The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general theory. Using a modified piston-tube apparatus, agreement between predicted and observed limit-cycle amplitudes is observed to be on the order of 1%.

Higher-order spectral analysis of acoustical waveforms can provide phase information that is not retained in calculations of power spectral density. In the propagation of high intensity sound, nonlinearity can cause substantial changes in the waveform as frequency components interact with one another. The bispectrum, which is one order higher than power spectral density, may provide a useful measure of nonlinearity in propagation by highlighting spectral regions of interaction. This thesis provides a review of the bispectrum, places it in the context of nonlinear acoustic propagation, and presents spectra calculated as a function of distance for numerically propagated acoustic waveforms. The calculated spectra include power spectral density, quad-spectral density, bispectrum, spatial derivative of the bispectrum, bicoherence, and skewness function. / text

The objective of this research is to presents new acoustic echo cancellation design methods that can effectively work in the nonlinear environment. Acoustic echo is an annoying issue for voice communication systems. Because of room acoustics and delay in the transmission path, echoes affect the sound quality and may hamper communications. Acoustic echo cancellers (AECs) are employed to remove the acoustic echo while keeping full-duplex communications. AEC designs face a variety of challenges, including long room impulse response, acoustic path nonlinearity, ambient noise, and double-talk situation. We investigate two parts of echo canceller design: echo cancellation algorithm design and control logic algorithm design. In the first part, our work focuses on the nonlinear adaptive and fast-convergence algorithms. We investigate three different structures: predistortion linearization, cascade structure, and nonlinear residual echo suppressor. Specifically, we are interested in the coherence function, since it provides a means for quantifying linear association between two stationary random processes. By using the coherence as a criterion to design the nonlinear echo canceller in the system, our method guarantees the algorithm stability and leads to a faster convergence rate. In the second part, our work focuses on the robustness of AECs in the presence of interference. With regard to the near-end speech, we investigate the double-talk detector (DTD) design in conjunction with nonlinear AECs. Specifically, we propose to design a DTD based on the mutual information (MI). We show that the advantage of the MI-based method, when compared with the existing methods, is that it is applicable to both the linear and nonlinear scenarios. With respect to the background noise, we propose a variable step-size and variable tap-length least mean square (LMS) algorithm. Based on the fact that the room impulse response usually exhibits an exponential decay power profile in acoustic echo cancellation applications, the proposed method finds optimal step size and tap length at each iteration. Thus, it achieves faster convergence rate and better steady-state performance. We show a number of experimental results to illustrate the performance of the proposed algorithms.

En phase d’approche, le bruit rayonné par l’entrée d’air des turboréacteurs est principalement dû aux interactions entre le rotor et le stator. Cependant les ondes de choc (ou ondes en N) générées par le rotor en régime transsonique peuvent devenir une source de bruit dominante durant le décollage et la montée de l’appareil. L’étude des ondes en N nécessite de se concentrer sur deux processus majeurs : 1) la génération des chocs par un rotor parfait (dont toutes les aubes sont identiques) et par un rotor réel (en tenant compte des irrégularités géométriques des aubes), et 2) la propagation de ces ondes en N à travers la nacelle, produisant du bruit dont le spectre se compose des harmoniques de la fréquence de passage des aubes pour un rotor régulier, et des harmoniques aux fréquences multiples de la rotation du rotor (FMR) pour un rotor irrégulier. Plusieurs approches analytiques et numériques ont été développées durant les 40 dernières années.Cette thèse relate dans un tout premier temps les principales théories de la propagation des ondes de choc ainsi que les modèles majeurs de génération de FMR. Une attention particulière est portée sur les liens entre les équations générales de la mécanique des fluides et ces modèles de propagation non linéaire afin de mettre en évidence les différentes hypothèses formulées dans ces