Dissertations / Theses on the topic 'Nonlinean acoustics'

Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009.
Committee Chair: G. Tong Zhou; Committee Co-Chair: Xiaoli Ma; Committee Member: David V. Anderson; Committee Member: James Stevenson Kenney; Committee Member: Liang Peng; Committee Member: William D. Hunt. Part of the SMARTech Electronic Thesis and Dissertation Collection.

High intensity focused ultrasound (HIFU) provides a wide range of noninvasive therapies ranging from drug delivery to the destruction of kidney stones. In particular, thermal ablation by HIFU presents an effective noninvasive method for the treatment of deep seated solid tumours. HIFU’s further uptake is limited by a need for improved treatment planning and monitoring. Two nonlinear acoustic phenomena that play key roles in HIFU treatment: finite amplitude effects that lead to the generation of harmonics and steepening of wavefronts, and acoustic cavitation. The former must be taken into careful consideration for treatment planning purposes, while the latter has the potential to provide fast, real-time, cost effective treatment monitoring. The first half of this thesis provides new measurements for the nonlinear acoustic properties of tissue, assesses the validity of two common modelling techniques for simulating HIFU fields. The second half develops a new method for combining passive acoustic mapping- an ultrasound monitoring technique- with MR thermometry, to assess estimates of cavitation enhanced heating derived from passive acoustic maps. In the first results chapter B/A was measured in ex-vivo bovine liver, over a heating/ cooling cycle replicating temperatures reached during HIFU ablation, adapting a finite amplitude insertion technique (FAIS), which also allowed for measurement of sound-speed and attenuation. The method measures the nonlinear progression of a plane-wave through liver and B/A was chosen so that numerical simulations matched measured waveforms. Results showed that attenuation initially decreased with heating then increased after denaturation, sound-speed initially increased with temperature and then decreased, and B/A showed an increase with temperature but no significant post-heating change. These data disagree with other reports that show a significant change and suggest that any nonlinear enhancement in the received ultrasound signal post-treatment is likely due to acoustic cavitation rather than changes in tissue nonlinearity. In the second results chapter two common methods of modelling HIFU fields were compared with hydrophone measurements of nonlinear HIFU fields at a range of frequencies and pressures. The two methods usedwere the KZK equation and the commercial package PZFlex. The KZK equation has become the standard method for modelling focused fields, while the validity of PZFlex for modelling these types of transducers is unclear. The results show that the KZK equation is able to match hydrophone measurements, but that PZFlex underestimates the magnitude of the harmonics. Higher order harmonics in PZFlex are not the correct shape, and do not peak around the focus. PZFlex performs worse at higher pressures and frequencies, and should be used with caution. In the final two chapters a system for estimating cavitation-enhanced heating from acoustic maps is developed and benchmarked against magnetic resonance thermometry methods. The first chapter shows that the ultrasound and MR monitoring systems are compatible, and registers the two imaging systems. The HIFUfocus is clearly visible in passive maps acquired in the absence of cavitation and these coincide with the centre of heating in MR temperature images. When cavitation occurs, it coincides spatially and temporally with the appearance of a clear spike in temperature, especially when the passive maps are processed using the Robust Capon Beamformer algorithm. The final chapter shows how passive maps can be converted into thermal heating inputs, and used to estimate cavitation-enhanced temperature increases. These estimates have the potential to closely match maximum temperature rise, and estimated thermal dose after the estimated temperature rise is spatially averaged. However, themethod is not always successful. This is partly due to uncertainties in MR thermometry estimates, partly due to uncertainties in the acoustic properties of tissue.

This dissertation is concerned with aspects of the newly-proposed approach to nonlinear acoustics in which the Lagrangian description of gas motion is followed. It contains a systematic survey of the approach which leads to the so-called dynamic piston problem. Then new situations regarding the piston problem are studied. These situations cover cases of varying applied pressure and results concerning the formation of shock discontinuities are presented.
Dissertation (MSc)--University of Pretoria, 2013.
Mathematics and Applied Mathematics
unrestricted

This thesis is concerned with long-range sound propagation in deep water.  The main area of interest is the stability of acoustic ray paths in wave guides in which there is a transition from single to double duct sound speed profiles, or vice-versa.  Sound propagation is modelled within a ray theoretical framework, which facilitates a dynamical systems approach of understanding long-range propagation phenomena, and the use of its tools of analysis. Alternative reduction techniques to the Poincaré sections are presented, by which the stability of acoustic rays can be graphically determined.  Beyond periodic driving, these techniques prove to be useful in case of the simplest quasiperiodic driving of the ray equations.  One of the techniques facilitates a special representation of ray trajectories for periodic driving. Namely, the space of sectioned trajectories is partitioned into nonintersecting regular and chaotic regions as with the Poincaré sections, when quasiperiodic and chaotic trajectories are represented by curve segments and area filling points, respectively.  In case of the simplest quasiperiodic driving – speaking about the same technique – regular trajectories are represented by curves similar to Lissajous curves, which are opened or closed depending on whether the two driving frequencies involved make relative primes or not. It is confirmed for a perturbed canonical profile that the background sound speed structure controls ray stability. It is also demonstrated for a particular double duct profile, when the singularity of the nonlinearity parameter for the homoclinic trajectory associated with this profile refers to the strong instability of corresponding perturbed trajectories.

