Acoustic metamaterials are sub-wavelength structures designed to overcome limitations in the material properties of conventional materials. The present research focuses on the nonlinear acoustic and dynamic response of a specific type of engineered microstructure called a snapping acoustic metamaterial (SAMM). Snapping of these elements is defined as large, rapid deformations induced by infinitesimal perturbations in the time-varying external pressure. Snapping behavior in SAMM elements results from their non-monotonic stress-strain response, which displays regimes of positive and negative stiffness. This work presents a modeling study of the nonlinear behavior of both individual SAMM elements and a heterogeneous material containing a dilute concentration of SAMM elements embedded in a nearly incompressible viscoelastic solid. Two different scenarios are considered: (i) nonlinear wave propagation in the heterogeneous medium, and (ii) forced nonlinear dynamics of inclusions embedded in a viscoelastic medium. The nonlinearity of the SAMM elements is represented by a cubic pressure-volumetric strain relationship based on finite element model results from previous work. The effective nonlinear response of a heterogeneous mixture of SAMM elements embedded in a matrix, characterized by the parameters B/A and C/A, is then determined using both a nonlinear mixture law and a nonlinear Hashin-Shtrikman approach. The former estimate is limited to matrix materials with zero shear modulus, which cannot stabilize SAMM inclusions in regimes of negative stiffness. The augmented Hashin-Shtrikman method, however, includes nonlinear elasticity and the shear modulus of the matrix material. It therefore provides accurate estimates of the homogenized material when SAMM elements display negative stiffness and enhanced acoustical nonlinearity. The distortion of an acoustic wave propagating through the effective medium is studied through numerical solution of a nonlinear evolution equation that includes both quadratic and cubic nonlinearity. Finally, the forced nonlinear dynamic response of both a single SAMM element in a matrix and a domain of effective medium material embedded in matrix is considered. This behavior is of interest for generating enhanced absorption of acoustic wave energy because snapping leads to large hysteresis in the stress-strain response. A generalized Rayleigh-Plesset analysis is adapted to model the large-deformation dynamics associated with the system. / text

<p>Acoustic metamaterials are engineered materials that were extensively investigated over the last years mainly because they promise properties otherwise hard or impossible to find in nature. Consequently, they open the door for improved or completely new applications (e.g. acoustic superlens that can exceed the diffraction limit in imaging or acoustic absorbing panels with higher transmission loss and smaller thickness than regular absorbers). Our objective is to surpass the limited frequency</p><p>operating range imposed by the resonant mechanism that s1ome of these materials have. In addition, we want acoustic metamaterials that could be experimentally demonstrated and used to build devices with overall performances better than the previous ones reported in the literature.</p><p>Here, we start by focusing on the need of engineered metamaterials in general and acoustic metamaterials in particular. Also, the similarities between electromagnetic metamaterials and acoustic metamaterials and possible ways to realize broadband acoustic metamaterials are briefly discussed. Then, we present the experimental realization</p><p>and characterization of a two-dimensional (2D) broadband acoustic metamaterial with strongly anisotropic effective mass density. We use this metamaterial to realize a 2D broadband gradient index acoustic lens in air. Furthermore, we optimize the lens design by improving each unit cell's performance and we also realize a 2D acoustic ground cloak in air. In addition, we explore the performance of some novel applications (a 2D acoustic black hole and a three-dimensional acoustic cloak) using the currently available acoustic metamaterials. In order to overcome the limitations of our designs, we approach the active acoustic metamaterials path, which offers a broader range for the material parameters values and a better control over them. We propose two structures which contain a sensing element (microphone) and an acoustic driver (piezoelectric membrane or speaker). The material properties are controlled by tuning the response of the unit cell to the incident wave. Several samples with interesting effective mass density and bulk modulus are presented. We conclude by suggesting few natural directions that could be followed for the future research based on the theoretical and experimental results presented in this work.</p> / Dissertation

