foundation, designed to remain elastic when verified with a response spectrum analysis at a return period of 2475 years (according to NTC 2018), reduced the tanks base shear on average by 30%. These results indicated that the foundation was feasible and functional in terms of construction practices and dynamic response, yet unpractical from an economic point of view. In order to tackle the issue of reducing the uneconomic system size, a negative stiffness mechanism was invented and implemented into the foundation as a periodic structure. This mechanism, based on a local instability, amplified the metamaterial like properties and thereby enhanced the overall system performance. Note that due to the considered instability, the device exerted a nonlinear force-displacement relationship, which had the interesting effect of reducing the band-gap instead of increasing it. Furthermore, time history analyses demonstrated that with 50% of the maximum admissible negative stiffness, the foundation could be reduced to 1/3 of its original size, while maintaining its performance. Last but not least, a study on wire ropes as resonator suspension was conducted. Their nonlinear behaviour was approximated with the Bouc Wen model, subsequently linearized by means of stochastic techniques and finally optimized with the algorithm developed earlier. The conclusion was that wire ropes could be used as a more realistic suspension mechanism, while maintaining the high damping values required by the optimized foundation layouts. In sum, a metamaterial-based foundation system is developed and studied herein, with the main findings being: (i) a structure of this type is feasible under common construction practices; (ii) the shear stiffness of the system has a fundamental impact on its functionality; (iii) the superstructure cannot be neglected when studying metamaterial-based foundations; (iv) the complete coupled system can be tuned with an optimization algorithm based on calculations in the frequency domain; (v) an experimental study suggests that the system could be advantageous to connected pipelines; (vi) wire ropes may serve as resonator suspension; and (vii) a novel negative stiffness mechanism can effectively improve the system performance.

The present research is concerned with developing analysis methods for analyzing and exploring finite-amplitude elastic wave propagation through periodic media. Periodic arrangements of materials with high acoustic impedance contrasts can be employed to control wave propagation. These systems are often termed phononic crystals or metamaterials, depending on the specific design and purpose. Design of these systems usually relies on computation and analysis of dispersion band structures which contain information about wave propagation speed and direction. The location and influence of complete (and partial) band gaps is a particularly interesting characteristic. Wave propagation is prohibited for frequencies that correspond to band gaps; thus, periodic systems behave as filters, wave guides, and lenses at certain frequencies. Controlling these behaviors has typically been limited to the manufacturing stage or the application of external stimuli to distort material configurations. The inclusion of nonlinear elements in periodic unit cells offers an option for passive tuning of the dispersion band structure through amplitude-dependence. Hence, dispersion analysis methods which may be utilized in the design of nonlinear phononic crystals and metamaterials are required. The approach taken herein utilizes Bloch wave-based perturbation analysis methods for obtaining closed-form expressions for dispersion amplitude-dependence. The influence of material and geometric nonlinearities on the dispersion relationship is investigated. It is shown that dispersion shifts result from both self-action (monochromatic excitation) and wave-interaction (multi-frequency excitation), the latter enabling dynamic anisotropy in periodic media. A particularly novel aspect of this work is the ease with which band structures of discretized systems may be analyzed. This connection enables topology optimization of unit cells with nonlinear elements. Several important periodic systems are considered including monoatomic lattices, multilayer materials, and plane stress matrix-inclusion configurations. The analysis methods are further developed into a procedure which can be implemented numerically with existing finite-element analysis software for analyzing geometrically-complex materials.

This thesis studies a new class of high gain planar resonant cavity antennas based on metamaterial surfaces. High-gain planar antennas are becoming increasing popular due to their significant advantages (e.g. low profile, small weight and low cost). Metamaterial surfaces have emerged over the last few years as artificial structures that provide properties and functionalities not readily available from existing materials. This project addresses novel applications of innovative metamaterial surfaces on the design of high-gain planar antennas. A ray analysis is initially employed in order to describe the beamfonning action of planar resonant cavity antennas. The phase equations of resonance predict the possibility of low-profile/subwavelength resonant cavity antennas and tilted beams. The reduction of the resonant cavity profile can be obtained by virtue of novel metamaterial ground planes. Furthermore, the EBG property of metamaterial ground planes would suppress the surface waves and obtain lower backlobes. By suppressing the TEM mode in a resonant cavity, a novel aperture-type EBG Partially Reflective Surface (PRS) is utilized to get low sidelobes in both planes (E-plane and H-plane) in a relatively finite structure. The periodicity optimization of PRS to obtain a higher maximum directivity is also investigated. Also it is shown that antennas with unique tilted beams are achieved without complex feeding mechanism. Rectangular patch antennas and dipole antennas are employed as excitations of resonant cavity antennas throughout the project. Three commercial electromagnetic simulation packages (Flomerics Microstripes ™ ver6.S, Ansoft HFSSTM ver9.2 and Designer ™ ver2.0) are utilized during the rigorous numerical computation. Related measurements are presented to validate the analysis and simulations.