Sensitive nonlinear acoustic methods are suitable for material characterization. This thesis describes three nonlinear acoustic methods that are proven useful for detection of defects like cracks and delaminations in solids. They offer the possibility to use relatively low frequencies which is advantageous because attenuation and diffraction effects are smaller for low frequencies. Therefore large and multi-layered complete objects can be investigated in about one second. Sometimes the position of the damage is required. But it is in general difficult to limit the geometrical extent of low-frequency acoustic waves. A technique is presented that constrains the wave field to a localized trapped mode so that damage can be located.

Until this present work, the acoustics of waveguides has been divided into two broadly distinct fields---linear acoustics in ducts of complex geometry such as those with curvature or varying width, and nonlinear acoustics restricted to simple geometry ducts without curvature or flare. This PhD unites these distinct branches to give a complete mathematical description of weakly nonlinear wave propagation in a general shaped duct in both two and three dimensions. Such ducts have important applications---the clearest example is that of brass instruments, where it has been demonstrated that nonlinear wave steepening gives rise to the characteristic 'brassy' sounds of, for example, the trombone. As the ducts of these instruments have a very complicated geometry involving curvature, torsion and varying width, the goal of the PhD is to address what effect, if any, such changes in duct geometry have on the acoustic properties of such instruments. Other potential applications include the study of acoustics in curved aircraft engine intakes and even the nonlinear sound propagation through the trunk of an elephant. The first results chapter is focused on the exposition of the method used for the remainder of the paper, with the introduction of a new ``nonlinear admittance term'' as well as the associated algebra for it. An elegant notation for the nonlinear algebra is also developed, greatly simplifying the equations. The method is applied to one and two dimensional ducts and some analytical results are derived relating the work to previously published results. Numerical results are also presented and compared to other sources. The concept of nonlinear reflectance is also introduced---illustrating the effect of wave amplitude on the amount of energy reflected in a duct. The next results chapter builds on this work extending it to three dimensions. Numerical results are presented for three characteristic ducts---a curved duct, a horn and a helical duct, being one of the first works to study acoustics in helical pipes for both linear and nonlinear sound propagation. The final results chapter, utilising all of the previous work, addresses the problem of an open ended duct of finite length with nonlinear effects included. Results are compared with the linear results from the Wiener-Hopf method and new results are presented illustrating the effect of geometry and nonlinearity on the resonances of finite length waveguides culminating in the study of the resonances of a trombone.