modèles. Dans un deuxième temps, les principales méthodes semi-analytiques de génération et de propagation des chocs seront évaluées et comparées en les appliquant à des configurations de turboréacteurs. En outre, un nouveau modèle de génération de FMR basé sur des considérations géométriques est élaboré par l’intermédiaire d’une campagne d’essais comportant d’une part des mesures de signaux de pression dans la nacelle et d’autre part les mesures des angles de calage des aubes pendant le fonctionnement du moteur. Le deuxième volet de la thèse concerne le développement d’une méthodologie de simulation numérique basée sur l’utilisation du code elsA de l’ONERA en résolvant les équations d’Euler (approche CAA). L’objectif de cette approche est de s’affranchir des limitations des modèles de propagation semi-analytiques et de tenir compte de la géométrie réelle de la nacelle ainsi que d’un écoulement réaliste. Des ondes de choc régulières et irrégulières sont directement injectées dans un plan proche de la soufflante et se propagent en remontant l’écoulement. Ces ondes de choc sont injectées par l’intermédiaire d’une condition limite de non-réflexion qui nécessite d’imposer le champ conservatif. La signature des chocs peut provenir d’un RANS, de mesures ou d’un signal analytique. Étant donné que les mesures ou le signal théorique ne permettent d’obtenir que la pression, une méthode de reconstruction du champ conservatif à partir des variations de pression induites par le choc a été élaborée. Cette méthode d’injection est tout d’abord appliquée à un conduit annulaire infiniment mince et validée par la méthode de propagation semi-analytique de McAlpine & Fisher. Ensuite, les effets de propagation 3D sont étudiés en augmentant l’épaisseur du conduit. Enfin, la méthode CAA est appliquée à des configurations de turboréacteurs modernes et des ondes de choc régulières et irrégulières sont propagées numériquement. Les résultats sont comparés aux solutions RANS ainsi qu’aux mesures disponibles. / Whereas the sound radiated from the inlet of turbofans is mainly due to rotor–stator interactions in approach flight, the shock waves (or N-waves) emitted by the rotor at transonic rotation speeds can be a dominant noise source during takeoff and climb. The study of N-waves needs to take account of two main processes: 1) the generation of N-waves for a perfect rotor (in which all blades are identical) and for a real rotor (considering small geometrical blade dispersion), and 2) the N-wave propagation through the inlet duct producing the blade passing harmonics for a perfect rotor, and the multiple pure tones (harmonics of the rotation frequency) for a real rotor. Several analytical and numerical approaches have been investigated for the past 40 years.This thesis first intends to relate the main propagation theories and to address the foremost MPT generation method hypotheses. The links between fluid dynamics equations and practical non-linear theories currently adopted are emphasized and discussed. In a second step, the main relevant semi-analytical methods are cross-checked by applying them to representative turbofan configurations. Moreover, a novel model of irregular N-wave generation based on geometrical considerations is investigated thanks to test data related to in-duct pressure signatures and blade stagger angle measurements during the engine operation. Then, a second part of the work investigates a numerical strategy based on elsA ONERA code, solving the full Euler’s equations (CAA approach). The objective is to prevent from the limitations of 2D analytical models and to take into account actual inlet geometry and realistic convection flow. Regular and non-regular shock waves are directly injected in a plane close to the fan and propagated through the inlet. These shock waves are injected through a non-reflective boundary condition which requires the conservative field. The initial shock description near the fan is provided either by a RANS computation or by experiment, or else from analytical model. As experiment or analytical signals only provide pressure signatures, a theory is set up to re-built the whole conservative field from the basis of a pressure shockwave. This injection method is firstly applied on an infinitely narrow annular duct and validated through the comparison with the McAlpine & Fisher analytical method. Then, the 3D propagation effects are pointed out by increasing the duct height. Finally, the CAA method is applied on actual intake geometry of modern turbofan demonstrators, and propagation of regular and irregular shock-waves are simulated. The numerical results are compared to RANS solutions and to available measurements.