<p>Metasurfaces are broadly defined as artificially engineered material interfaces that have the ability to determinately control the amplitude and phase signatures of an incident electromagnetic wave. Subwavelength sized optical scatterers employed at the planar interface of two media, introduce abrupt modifications to impinged light characteristics. Arbitrary engineering of the optical interactions and the arrangement of the scatterers on plane, enable ultra-compact, miniaturized optical systems with a wide array of applications (e.g. nanoscale and nonlinear optics, sensing, detection, energy harvesting, information processing and so on) realizable by the metasurfaces. However, maturation from the laboratory to industry scale realistic systems remain largely elusive despite the expanding reach and vast domains of functionalities demonstrated by researchers. A large part of this multi-faceted problem stems from the practical constraints posed by the commonly used plasmonic materials that limit their applicability in devices requiring high temperature stability, robustness in varying ambient, mechanical durability, stable growth into nanoscale films, CMOS process compatibility, stable bio-compatibility, and so on. </p> <p>Aiming to create a whole-some solution, my research has focused on developing novel, high-performance, functional plasmonic metasurface devices that utilize the inherent benefits of various emerging and alternative material platforms. Among these, the two-dimensional MXenes and the refractory transition metal nitrides are of particular importance. By exploiting the plasmonic response of thin films of the titanium carbide MXene (Ti₃C₂T_x) in the near infrared spectral window, a highly broadband metamaterial absorber has been designed, fabricated and experimentally demonstrated. In another work, high efficiency photonic spin Hall Effect has been experimentally realized in robust phase gradient metasurface devices based on two different refractory transition metal nitrides –titanium nitride (TiN) and zirconium nitride (ZrN). Further, taking advantage of the refractory nature of these plasmonic nitrides, a metasurface based temperature sensor has been developed that is capable of remote, optical sensing of very high temperatures ranging up to 1200^oC.</p>

Ce travail de thèse a été consacré à l'étude théorique et numérique de métamatériaux pour la gamme submillimétrique (domaine térahertz), formés de sphères diélectriques présentant des résonances dipolaires de Mie électrique et magnétique, dispersées dans un milieu-hôte. Tout d'abord, les matériaux à utiliser ainsi que les tailles et fraction volumique des sphères permettant l'obtention d'effets de perméabilité ont été précisées. Ensuite, nous avons mené une étude de la polydispersité en taille, mettant en évidence qu'une polydispersité contrôlée pouvait engendrer un élargissement des zones de perméabilité négative ou une zone de perméabilité nulle. Enfin, nous avons étudié le comportement électromagnétique d'assemblages bidisperses de sphères par simulations numériques, et avons procédé à une analyse des modes de Bloch, semblant indiquer l'existence d'une bande d'indice négatif pour des fractions volumiques élevées. / This PhD work was dedicated to the theoretical and numerical study of metamaterials in the terahertz range made of dielectric spheres embedded in a host medium and exhibiting dipolar electric and magnetic Mie resonances. The materials as well as the sizes and the filling fractions of the spheres to use to achieve magnetism in this range of frequency were precised. As a second step, we interested in the size distribution effects on the effective permeability, and showed that a controlled polydispersity can generate a widening of the negative permeability zone with a magnitude close to zero. Finally, we studied the electromagnetic behaviour of bidisperse array of TiO2 spheres with numerical simulations, and a Bloch mode analysis seems to proove the existence of a negative index band for high filling fractions.