La théorie des systèmes linéaires invariant a fait l’objet de nombreuses études au cours de ces dernières décennies, et l’estimation d’un tel système à partir du signal de sortie lorsque le signal d’entrée est connu est un problème aujourd’hui résolu. Cependant, le comportement de tout système réel est plus ou moins non-linéaire. Dans le cas de faibles non-linéarités, une approximation linéaire peut être effectuée, mais lorsque les non-linéarités sont plus importantes, cette approximation linéaire n’est plus valide et il est nécessaire d’utiliser une représentation non-linéaire. L’objet de ce travail de thèse est de développer des méthodes simples pour l’identification de systèmes non-linéaires. Ces méthodes doivent être suffisamment précises et robustes pour être utilisées dans différents domaines d’application, même si l’étude est principalement limitée aux domaines de l’audio et de l’acoustique dans le cadre de ce travail de thèse. L’identification d’un système non-linéaire consiste à déterminer un modèle générique non-linéaire de ce système, de telle sorte que le modèle et le système réel étudié délivrent un même signal de sortie lorsqu’ils sont excités par un signal d’entrée identique. Deux méthodes sont développées, toutes deux basées sur un modèle de type "Multiple Input – Single Output" (MISO). Suivant cette modélisation, le système étudié peut être représenté par un ensemble de branches en parallèle, chaque branche comportant deux blocs-fonctions distincts : une fonction non-linéaire statique et un filtre linéaire dynamique. La première méthode développée utilise un bruit blanc gaussien comme signal d’excitation nécessaire à la procédure d’identification. Cette méthode donne de bons résultats lorsqu’elle est appliquée à l’étude de systèmes simulés. Cependant, elle montre des limitations rédhibitoires lorsqu’elle est appliquée à l’étude de systèmes réels. La deuxième méthode développée est basée sur le principe de déconvolution non-linéaire et utilise un "swept sine" comme signal d’excitation. Cette méthode donne de bons résultats lorsqu’elle est appliquée à l’étude de systèmes simulés. Par ailleurs, une étude théorique montre, sur des cas simulés, que cette méthode peut être utilisée pour l’identification de systèmes dont le comportement révèle une hystérésis dynamique particulière (encore appelée hystérésis "de type visqueux"). Deux systèmes non-linéaires bien connus, un limiteur audio et un guide d’ondes acoustiques, sont utilisés pour effectuer une validation expérimentale de la deuxième méthode. La validation est basée sur la comparaison entre les signaux obtenus en sortie de ces systèmes réels et en sortie de leurs modèles lorsqu’un même signal d’excitation est utilisé. Cette comparaison est réalisée à la fois de manière subjective (simple comparaison visuelle entre les signaux, dans le domaine temporel et dans le domaine fréquentiel) et de manière objective (critère d’erreur relative). Une fois validée, cette méthode est utilisée dans le cadre plus large de l’étude de la qualité des haut-parleurs électrodynamiques. Des résultats préliminaires sont présentés, qui permettent d’envisager l’utilisation de la méthode pour identifier, voire pour corriger par filtrage inverse, les non-linéarités présentées par ce type de haut-parleur
The theory of linear time-invariant (LTI) systems has been extensively studied over decades and the estimation of any unknown LTI system, knowing both the input and output of the system, is a solved problem. Nevertheless, almost all real-world devices exhibit more or less nonlinear behavior. In the case of very weak nonlinearities, a linear approximation can be used. If the nonlinearities are stronger, the linear approximation fails and systems have to be described using a nonlinear model. The goal of this thesis is to design and develop simple methods for nonlinear systems identification that would be accurate and robust enough to be applicable for analysis and identification of nonlinear systems in several domains, even if the main focus here is on the domain of audio and acoustics. The goal is to identify a nonlinear system and find its generic nonlinear model in such way that the response of the model to any input signal would be the same as the one of the real-world nonlinear system under test. Two methods are developed in the thesis. Both methods are based on Multiple Input – Single Output (MISO) model. The model consists of several parallel branches, each branch consisting of two separated blocks: a nonlinear static function and a linear dynamic filter. The first method uses a white Gaussian noise as the excitation signal for the identification. This method is successfully tested on several simulation examples, but fails when identifying real world nonlinear systems. The second method is based on the nonlinear convolution and uses swept sine excitation signal. This method is successfully tested on several simulation examples. Moreover, it is theoretically shown that it could be used for the identification of systems exhibiting specific dynamical hysteresis (called hysteresis with viscosity-type effect). Two well known real world nonlinear systems (an audio limiter and an acoustic waveguide) are used to validate the second method. The validation is based on the comparison between the output of these real world systems and the output of their estimated models, when excited with the same input signal. The comparison is performed both subjectively, using a simple visual comparison in time or frequency domains, and objectively, using a relative mean square error criterion. Once validated, the method is used in the general frame of the study of electrodynamic loudspeaker quality. Preliminary results show that this method could be used for the nonlinearities loudspeakers identification, and that an inverse filtering minimizing these nonlinearities could possibly be performed with the help of this method

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.

