This thesis investigates the damping effects of a metamaterial, on structural vibration, by inducing periodic voids in the base damping material as opposed to infusing the damping material with other material. Metamaterials have been used previously to improve the damping of vibrational waves and acoustic waves through wave scattering and wave reflection at periodic impedance changes. Impedance changes can occur at both material boundaries and geometric changes of the medium. Impedance changes cause wave scattering, wave reflection, and changing of wave speed. The low frequency region of the vibration spectrum is generally harder to dampen due to the longer wavelengths. By slowing the waves down, the wavelength can be shortened and the viscoelastic material will be more effective at damping the waves. The metamaterial in the thesis has one, two, three, and four periodically located voids in the viscoelastic damping material to determine the effectiveness of the damping compared to the same beam with no damping material applied and the beam covered completely with the standard viscoelastic damping material. This research will include both finite element models of the beam and concept testing to explore the damping effects of the metamaterial. / Master of Science / In the field of mechanical engineering vibrations are one of the main causes of failure of machinery components. Reducing vibrations greatly effects the longevity and effectiveness of a machine. The research in this thesis focuses on how to reduce the vibration in a beam by using a metamaterial. Standard damping materials provide damping, reduction of vibration, at various quantities depending on the frequency and wavelength of the vibrational wave. Metamaterials are particular materials designed to reduce vibration by influencing the physical phenomena of a wave as it travels through the material usually by periodic wave scatters. The metamaterial in this research is designed to slow the flexural waves down, therefore shortening the wavelength, making it easier to dampen the vibration compared to a standard damping material. The damping effectiveness of the metamaterials explored in this research will be quantified via finite element modeling and testing in a laboratory.

This thesis describes the results of the experimental investigations into some new geometrical configurations in plate-like structures materialising one-dimensional (1D) acoustic black holes for flexural waves (wedges of power-law profile) and two-dimensional (2D) acoustic black holes for flexural waves (circular indentations of power-law profile). Such acoustic black holes allow the user to reduce the amplitudes of the vibration responses of plate-like structures to a maximum effect, while not increasing the mass of the structures. This thesis also suggests some new real world practical applications for this damping technique. Initially, the effects of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power-law profile (1D black holes) were investigated, demonstrating that this method of damping is robust enough for practical applications. Then, damping of flexural vibrations in turbofan blades with trailing edges tapered according to a power-law profile has been investigated. In addition, experimental investigations into power-law profiled slots within plates have been also conducted. Another important configuration under investigation was that of circular indentations (pits) of power-law profile within the plate. In the case of quadratic or higher-order profiles, such indentations materialise 2D acoustic black holes for flexural waves. To increase the damping efficiency of power-law profiled indentations, the absorption area has been enlarged by increasing the size of the central hole in the pit, while keeping the edges sharp. The next step of investigation in this thesis was using multiple indentations of power-law profile (arrays of 2D black holes). It was shown that not only do multiple indentations of power-law profile provide substantial reduction in the damping of flexural vibrations, but also a substantial reduction in radiated sound power. The experimental results have been obtained also for a cylindrical plate incorporating a central hole of quadratic profile. They are compared to the results of numerical predictions, thus validating the results and the experimental technique. Investigations into the effects of indentations of power-law profile made in composite plates and panels and their subsequent inclusion into composite honeycomb sandwich panels are also reported. These indentations again act as 2D acoustic black holes for flexural waves and they effectively damp flexural vibrations within the panels. It was also demonstrated that these indentations can be enclosed in smooth surfaced panels and that no additional damping layer is required to induce the acoustic black hole effect in composite structures. In conclusion, it has been confirmed in this thesis that one and two-dimensional acoustic black holes represent an effective method of damping flexural vibrations and reducing the associated structure-borne sound. Furthermore, this thesis has shown that acoustic black holes can be efficiently employed in practical applications, such as trailing edges of jet engine fan blades, composite panels, and composite honeycomb sandwich structures.