Les effets non-linéaires produits par l'interaction entre une onde et une fissure fermée peuvent être un moyen potentiel pour la détection de ces fissures. Ce travail porte sur l'étude et l'analyse de la non-linéarité de contact générée par la propagation d'une onde à travers une fissure fermée. Notre approche repose sur la modélisation numérique par Eléments finis (EF) dont la résolution est effectuée dans le domaine temporel. La fissure est modélisée par une loi de contact unilatéral avec frottement de Coulomb. L'outil numérique mis en place est utilisé pour l'analyse de la méthode de génération d'harmoniques et sa relation avec la dynamique de contact. Le cas d'une interface de contact entre deux solides a permis d'estimer l'influence de l'état de contrainte sur le comportement non-linéaire, et a fait l'objet d'une validation expérimentale. La diffusion non-linéaire d'une fissure fermée orientée est ensuite obtenue en couplant la solution numérique à une méthode semi-analytique afin d'obtenir les diagrammes de directivité. Les mécanismes impliqués dans l'interaction onde - fissure sont mis en évidence. Ces résultats nous permettent ensuite d'appliquer la méthode du mixage d'ondes non-colinéaire, d'abord sur une interface de contact puis sur une fissure fermée. L'étude numérique et les premiers résultats expérimentaux démontrent le potentiel de la méthode en terme de détection, de caractérisation et d'imagerie. / The nonlinear effects produced by the interaction between a closed crack and an ultrasonic wave can be a good mean for the detection or thecharacterization of such cracks. This work is dedicated to the study and the analysis of the contact acoustic nonlinearity involved during the interaction of acoustic waves and closed cracks. Our approach is based on Finite Element (FE) modeling. The crack is modeled by unilateral contact with Coulomb's friction law, and numerical solutions are computed in the time domain. The numerical tool is used to analyze the method of higher harmonic generation and its relation with contact dynamics. First, the case of an interface between two solids in contact is considered, both numerically and experimentally, and it was shown that the nonlinear behavior depend on the state of stress. Then, nonlinear elastic scattering by a closed crack of various orientations was calculated. A hybrid model coupling FE and semi-analytical solutions was set up to compute the scattered field and to plot directivity diagrams. The nonlinear mechanisms involved in the interaction between a wave and a closed crack are highlighted. Using those results, the non-collinear mixing technique was applied for measuring the nonlinear response of a contact interface and a closed crack. The numerical results, as well as the first experimental results, are very promising for detecting, locating and imaging closed cracks.

Polymer components are used in many different applications, including in industries where critical applications put high requirements regarding quality assessment. Such applications might include medical or food where the presence of discontinuities might induce bacterial growth or other unpleasantries, thus certain manufacturers must be able to maintain a zero-tolerance towards damaged components. This leads to the need for efficient testing methods of nondestructive nature capable of testing large quantities of components in a production line environment. The authors have been tasked by Acoustic Agree AB and Trelleborg AB, a world-leading producer of polymer engineered solutions, to find a nondestructive testing method capable of detecting discontinuities in thin polymer components in a production line environment. Implementation in production line environments puts requirements on test cycle time and a goal is to complete a test cycle within 3-4 seconds. Due to restrictions regarding available equipment and expertise, the focus has been put on applying nonlinear acoustic methods for nondestructive testing instead of more conventional methods. These methods utilize the nonlinear distortion of acoustic waves which causes certain characteristics to appear, such as the generation of Higher Harmonics (HH), frequency modulation (NWMS), resonance frequency shift (NRUS), and amplitude recovery (IDAR). Visual testing was used to discern visibly damaged samples from seemingly undamaged ones. The only methods which showed the possibility of discerning damaged thin polymer components were NRUS and IDAR. Only the latter has the capability to maintain the prescribed test cycle time. Nonlinear acoustic methods seem to be capable of detecting discontinuities in thin polymer components within the given time frame. More work is required to properly investigate the performance of NWMS and IDAR. The configuration used in this work was mainly focused on IDAR, resulting in specific calibration for NWMS was neglected. The sample population was also too low to collect sufficient data to ensure statistical certainty regarding the performance for either method. / Polymerkomponenter används i många olika tillämpningar, i synnerhet i industrier där kritiska tillämpningar ställer höga krav på kvalitetsbedömning. Sådana tillämpningar kan finnas inom medicinska- eller livsmedelsindustrier där förekomsten av diskontinuiteter kan inducera bakterietillväxt eller andra obehagliga egenskaper, därför måste vissa tillverkare upprätta nolltolerans mot skadade komponenter. Detta leder till behovet av effektiva provningsmetoder av oförstörande natur som kan utvärdera stora mängder komponenter i en produktionslinjemiljö. Författarna har fått uppdrag av Acoustic Agree AB och Trelleborg AB, en världsledande producent av polymertekniska lösningar, för att finna en oförstörande provningsmetod som kan detektera diskontinuiteter i tunna polymerkomponenter i en produktionslinjemiljö. Implementering i produktionslinjemiljöer ställer krav på testcykeltid och ett mål är att kunna slutföra en testcykel inom 3-4 sekunder. Begränsningen av tillgänglig utrustning och expertis har lett till att författarna har fokuserat på att tillämpa olinjära akustiska metoder för oförstörande provning istället för mer konventionella metoder. Dessa metoder utnyttjar olinjär distortion av akustiska vågor vilket medför att vissa egenskaper uppträder, såsom generering av övertoner (HH), frekvensmodulering (NWMS), resonansfrekvensskift (NRUS) och amplitudåtergång (IDAR). Visuell provning användes för att skildra synligt skadade prover från till synes oskadade. De enda metoder som visade möjligheten att urskilja skadade tunna polymerkomponenter var NRUS och IDAR. Endast den sistnämnda har förmågan att utföra provning inom den föreskrivna provcykeltiden. Olinjära akustiska metoder verkar kunna detektera diskontinuiteter i tunna polymerkomponenter inom den givna tidsramen. Mer arbete krävs för att korrekt utvärdera prestandan av NWMS och IDAR. Konfigurationen som användes i detta arbete var huvudsakligen inriktad på IDAR, vilket resulterade i att specifik kalibrering för NWMS ej utförts. Provpopulationen var även för låg för att kunna samla in tillräckligt med data för att uppnå statistisk säkerhet angående metodernas prestanda.