Acoustic-structural interaction is the key to understand a wide range of engineering problems such as membrane-based dynamic pressure sensors, hearing devices for sound source localization, and acoustic absorbers for noise reduction. Despite tremendous developments in the last decades, there is still a fundamental size limitation in these areas. In the case of dynamic pressure sensors, sensitivity usually suffers for miniature sensors; the available acoustic directional cues proportionally decrease with size, which adversely affects the localization performance; thick panels are required to achieve superior sound attenuation, particularly for low-frequency sound. It is the motivation of this dissertation research to address the abovementioned size limitation that involves acoustic-structural interaction. The overall goal of this dissertation work is to achieve an enhanced understanding of the acoustic-structural interaction between diaphragms and air cavity and to apply this understanding to develop high-performance miniature acoustic sensors and noise reduction metamaterials. First, a finite element method (FEM) model and large-scale device are developed to understand how the interaction between the diaphragm and its backing air cavity affects the equivalent mass, stiffness, and damping of air-backed diaphragms. The numerical and experimental study shows that the complex interaction cannot be captured by the commonly used lump model. Then, air-backed graphene diaphragms are used to develop fiber optic sensors with sub-millimeters footprint and high sensitivity. Two different configurations are designed to enhance the sensor sensitivity limited by the backing air cavity. One is to increase the mechanical sensitivity by using a larger backing volume, the other is to increase the optical sensitivity by using silver-graphene composite diaphragm. Next, acoustic metamaterials with air-coupled diaphragms as unit cells are developed to achieve perfect acoustic absorption with thickness much smaller than the sound wavelength, which cannot be realized using natural materials. Finally, an expanded configuration of two diaphragms coupled by an air-filled tunnel is experimentally developed to mimic the hearing system of small vertebrates. The goal is to amplify the small directional cues available to the small animals so that a high angular resolution can be achieved. This dissertation provides a quantitative and mechanistic explanation for the interaction between the diaphragms and the sealed air cavity. It offers several frameworks for the development of miniature pressures, directional sensors, and thin sound absorbers. / Mechanical Engineering

Acoustic metamaterials have been shown to support acoustic surface waves when excited by a broadband signal in a quiescent environment and these waves could be manipulated by varying the geometry of the structure making up the metamaterial. The study presented here demonstrates the generation of trapped acoustic surface waves when excited by a turbulent flow source. The metamaterial and flow were interfaced using a Kevlar covered single cavity whose Kevlar side faced the flow to ensure no significant disturbance to the flow and the other side was open to a quiescent (stationary) environment housing the metamaterial. Acoustic measurements were performed very close to the surface of the metamaterial in the Anechoic Wall Jet Facility at Virginia Tech using two probe-tip microphones and correlation analysis yielded the structure of the surface waves. Two different metamaterials; slotted array and meander array were tested and characterized by their dispersion relations, temporal correlations, and spatial-temporal structure. The measurements proved the existence of surface waves with propagating speeds of a tenth of the speed of sound, when excited by a turbulent boundary layer flow. These waves were much weaker than the overlying flow exciting them but showcased excellent attenuation properties away from the source of excitation. Measurements along the length of the unit-cell geometry of the metamaterial demonstrated high coherence over a range of frequencies limited by the dimension of the cell. This was a surprising behavior provided the cavity was excited by a fully developed turbulent flow over a flat plate and indicated to an area averaging phenomenon. A wall normal two-dimensional particle image velocimetry (2D-PIV) measurement was performed over the Kevlar covered cavity and a smooth surface to study the effects of the cavity on the flow. The field of view was the same for both cases which made direct flow comparison possible. Flow characteristics such as the boundary layer profiles, Reynolds stress profiles and fluctuating velocity spectrum were studied over the cavity and at downstream locations to quantify the differences in the flows. The boundary layer profiles collapsed in the inner region of the boundary layer but there were small differences in the outer region. The Reynolds stress profiles were also very similar with differences within the uncertainties of processing the images and it reflected similar average behavior of the flow over a smooth wall and a Kevlar covered cavity. The fluctuating velocity spectrum studied over the cavity location showed some differences at low frequencies for all wall normal locations while at higher frequencies the differences were within ±3 dB. These measurements showcased the underlying physics behind the interaction of acoustic metamaterials and turbulent boundary layer flows creating possibilities of using these devices for flow control although further analysis/optimization is needed to fully understand the capabilities of these systems. The demonstration of no significant effect on flow by the Kevlar covered cavity stimulated development of sensors which can average over a region of the wall pressure spectrum. / M.S. / In the field of physics, acoustic metamaterials have gained popularity due to their ability to exhibit certain properties such as sound manipulation which cannot be seen in regular materials. These materials have a key feature which is the periodic arrangement of geometric elements in any dimension. These materials can support a phenomenon termed as acoustic surface waves which are essentially pressure disturbances in the medium which behave