Os metamateriais acústicos/elásticos são materiais que apresentam características elásticas diferentes dos materiais comuns encontrados na natureza, sendo o índice de refração negativo a principal característica destes novos materiais. A literatura reporta que esta propriedade é atingida para uma faixa muito estreita de frequências, sendo um efeito muito localizado, e, adicionalmente, as estruturas propostas são ideais em extremo, o que dificulta sua aplicação prática em dispositivos acústicos. O objetivo do presente trabalho foi projetar metamateriais acústicos e elásticos tridimensionais com índice de refração negativo numa faixa de frequência mais longa em relação ao reportado na literatura, e utilizando geometrias e materiais que tornem viável sua implementação prática para a fabricação de dispositivos. Com este propósito foi desenvolvido um formalismo da teoria de meio efetivo (TME), no limite de comprimento de onda longa e baixas frações de preenchimento. Com a TME desenvolvida foi estudado o espalhamento de inclusões esféricas simples, revestidas e duplamente revestidas em diferentes matrizes hospedeiras. Os resultados mostraram a existência de bandas ressonantes nos coeficientes da matriz T relacionadas aos modos monopolares, dipolares e quadrupolares. Materiais compósitos constituídos por esferas simples, revestidas ou duplamente revestidas foram analisados utilizando o formalismo TME. Os resultados mostraram que os valores negativos dos parâmetros elásticos nestes materiais estão completamente relacionados aos efeitos ressonantes das inclusões esféricas. Metamateriais elásticos e acústicos foram projetados sobrepondo dois ou mais compósitos diferentes, cada um com diferentes propriedades, de tal forma que o efeito total no metamaterial apresente as características definidas no projeto inicial. O metamaterial elástico foi projetado utilizando a sobreposição de três compósitos de inclusões esféricas diferentes. Este metamaterial apresentou índice de refração negativa na região de 2 kHz, numa faixa de largura igual a 80 Hz. O metamaterial acústico foi projetado sobrepondo dois compósitos de inclusões esféricas diferentes. Este material apresentou índice de refração negativa na região de 7 kHz, numa faixa de 500 Hz. As geometrias e materiais utilizados no projeto destes metamateriais são acessíveis e de fácil manipulação, o que facilitará sua futura fabricação em laboratório. Os resultados obtidos neste trabalho sugerem a possibilidade de fabricar estes metamateriais no laboratório e empregá-los no controle de ondas acústicas, elásticas e sísmicas, assim como também no projeto de um manto de invisibilidade acústica/elástica. / The acoustic/elastic metamaterials are materials that show different elastic features from common materials found in nature and their main characteristics are their negative refractive index. The literature reports that this property is reached for a very narrow range of frequencies, as a very localized phenomenon, and additionally, the proposed structures are extremely ideals, which makes its practical application difficult on acoustic devices. The objective of this work was to design acoustic/elastic three-dimensional Metamaterials with negative refractive index in a wider frequency band than that reported in the literature, and using geometries and materials that make it possible their practical implementation for manufacturing acoustic/elastic devices. With this purpose a formalism of the effective medium theory (EMT) was developed, in the limit of wavelength and low fill fractions. With the developed EMT, the scattering of simple spherical inclusions, coated and doubly coated in different host substrates were studied. The results showed the existence of resonant bands in the coefficients of the T matrix related to monopolar, dipolar and quadrupolar modes. Composite materials consisting of simple, coated or double coated spheres were analyzed using the EMT formalism. The results showed that the negative values of elastic parameters in these materials are completely related to resonant effects of the spheres of inclusion. Elastic and acoustic Metamaterials were designed by overlaying two or more different composites, each with different properties, such that the overall effect on the metamaterial shows the desired features defined in the initial project. The elastic metamaterial was designed by overlapping three different composites of different spherical inclusions. This metamaterial shows negative refractive index in the region of 2 kHz, in a band of width of 80 Hz. The acoustic metamaterial was designed by overlapping two composites of different spherical inclusions. This material shows negative refractive index in the region of 7 kHz, in a band of width of 500 Hz. The geometries and materials used in the design of these Metamaterials are affordable and easy to handle, which will facilitate their future fabrication in the laboratory. The results obtained in this study suggest the possibility to manufacture these metamaterials in the laboratory and use them in the control of acoustic, elastic and seismic waves, as well as in the design of invisible cloak.