Ultrasound acoustic energy transfer (UAET) is an emerging contactless technology that offers the capability to safely and efficiently power sensors and devices while eliminating the need to replace batteries, which is of interest in many applications. It has been proposed to recharge and communicate with implanted medical devices, thereby eliminating the need for invasive and expensive surgery and also to charge sensors inside enclosed metal containers typically found in automobiles, nuclear power plants, space stations, and aircraft engines. In UAET, energy is transferred through the reception of acoustic waves by a piezoelectric receiver that converts the energy of acoustic waves to electrical voltage. It has been shown that UAET outperforms the conventional CET technologies that use electromagnetic waves to transfer energy, including inductive coupling and capacitative coupling. To date, the majority of research on UAET systems has been limited to modeling and proof-of-concept experiments, mostly in the linear regime, i.e., under small levels of acoustic pressure that result in small amplitude longitudinal vibrations and linearized piezoelectricity. Moreover, existing models are based on the "piston-like" deformation assumption of the transmitter and receiver, which is only accurate for thin disks and does not accurately account for radiation effects. The linear models neglect nonlinear effects associated with the nonlinear acoustic wave propagation as well as the receiver's electroelastic nonlinearities on the energy transfer characteristics, which become significant at high source strengths. In this dissertation, we present experimentally-validated analytical and numerical multiphysics modeling approaches aimed at filling a knowledge gap in terms of considering resonant acoustic-piezoelectric structure interactions and nonlinear effects associated with high excitation levels in UAET systems. In particular, we develop a reduced-order model that can accurately account for the radiation effects and validate it by performing experiments on four piezoelectric disks with different aspect ratios. Next, we study the role of individual sources of nonlinearity on the output power characteristics. First, we consider the effects of electroelastic nonlinearities. We show that these nonlinearities can shift the optimum load resistance when the acoustic medium is fluid. Next, we consider the nonlinear wave propagation and note that the shock formation is associated with the dissipation of energy, and as such, shock formation distance is an essential design parameter for high-intensity UAET systems. We then present an analytical approach capable of predicting the shock formation distance and validate it by comparing its prediction with finite element simulations and experimental results published in the literature. Finally, we experimentally investigate the effects of both the nonlinearity sources on the output power characteristics of the UAET system by considering a high intensity focused ultrasound source and a piezoelectric disk receiver. We determine that the system's efficiency decreases, and the maximum voltage output position drifts towards the source as the source strength is increased. / Doctor of Philosophy / Advancements in electronics that underpinned the development of low power sensors and devices have transformed many fields. For instance, it has led to the innovation of implanted medical devices (IMDs) such as pacemakers and neurostimulators that perform life-saving functions. They also find applications in condition monitoring and wireless sensing in nuclear power plants, space stations, automobiles and aircraft engines, where the sensors are enclosed within sealed metal containers, vacuum/pressure vessels or located in a position isolated from the operator by metal walls. In all these applications, it is desired to communicate with and recharge the sensors wirelessly. Such a mechanism can eliminate the need for invasive and expensive surgeries to replace batteries of IMDs and preserve the structural integrity of metal containers by eliminating the need for feed through wires. It has been shown that ultrasound acoustic energy transfer (UAET) outperforms conventional wireless power transfer techniques. However, existing models are based on several assumptions that limit their potential and do not account for effects that become dominant when a higher output power is desired. In this dissertation, we present experimentally validated numerical and theoretical investigations to fill those knowledge gaps. We also provide crucial design recommendations based on our findings for the efficient implementation of UAET technology.