differently than some known phenomenon such as sound waves when excited by a broadband pressure signal in a stationary medium. Also, it has been shown that these materials can change the nature of the acoustic surface waves if their geometry is changed. Here a successful attempt has been made to link two different fields in physics: acoustic metamaterials (acoustics) and turbulent flows (fluid dynamics). The study here uses turbulent boundary layer flows to excite these metamaterials to show the existence of acoustic surface waves. This is done by creating an interface between the flow and the metamaterial using a Kevlar covered through cavity which is essentially a through hole connecting to different sides: flow side and the stationary air/quiescent side. This cavity acted as the source of excitation for the metamaterial. The Kevlar covering ensures that the flow does not get disturbed due to the cavity which was also proved in this study using a visualization technique: Particle Image Velocity (PIV). Two microphones were used to study the pressure field very close to two metamaterials; one was referred to as the slotted array comprised of slot cavities arranged in one dimension (along the direction of the flow), while the other was termed as the meander array and it comprised of a meandering channel. The pressure field was well characterized for both the acoustic metamaterials and it was proved that these metamaterials could support acoustic surface waves even when excited by a turbulent flow. The idea here was to fundamentally understand the interaction of acoustic metamaterials and turbulent flows, possibly finding use in applications such as trailing edge noise reduction. The use of these metamaterials in direct applications needs further investigation. A finding from the pressure field study showed that the pressure measured along the length of the Kevlar covered cavity was uniform. The flow visualization study looked at the turbulent flow on a smooth wall and over a Kevlar covered cavity. This was done by injecting tiny particles in air and shooting a laser sheet over these to illuminate the flow. Images were recorded using a high-speed camera to track the movement of these particles. It was found that the flow was unaffected with or without the presence of a Kevlar covered cavity. This result coupled with the pressure field uniformity could have some wide applications in the field of pressure sensing.

Cette thèse porte sur la propagation d’ondes non-linéaires dans des métamatériaux acoustiques unidimensionnels. Plus précisément, nous voulons étudier les interactions entre les non-linéarités, les pertes et la dispersion. Ce travail combine des calculs analytiques, des simulations numériques et des résultats expérimentaux. En particulier, nous concentrons notre analyses sur deux phénomènes : la génération du second harmonique et la formation de solitons acoustiques. Deux types différents de métamatériaux sont étudiés : (i) un guide d’onde chargé par une distribution périodique de trous latéraux (milieu à densité effective négative) et (ii) un guide d’onde chargé périodiquement par des  plaques élastiques encastrées (milieu à masse effective négative). En s’appuyant sur une analogie électroacoustique et sur la théorie des lignes de transmission, un modèle discret de la propagation est développé pour chaque système. L’approximation des grandes longueurs d’ondes est ensuite utilisée pour obtenir une modèle continu permettant d’établir une équation non-linéaire, dispersive et dissipative pour la propagation. Cette dernière est analysée à l’aide de la méthode des perturbations conduisant à une expression analytique pour la génération du second harmonique. De plus, la méthode des échelles multiples est utilisée pour obtenir les diverses solutions de solitons d’enveloppe (bright, dark et gray) présents dans les systèmes. Les prédictions analytiques sont corroborées par des simulations numériques directes et des mesures de la génération de second harmonique sont effectuées mettant en lumière un bon accord avec le modèle théorique. / The subject of this PhD thesis is the propagation of nonlinear waves in 1D acoustic metamaterials. More specifically we aim to study the interplay between nonlinearity, loss and dispersion. Our studies combine analytical calculations, numerical simulations and experimental results. In particular we focus our analysis on two main phenomena: the second harmonic generation and the formation of solitary waves. Two different acoustic metamaterials are studied: (i) A waveguide loaded with a periodic distribution of side holes (featuring negative effective bulk modulus) and (ii) a waveguide periodically loaded with clamped elastic plates (featuring negative effective mass density). Relying on the electroacoustic analogy and the transmission line approach, we derive a discrete lattice model for each system. The corresponding long wavelength, continuum approximation of the lattice models, leads to a nonlinear, dispersive and dissipative wave equation. From the latter, by utilising a perturbation method, we obtain analytical results regarding the second harmonic generation. Furthermore with the use of a multiple scale analysis we find various envelope (bright, gap, black and gray) soliton solutions supported by the acoustic metamaterial. The analytical predictions are corroborated by direct numerical simulations. We finally perform experiments on an acoustic waveguide loaded with a periodic distribution of side holes and measure the second harmonic generation in close agreement with our theoretical predictions.