Orientador: Michael John Brennan / Abstract: The guarantee of security in transport vehicles, buildings, bridges and critical structures is extremely important for people and the environment. Therefore, in the last decades, several Structural Health Monitoring (SHM) techniques have been proposed and developed for many areas. One technique to detect corrosion could be the use of guided waves. Considering one wave travelling in a structure and impinging on a discontinuity (damage), this wave will interact with this discontinuity and will be scattered. Thus wave motion in structures may be a powerful way to indicate the presence of damage in a structure. This work aims to investigate wave propagation in a thin Euler-Bernoulli infinite beam, and the way in which these waves interact with simulated corrosion damage (symmetric and asymmetric). The studies show the importance to know the behavior of waves before chose main frequencies to used for a SHM system. Piezoelectric elements are used to excite and sense the waves. The behavior of the systems studied are widely discussed in frequency and time domains. In order to detect and quantify the damage, reflected waves showed better sensitivity and proportionality with damage severity for all configuration studied. The longitudinal wave incident in the damage is easier to be used in a SHM system than flexural waves because longitudinal waves present simplicity compared to flexural. However, is important to choose appropriate frequency range in order to generate good levels of th... (Complete abstract click electronic access below) / Resumo: A garantia de segurança em veículos de transporte, edifícios, pontes e estruturas críticas é extremamente importante para as pessoas e o meio ambiente. Portanto, nas últimas décadas, várias técnicas de Monitoramento da Integridade Estrutural (SHM) foram propostas e desenvolvidas para diversas áreas. Uma técnica para detectar corrosão pode ser o uso de ondas guiadas. Considerando uma onda propaganda em uma estrutura e se chocando a uma descontinuidade (dano), esta onda irá interagir com esta descontinuidade e será transformada (parte é refletida e parte transmitida). Assim, o movimento de ondas em estruturas pode ser uma maneira poderosa de indicar a presença de dano em estruturas. Este trabalho tem como objetivo investigar a propagação de ondas em uma viga de Euler-Bernoulli e a forma como estas ondas interagem com danos simulados de corrosão (simétricos e assimétricos). Os estudos mostram a importância de conhecer o comportamento das ondas antes de escolher as freqüências principais a serem usadas em um sistema SHM. Elementos piezelétricos são usados para gerar sensoriar as ondas. O comportamento dos sistemas estudados é amplamente discutido nos domínios de frequência e tempo. Para detectar e quantificar os danos, as ondas refletidas apresentaram melhor sensibilidade e proporcionalidade com a severidade do dano para todas as configurações estudadas. As ondas longitudinais incidentes no dano são mais recomendadas pelo sistema SHM por apresentarem maior simplicidade em relação... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor

Le contrôle des vibrations à basse fréquence adapté aux structures légères est un défi scientifique ettechnologique en raison de contraintes économiques et écologiques de plus en plus strictes. De récentes études enacoustique ont portées sur l’absorption totale d’ondes basses fréquences à l’aide d’absorbeurs parfaits sublongueursd’onde. Ces métamatériaux sont obtenus en exploitant la condition de couplage critique. Unegénéralisation de cette méthode pour le domaine élastodynamique serait d’un grand intérêt pour répondre auxexigences du contrôle des vibrations de structures légères à basse fréquence.Cette thèse vise à adapter le problème d’absorption parfaite des ondes de flexion dans des systèmes 1D et 2D avecdes résonateurs locaux en utilisant la condition de couplage critique. Une étude préliminaire sur des systèmes 1D àgéométries simples sont d’abord proposée. Celle-ci propose une méthode de conception de résonateurs simplespour une absorption efficace des ondes de flexion. Une complexification du système 1D est ensuite considérée avecl’étude du couplage critique de Trou Noir Acoustique (TNA) 1D. Ceci a motivé l’interprétation de l’effet TNA à l’aidedu concept de couplage critique afin de présenter des outils clés à de futures procédures d’optimisation pour ce typede terminaisons. La condition de couplage critique est ensuite étendue aux systèmes 2D. L’absorption parfaite parle premier mode axisymétrique d’un résonateur circulaire inséré dans une plaque mince infinie est analysée. Ladiffusion multiple par une ligne de résonateurs circulaires insérés dans une plaque mince 2D infinie ou semi-infinie,appelée métaplaque, est aussi considérée dans l’optique de se rapprocher d’une application industrielle. A traverscette thèse, des modèles analytiques, des simulations numériques et des expériences sont présentés pour valider lecomportement physique des systèmes présentés. / The vibration control adapted to light structures is a scientific and technological challenge due toincreasingly stringent economic and ecological standards. Meanwhile, recent studies in audible acoustics havefocused on broadband wave absorption at low frequencies by means of subwavelength perfect absorbers. Suchmetamaterials can totally absorb the energy of an incident wave. The generalisation of this method for applicationsin elastodynamics could be of great interest for the vibration control of light structures.This thesis aims at adapting the perfect absorption problem for flexural waves in 1D and 2D systems with localresonators using the critical coupling condition. A study of 1D systems with simple geometries is first proposed. Thisprovides methods to design simple resonators for an effective absorption of flexural waves. The 1D systems thenbecome more complex by studying the critical coupling of 1D Acoustic Black Holes (ABH). The ABH effect is theninterpreted using the concept of critical coupling, and key features for future optimisation procedures of ABHs arepresented. The critical coupling condition is then extended to 2D systems. The perfect absorption by the firstaxisymmetric mode of a circular resonator inserted in a thin plate is analysed. Multiple scattering by an array ofcircular resonators inserted in an infinite or semi-infinite 2D thin plate, called metaplate, is also considered to getclose to practical applications. Through this thesis, analytical models, numerical simulations and experiments areshown to validate the physical behaviour of the systems presented.