Contactless ultrasonic power transfer (UPT), using piezoelectric transducers, is based on transferring energy using acoustic waves, in which the waves are generated by an acoustic source or transmitter and then transferred through an acoustic medium such as water or human tissue to a sensor or receiver. The receiver then converts the mechanical strain induced by the incident acoustic waves to electricity and delivers to an electrical load, in which the electrical power output of the system can be determined. The execution and efficiency of this technology can be significantly enhanced through patterning, focusing, and localization of the transmitted acoustic energy in space to simultaneously power pre-determined distributed sensors or devices. A passive 3D-printed acoustic hologram plate alongside a single transducer can generate arbitrary and pre-designed ultrasound fields in a particular distance from the hologram mounted on the transmitter, i.e., a target plane. This dissertation presents the use of these simple, cost-effective, and high-fidelity acoustic holograms in UPT systems to selectively enhance and pattern the electrical power output from the receivers. Different holograms are numerically designed to create single and multi-focal pressure patterns in a target plane where an array of receivers are placed. The incident sound wave from a transmitter, after passing through the hologram, is manipulated, hence, the output field is the desired pressure field, which excites the receivers located at the pre-determined focal points more significantly. Furthermore, multi-functional holograms are designed to generate multiple images at different target planes and driving frequencies, called, respectively, multi-image-plane and multi-frequency patterning holograms. The multiple desired pressure distributions are encoded on the single hologram plate and each is reconstructed by changing the axial distance and by switching the frequency. Several proof-of-concept experiments are performed to verify the functionality of the computationally designed holograms, which are fabricated using modern 3D-printers, i.e., the desired wavefronts are encoded in the hologram plates' thickness profile, being input to the 3D-printer. The experiments include measurement of output pressure fields in water using needle hydrophones and acquisition of receivers' voltage output in UPT systems. Another technique investigated in this dissertation is the implementation of acoustic impedance matching layers deposited on the front leading surface of the transmitter and receiver transducers. Current UPT systems suffer from significant acoustic losses through the transmission line from a piezoelectric transmitter to an acoustic medium and then to a piezoelectric receiver. This is due to the unfavorable acoustic impedance mismatch between the transducers and the medium, which causes a narrow transducer bandwidth and a considerable reflection of the acoustic pressure waves at the boundary layers. Using matching layers enhance the acoustic power transmission into the medium and then reinforce the input as an excitation into the receiver. Experiments are performed to identify the input acoustic pressure from a cylindrical transmitter to a receiver disk operating in the 33-mode of piezoelectricity. Significant enhancements are obtained in terms of the receiver's electrical power output when implementing a two-layer matching structure. A design platform is also developed that can facilitate the construction of high-fidelity acoustically matched transducers, that is, the material layers' selection and determination of their thicknesses. Furthermore, this dissertation presents a numerical analysis for the dynamical motions of a high-intensity focused ultrasound (HIFU)-excited microbubble or stable acoustic cavitation, which includes the effects of acoustic nonlinearity, diffraction, and absorption of the medium, and entails the problem of several biomedical ultrasound applications. Finally, the design and use of acoustic holograms in microfluidic channels are addressed which opens the door of acoustic patterning in particle and cell sorting for medical ultrasound systems. / Doctor of Philosophy / This dissertation presents several techniques to enhance the wireless transfer of ultrasonic energy in which the sound wave is generated by an acoustic source or transmitter, transferred through an acoustic medium such as water or human tissue to a sensor or receiver. The receiver transducer then converts the vibrational energy into electricity and delivers to an electrical load in which the electrical power output from the system can be determined. The first enhancement technique presented in this dissertation is using a pre-designed and simple structured plate called an acoustic hologram in conjunction with a transmitter transducer to arbitrarily pattern and shape ultrasound fields at a particular distance from the hologram mounted on the transmitter. The desired wavefront such as single or multi-focal pressure fields or an arbitrary image such as a VT image pattern can simply be encoded in the thickness profile of this hologram plate by removing some of the hologram material based on the desired shape. When the sound wave from