Les matériaux acoustiques super absorbants, sub-longueur d’ondes et large bande, ouvrent de nouvelles perspectives prometteuses pour l’isolation sonore. Dans ce contexte, nous avons conçu et synthétisé des structures hétérogènes comportant des microbilles sphériques de silicone poreux « ultra-lentes », distribuées dans des matrices aqueuses ou élastomériques. Dans un premier temps, nous avons démontré pourquoi la vitesse du son est aussi basse dans les silicones poreux (<100 m/s) comparativement à celle de milieux homogènes (~1000 m/s). Ce fort contraste de propriétés acoustiques entre phases étant susceptible d’induire des propriétés extrêmement diffusantes des microbilles, nous avons étudié l’impact de la nature de la matrice et de l’arrangement (aléatoire ou périodique) des microbilles sur les propriétés acoustiques d’échantillons se présentant sous forme de plaques sub-longueurs d’ondes à faces parallèles. Nous avons montré que la présence de minima prononcés dans le coefficient de transmission de ces métaplaques était pilotée par la résonance monopolaire des microbilles, et était fortement conditionnée par la nature de la matrice environnante. Enfin, toutes les mesures ultrasonores de l’étude ont été confrontées avec succès à des prédictions issues de modèles de diffusion multiple. / Acoustic metamaterials may behave like sub-wavelength and broadband sound-absorbers, opening thus new promising routes for sound insulation. In this context, we have designed and achieved heterogeneous structures composed of soft porous silicone rubber microbeads with ultra-low sound speeds, dispersed in various aqueous or elastomeric matrices. First, we show why the sound speed is so low in soft porous silicone rubber materials (<100m/s) in comparison with soft homogeneous materials (~1000m/s). Such a large sound-speed contrast resulting in strongly scattering properties of the microbeads, we have studied the influence of the matrix characteristics as well as the arrangement of microbeads (random or ordered) on the acoustic properties of the samples in form of sub-wavelength slabs. We have evidenced deep and wide minima of acoustic transmission due to the strong monopolar resonances of the microbeads, which strongly depend on the properties of the surrounding matrix. All our ultrasonic measurements have been compared with theoretical predictions based on various Multiple Scattering Theories, revealing an excellent quantitative agreement.

No description available.

Phased microphone arrays are valuable tools for aeroacoustic measurements that can measure the directivity of multiple acoustic sources. However, when deployed in closed test-section wind tunnels, the acoustics suffer due to intense pressure fluctuations contained in the wall-bound turbulent boundary layer. Furthermore, phased microphone arrays require many sensors distributed over a large aperture to ensure good spatial resolution over a wide frequency range. Microphone arrays of such large count are not always feasible due to constraints in space and cost. This thesis describes an alternative approach for measuring single broadband acoustic sources that uses an acoustic metasurface. The metasurface is comprised of a meandering channel of quarter-wave cavities and an array of equally spaced half-wave open through-cavities. A series of tests were conducted in Virginia Tech's Anechoic Wall-Jet Tunnel where combinations of a wall-bound turbulent jet-flow and a single broadband acoustic source were used to excite the metasurface and produce acoustic surface waves. Measurements of the acoustic surface waves were performed using two methods: a pair of traversing microphones scanning the pressure field along the length of the metasurface 0.25 mm beneath its bottom face, and an array of unequally spaced microphones embedded inside the metasurface. Spectral analysis on the measurements revealed that the inclusion of multiple through-cavities leads to constructive reinforcement of select acoustic surface waves as a function of the acoustic source location. In the case of the embedded microphones, acoustic beamforming was applied in order to extract spatial information. This reinforcement was observed during measurements made with both flow and acoustic excitation, up to Wall-Jet Tunnel nozzle exit speeds of 40 m/s beyond which it was no longer seen. A series of quiescent measurements made with a range of speaker locations constituted a calibration for the metasurface which was used to locate an unknown broadband acoustic source within an The Root-Mean-Square (RMS) error of 1.06 degrees. / Master of Science / Phased microphone arrays are valuable tools for aeroacoustic measurements that can measure the directivity of multiple acoustic sources within a sound field. When used in conjunction with signal processing techniques, such as delay-and-sum beamforming, a researcher or engineer can obtain an intuitive