La sensibilité des méthodes acoustiques non-linéaires à la présence ainsi qu’à l’évolution des microendommagements a été prouvée dans différents travaux sur une large gamme de matériaux. Parmi les méthodes appliquées figure la résonance non-linéaire dont la sensibilité à l’endommagement est prouvée pour un seul mode de vibration à travers la décroissance de la fréquence de résonance ƒ et celle facteur de qualité Q en fonction de la déformation dynamique. Ainsi, les paramètres non-linéaires hystérétiques (NLH) ƒ et Q ne sont connus que dans une gamme fréquentielle réduite. Le présent travail de thèse propose l’utilisation d’une approche originale permettant de suivre la dispersion des paramètres ƒ et Q à travers la génération d’ondes guidées dans des plaques en composites à matrices polymère et métallique. De plus, l’approche en ondes guidées a également permis de définir un nouveau paramètre NLH V liée au mode de Lamb A0. L’un des résultats originaux de ce travail est que le rapport V/ƒ s’avère constant (~ 2) quelle que soit la fréquence considérée et ce pour les deux types de composites. Ce résultat prometteur montre pour la première fois qu’il est possible de généraliser le comportement NLH dans les structures en plaques moyennant le formalisme de Lamb. Finalement, le travail de thèse s’est également intéressé à la définition d’un nouveau paramètre NLH large bande, noté ∆S, afin de suivre la sensibilité du spectre de vibration à l’endommagement. Les mesures ont montré que ∆S pouvait se distinguer de par une réponse pouvant être nonlinéaire dès les premiers niveaux d’excitation ou à partir d’un niveau seuil. Ce résultat très prometteur montre à quel point il est important d’élargir le domaine fréquentiel pour une détection précoce de l’endommagement et ce même à des niveaux d’excitation où l’on croyait le matériau se comporter de façon linéaire. / Sensitivity of non-linear acoustics techniques to the presence and evolution of micro-damage has been proven on a large scale of materials. In particular, different works showed the use of the nonlinear resonance as a reliable method to characterise damage in heterogeneous materials through the drop of the resonance frequency ƒ and the quality factor Q as a function of the dynamic strain. Therefore, nonlinear hysteretic parameters (NLH) ƒ and Q have only been determined in a narrow frequency band. The present work develops an original approach, which allows to follow the frequency dispersion of ƒ and Q by using guided waves propagating in polymer and metal based composite plates. Furthermore, the guided wave approach made possible the definition of a new NLH parameter V through the A0 Lamb mode. One of the original results is that the ratio V/ƒ remains constant for both materials (~2) despite the considered frequency. This encouraging result allows for the first time to show that it is possible to generalise the NLH behaviour in the case of a plate-like structures using the Lamb formalism. Finally, this present PhD thesis defines a new large frequency band NLH parameter ∆S in order to follow the sensitivity of the vibration spectrum to the present damage. The performed experiments have shown that ∆S can be nonlinear either at the very first excitation levels or at a given threshold. This encouraging experimental result shows that there is a real interest in broadening the frequency domain in order to better understand the changes that occur in heterogeneous materials when the dynamic strain is increased.