Os metamateriais acústicos/elásticos são materiais que apresentam características elásticas diferentes dos materiais comuns encontrados na natureza, sendo o índice de refração negativo a principal característica destes novos materiais. A literatura reporta que esta propriedade é atingida para uma faixa muito estreita de frequências, sendo um efeito muito localizado, e, adicionalmente, as estruturas propostas são ideais em extremo, o que dificulta sua aplicação prática em dispositivos acústicos. O objetivo do presente trabalho foi projetar metamateriais acústicos e elásticos tridimensionais com índice de refração negativo numa faixa de frequência mais longa em relação ao reportado na literatura, e utilizando geometrias e materiais que tornem viável sua implementação prática para a fabricação de dispositivos. Com este propósito foi desenvolvido um formalismo da teoria de meio efetivo (TME), no limite de comprimento de onda longa e baixas frações de preenchimento. Com a TME desenvolvida foi estudado o espalhamento de inclusões esféricas simples, revestidas e duplamente revestidas em diferentes matrizes hospedeiras. Os resultados mostraram a existência de bandas ressonantes nos coeficientes da matriz T relacionadas aos modos monopolares, dipolares e quadrupolares. Materiais compósitos constituídos por esferas simples, revestidas ou duplamente revestidas foram analisados utilizando o formalismo TME. Os resultados mostraram que os valores negativos dos parâmetros elásticos nestes materiais estão completamente relacionados aos efeitos ressonantes das inclusões esféricas. Metamateriais elásticos e acústicos foram projetados sobrepondo dois ou mais compósitos diferentes, cada um com diferentes propriedades, de tal forma que o efeito total no metamaterial apresente as características definidas no projeto inicial. O metamaterial elástico foi projetado utilizando a sobreposição de três compósitos de inclusões esféricas diferentes. Este metamaterial apresentou índice de refração negativa na região de 2 kHz, numa faixa de largura igual a 80 Hz. O metamaterial acústico foi projetado sobrepondo dois compósitos de inclusões esféricas diferentes. Este material apresentou índice de refração negativa na região de 7 kHz, numa faixa de 500 Hz. As geometrias e materiais utilizados no projeto destes metamateriais são acessíveis e de fácil manipulação, o que facilitará sua futura fabricação em laboratório. Os resultados obtidos neste trabalho sugerem a possibilidade de fabricar estes metamateriais no laboratório e empregá-los no controle de ondas acústicas, elásticas e sísmicas, assim como também no projeto de um manto de invisibilidade acústica/elástica. / The acoustic/elastic metamaterials are materials that show different elastic features from common materials found in nature and their main characteristics are their negative refractive index. The literature reports that this property is reached for a very narrow range of frequencies, as a very localized phenomenon, and additionally, the proposed structures are extremely ideals, which makes its practical application difficult on acoustic devices. The objective of this work was to design acoustic/elastic three-dimensional Metamaterials with negative refractive index in a wider frequency band than that reported in the literature, and using geometries and materials that make it possible their practical implementation for manufacturing acoustic/elastic devices. With this purpose a formalism of the effective medium theory (EMT) was developed, in the limit of wavelength and low fill fractions. With the developed EMT, the scattering of simple spherical inclusions, coated and doubly coated in different host substrates were studied. The results showed the existence of resonant bands in the coefficients of the T matrix related to monopolar, dipolar and quadrupolar modes. Composite materials consisting of simple, coated or double coated spheres were analyzed using the EMT formalism. The results showed that the negative values of elastic parameters in these materials are completely related to resonant effects of the spheres of inclusion. Elastic and acoustic Metamaterials were designed by overlaying two or more different composites, each with different properties, such that the overall effect on the metamaterial shows the desired features defined in the initial project. The elastic metamaterial was designed by overlapping three different composites of different spherical inclusions. This metamaterial shows negative refractive index in the region of 2 kHz, in a band of width of 80 Hz. The acoustic metamaterial was designed by overlapping two composites of different spherical inclusions. This material shows negative refractive index in the region of 7 kHz, in a band of width of 500 Hz. The geometries and materials used in the design of these Metamaterials are affordable and easy to handle, which will facilitate their future fabrication in the laboratory. The results obtained in this study suggest the possibility to manufacture these metamaterials in the laboratory and use them in the control of acoustic, elastic and seismic waves, as well as in the design of invisible cloak.