the transmitter passes this structured plate, it is locally delayed in proportion to the hologram thickness due to the different speed of sound in the hologram material compared to water. In this dissertation, various hologram types are designed numerically to implement in the ultrasonic power transfer (UPT) systems for powering receivers located at the predetermined focal points more significantly and finally, their functionality and performances are verified in several experiments. Current UPT systems suffer from significant acoustic losses through the transmission from a transmitter to an acoustic medium and then to a receiver due to the different acoustic impedance (defined as the product of density and sound speed) between the medium and transducers material, which reflects most of the incident pressure wave at the boundary layers. The second enhancement technology addressed in this dissertation is using intermediate materials, called acoustic impedance matching layers, bonded to the front side of the transmitter and receiver face to alleviate the acoustic impedance mismatch. Experiments are performed to identify the input acoustic pressure from a transmitter to a receiver. Using a two-layer matching structure, significant enhancements are observed in terms of the receiver's electrical power output. A design platform is also developed that can facilitate the construction of high-fidelity acoustically matched transducers, that is, the material layers' selection and determination of their thicknesses. Furthermore, this dissertation presents a numerical analysis for the dynamical motions of a microbubble exposed to a high-intensity focused ultrasound (HIFU) field, which entails the problem of several biomedical ultrasound applications such as microbubble-mediated ultrasound therapy or targeted drug delivery. Finally, an enhancement technique involving the design and use of acoustic holograms in microfluidic channels is addressed which opens the door of acoustic patterning in particle and cell sorting for medical ultrasound systems.

Dans cette thèse nous proposons de développer un système d’imagerie ultrasonore innovante de micro- défauts basé sur l’utilisation conjointe de techniques d’acoustique non linéaire et du concept de "transducteur à cavité chaotique". Ce transducteur correspond à la combinaison d’une céramique piézoélectrique collée sur une cavité de forme chaotique et du principe de retournement temporel. La faisabilité et les performances de ce nouveau système sont explorées par des simulations numériques. Des paramètres optimaux d’utilisation pour une implémentation expérimentale sont proposés. Une grande partie des travaux menés dans le cadre de cette thèse se concentre sur le développement d’outils numériques permettant l’amélioration de telles techniques d’imagerie. Un schéma d’éléments finis de type Galerkin Discontinu (GD) est étendu à l’élastodynamique non linéaire. Un type de zone absorbante parfaitement adaptée, appelée "Nearly Perfectly Matched Layer" (NPML) a aussi été développé. Dans le cas de matériaux orthotropes, comme des problèmes de stabilité apparaissent, un mélange de NPML et de zone atténuante, dont on contrôle la proportion respective, est introduit afin de stabiliser les NPML. Une validation expérimentale du concept de "transducteur à cavité chaotique" pour la focalisation dans un milieu solide, réverbérant ou non, en utilisant une seule source est réalisée. Les méthodes de retournement temporel et de filtre inverse sont présentées et comparées. La démonstration expérimentale qu’un "transducteur à cavité chaotique" peut être utilisé conjointement avec les méthodes d’inversion d’impulsion afin de réaliser une image de non linéarités localisées est présentée / In this thesis we propose the development of an innovative micro-damage imaging system based on a combination of Nonlinear Elastic Wave Spectroscopy techniques and “chaotic cavity transducer” concept. It consists of a combination of a PZT ceramic glued to a cavity of chaotic shape with the time reversal principle. The feasibility and capabilities of these new ideas is explored by numerical simulations, and optimal operational parameters for experimental implementation are suggested based on the modelling support. A large part of the research work conducted in this thesis is concentrated on the development of numerical simulation tools to help the improvement of such nonlinear imaging methods. A nodal Discontinuous Galerkin Finite Element Method (DG-FEM) scheme is extended to nonlinear elasto-dynamic including source terms. A Perfectly Matched Layer absorbing boundary condition well adapted to the DG-FEM scheme, called Nearly Perfectly Matched Layer (NPML), is also developed. In the case of orthotropic material as stability problems appear, a mixture of NPML and sponge layer, with a controllable ratio of these two kinds of absorbing layers, is introduced. The experimental validation of “chaotic cavity transducer” to focalize in reverberant and non-reverberant solid media with only one source is made. Classical time reversal, inverse filter and 1 Bit time reversal process are discussed and compared. The experimental demonstration of the use of a “chaotic cavity transducer”, in combination with the pulse inversion and 1-bit methods, to obtain an image of localized nonlinearity is made. This opens the possibility for high resolution imaging of nonlinear defects