view of the sound field and distinguish between multiple sources over a wide frequency range. However, these microphone arrays often utilize dozens of microphones which raises the array's complexity and cost. Furthermore, when a phased microphone array is mounted flush to the wall of a wind tunnel test section, it is submerged under a turbulent boundary layer which imposes intense pressure fluctuations on the microphones making it difficult to identify acoustic sources. Boundary layers form at the interface between a fluid and solid interface. This thesis describes experimentation performed in the Virginia Tech Anechoic Wall-Jet Tunnel on a new type of pressure sensing microphone array that leverage acoustic metamaterial technology. The acoustic metamaterial shields the microphones from the flow, lessening the influence of the turbulent boundary layer on the measurement. The focus in this thesis is on the novel array's ability to locate a single broadband acoustic source using as few as six microphones. The metasurface was installed in the Wall-Jet Tunnel test plate such that an array of evenly spaced through-cavities are flush to the surface. The through-cavities communicate the pressure field on top of the test surface to a meandering channel of interconnected closed cavities below. Near the resonant depth frequencies of the closed cavities, acoustic surface waves form which are evanescent pressure waves that are bound to the surface or structure that support them. The interference between the acoustic surface waves generated at each through-cavity leads to reinforced acoustic surface waves which are sensitive to the direction of a broadband source. In all, an acoustic metamaterial was tested under a variety of conditions such as: Wall-Jet Tunnel flow speed, speaker location, and the number of through-cavities open. The performance of the novel array and future plans are discussed.

Le domaine des métamatériaux acoustiques connaît un succès grandissant depuis maintenant une vingtaine d’années, notamment en raison de phénomènes exotiques aux perspectives d’applications plus que prometteuses : « l’invisibilité » acoustique en est l’exemple le plus manifeste. Dans cette thèse, nous présentons des métamatériaux acoustiques à résonances locales, et qui permettent de générer aussi bien de l’opacité que de la transparence acoustique. C’est plus particulièrement le couplage entre résonateurs de différentes formes qui est l’objet de nos investigations. Notre étude nous a permis de comprendre que la diffraction est l’une des principales limitation à l’omnidirectionalité des performances d’opacité, que nous avons caractérisé au moyen d’un banc ultrasonore motorisé. Un tel phénomène de diffraction est dû à la présence d’un réseau, et nous proposons dans notre étude des solutions qui permettent de dépasser cette limitation. A partir de cette étude, nous avons ainsi pu transposer au domaine sonore les résultats obtenus pour les ultrasons, ce qui nous a permis de réaliser deux principaux types de dispositifs : des métamatériaux acoustiques aux fonctions de réflecteur d’une part et d’absorbant basses fréquences d’autre part. Enfin, l’étude en homogénéisation de ce type de structure a aussi révélé un effet de densité effective quasi-nulle, dont les applications vont du contrôle de front d’onde, à la furtivité acoustique. De tels résultats offrent un potentiel d’application dans de nombreux champs, que ce soit pour le bâtiment ,l’automobile, l’aéronautique, ou l’acoustique sous-marine. / For more than twenty years now, Acoustic Metamaterials are experiencing a growing success, partlydue to exotic phenomena and their wide variety of extremely promising applications: “InvisibilityCloak” is the most vivid example of this. In this thesis, we report on designs of locally resonantacoustic metamaterials, that enable us to generate both sound opacity and transparency. It is moreparticularly coupling between resonators having different forms which is the focus of our work.This study permit us to understand that diffraction is one of the main limitation of omnidirectionalcapabilities involving locally resonant perforated plates, as supported by experimental investigationsrealized using a motorized ultrasonic set-up. We proposed solutions to overcome such a limitation,in the case where the opacity mechanism uses diffraction gratings. From this, we transposed theresults obtained in ultrasonic frequencies to the audible range, which permits us to develop twomain kinds of acoustic devices based on metamaterials: broadband reflectors and low-frequencyabsorbers. Finally, homogenization study of such structures revealed an effect of density near-zero,with applications from shaping wave front, to acoustic furtiveness. Such results paves the way forpromising applications in various field, including construction, automotive and aeronautical industries,submarine acoustics and so on.