Dans ce travail de thèse, les mécanismes à l'origine de la formation des chocs associés à la perception de crackle proche de jets supersoniques axisymétriques sont étudiés à l'aide de simulations numériques. Dans ces simulations, les équations de Navier-Stokes instationnaires et compressibles sont résolues en coordonnées cylindriques à l'aide de différences finies d'ordre élevé peu dissipatives et peu dispersives. Quatre jets temporels à des nombres de Mach de 2 et~3 et à des nombres de Reynolds compris entre 3125 et 50000 sont simulés dans un premier temps. Des ondes acoustiques de forte amplitude présentant d'importants gradients de pression sont mises en évidence à proximité des jets. Elles se forment par un mécanisme de raidissement à la source qui est étudié par le calcul de moyennes conditionnelles synchronisées autour des pics de pression en champ proche. Ces moyennes montrent un lien direct entre ces ondes non linéaires et la convection de structures cohérentes à desvitesses supersoniques dans les couches de~mélange. L'influence de la température sur la formation de ces ondes est examinée dans un second temps par le calcul de cinq jets temporels à des rapports de température de 1, 2 et 4, et à des nombres de Mach acoustique compris entre 2 et 4. À vitesse d'éjection constante, les niveaux de bruit produits par les jets chauds sont moins élevés que ceux du jet isotherme, mais les ondes non linéaires qu'ils rayonnent sont peu affectées par une hausse de température. À nombre de Mach constant, les niveaux augmentent avec la température, de même que l'asymétrie des fluctuations de pression, traduisant un renforcement du caractère non linéaire des ondes rayonnées. Ces variations pourraient être dues à celles de la vitesse de convection des structures cohérentes, qui augmente de façon significative avec la température lorsque le nombre de Mach est constant, mais diminue légèrement à vitesse~constante. Finalement, trois simulations de jets spatiaux isothermes et chauds à un nombre de Mach acoustique de 2 et à des nombres de Reynolds de 12500 et 50000 sont mises en \oe uvre. Des ondes de Mach présentant d'importants gradients de pression sont visibles au voisinage direct des jets. La formation de ces ondes est liée, comme dans le cas des jets temporels, à la convection supersonique de structures cohérentes dans les couches de mélange. Le champ lointain acoustique est enfin déterminé par des méthodes d'extrapolation linéaire et non linéaire. Lorsque la propagation est non linéaire, un raidissement additionnel des fronts d'onde est constaté en champ lointain. / Numerical simulations are carried out with the aim of investigating the formation of nonlinear steepened waves at the origin of crackle in the near acoustic field of supersonic jets. In these simulations, the compressible Navier-Stokes equations are solved in cylindrical coordinates using high-order low-dissipative and low-dispersive finite difference schemes.Four temporally-developing isothermal round jets are first simulated at Mach numbers of~2 and~3 and at Reynolds numbers ranging from 3,125 to 50,000. Strong acoustic waves containing sharp pressure variations are observed in the vicinity of the jets. Their formation process is described by the computation of conditional averages which are triggered by the detection of strong pressure peaks in the near field. Such steepened waves are then shown to be produced by the supersonic motion of coherent structures inside the jet shear layers.Temperature effects are then investigated by considering five temporal round jets at temperature ratios of 1, 2 and~4 and at acoustic Mach numbers of 2, 2.8 and 4. For a given jet speed, the sound levels produced by the hot jets are lower than those of the isothermal one. However, the properties of the steepened waves they generate are not significantly affected by a rise of temperature. On the contrary, when the Mach number is held constant, pressure levels are higher at high temperature. The skewness and kurtosis factors of pressure fluctuations are also increased, which indicates a strengthening of the asymmetry and the intermittency of the pressure fluctuations. It is likely that the influence of temperature on these waves results from the variations of the convection speed, which is found to significantly increase with temperature at constant Mach number, but to slightly decrease at constant jet speed.Finally, three simulations of spatially-developing axisymmetric, isothermal and hot jets at a Mach number of~2 and at Reynolds numbers of 12500 and 50000 are performed. Strong Mach waves possessing the distinctive features of crackle are visible in the near vicinity of the jets. As observed for temporal simulations, their formations are associated with the supersonic motion of large-scale coherent structures inside the jet shear layers. The far acoustic field is determined using linear as well as nonlinear extrapolation methods. When nonlinear propagation effects are taken into account, a further steepening of the wavefronts is observed with increasing propagation distance.