Harsh environment acoustic emission and ultrasonic wave sensing applications often benefit from placing the sensor in a remote and more benign physical location by using waveguides to transmit elastic waves between the structural location under test and the transducer. Waveguides are normally designed to have high fidelity over broad frequency ranges to minimize distortion - often difficult to achieve in practice. This thesis reports on an examination of using nonlinear ball chain waveguides for the transmission of acoustic emission and ultrasonic waves for the monitoring of thermal protection systems undergoing severe heat loading, leading to ablation and similar processes. Experiments test the nonlinear propagation of solitary, harmonic and mixed harmonic elastic waves through a copper tube filled with steel and elastomer balls and various other waveguides. Triangulation of pencil lead breaks occurs on a steel plate. Data are collected concerning the usage of linear waveguides and a water-cooled linear waveguide. Data are collected from a second water-cooled waveguide monitoring Atmospheric Reentry Materials in UVM's Inductively-Coupled Plasma Torch Facility. The motion of the particles in the dimer waveguides is linearly modeled with a three ball and spring chain model and the results are compared per particle. A theoretical nonlinear model is presented which is capable of exactly modeling the motion of the dimer chains. The shape of the waveform propagating through the dimer chain is modeled in a sonic vacuum. Mechanical pulses of varying time widths and amplitudes are launched into one end of the ball chain waveguide and observed at the other end in both time and frequency domains. Similarly, harmonic and mixed harmonic mechanical loads are applied to one end of the waveguide. Balls of different materials are analyzed and discriminated into categories. A copper tube packed with six steel particles, nine steel or marble particles and a longer copper tube packed with 17 steel particles are studied with a frequency sweep. The deformation experienced by a single steel particle in the dimer chain is approximated. Steel ball waveguides and steel rods are fitted with piezoelectric sensors to monitor the force at different points inside the waveguide during testing. The corresponding frequency responses, including intermodulation products, are compared based on amplitude and preloads. A nonlinear mechanical model describes the motion of the dimer chains in a vacuum. Based on the results of these studies it is anticipated that a nonlinear waveguide will be designed, built, and tested as a possible replacement for the high-fidelity waveguides presently being used in an Inductively Coupled Plasma Torch facility for high heat flux thermal protection system testing. The design is intended to accentuate acoustic emission signals of interest, while suppressing other forms of elastic wave noise.

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

Welded steel pipes are an essential structural part of any power plant. Longer lifetimes and higher pressures in the pipes cause an increased probability of failure due to creep damage. To maintain safe operation, nondestructive evaluation techniques to detect creep damage are needed. Nonlinear acoustic techniques employing longitudinal waves have been proven to be sensitive to creep damage. The objective of this research is to develop a robust experimental procedure to reliably measure the acoustic nonlinearity parameter using longitudinal waves, and then to validate the procedure on samples of different materials and sizes. Finally the technique is applied to characterize creep damage levels around the weld of a welded steel pipe. While the experimental technique presented can only measure the relative nonlinearity, it is accurate enough to detect changes in nonlinearity due to creep damage. Measurements show an increase in nonlinearity in the heat affected zone (HAZ). Experiments after annealing the creep damaged specimen show a decrease in nonlinearity in accordance with a decrease in dislocation density. Measurements on an undamaged welded A36 steel component suggest that the heat itself is not responsible for the increase in nonlinearity.

This Ph.D. is concerned with wave propagation problems. The main focus is on nonlinear acoustics, looking at sonic boom propagation in a physically realistic atmosphere, whilst a secondary part will look at the problem of landmine detection and how to improve the target detection rates. The work on nonlinear acoustics emerged as a desire to model the behaviour of the sonic booms formed by supersonic aircraft in the atmosphere to see what environmental impact they would have on people and animals on the ground, in terms of the form of the sound waves once they reach the ground. The work on landmine detection originated from a Knowledge Transfer Partnership between the University of East Anglia (UEA) and Cobham Technical Services (CTS) organised through the Knowledge Transfer Network (KTN). This partnership took the form of a six month internship with work undertaken afterwards to publish the findings of the internship.

Acoustic echo cancellation (AEC) is an essential component of effective hands-free telephony. Conventional AEC systems employ linear adaptive filters; therefore transmission channel nonlinearities caused by nonlinear components (especially the vocoders in digital networks) can severely degrade performance.
This dissertation examines the performance of popular conventional AEC algorithms based on adaptive filtering theory in nonlinear channels. In order to study the degradation of the algorithms in nonlinear channels, properties of nonlinear devices such as vocoders and loudspeakers are investigated, and a local linearization model is developed for the analysis of the nonlinear devices. This local linearization model is justified by experiments.
A variable step-size adaptive cross-spectral algorithm is proposed so the acoustic echo can be suppressed even during double-talk (DT) periods. This is important since adaptation is frozen during DT periods in order to avoid divergence of the conventional adaptive filtering algorithm; therefore the power of the residual echo may become higher than that of the original echo in nonlinear channels. In addition, the proposed algorithm does not need a DT detector, which is still part of AEC.
To compensate the echo attenuation loss of AEC algorithms caused by channel non-linearities, post-filtering techniques are exploited. Combined with a linear adaptive filter, post-filters based on various approaches, namely: Wiener-type post-filter, spectral subtraction, subspace method and pitch extraction, are proposed to further attenuate the echo. Experimental results show that the combined AEC system can suppress the acoustic echo to a satisfactory level in the nonlinear channel.
Subband adaptive filtering is also studied to reduce the computational complexity of the AEC system so that it can be implemented in real-time. To this end, an improved simple design of DFT filter banks is proposed. Furthermore, a post-filter is integrated with an adaptive filter in the subband to significantly suppresses the acoustic echo in the presence of channel nonlinearities. This approach also significantly reduces the computational burden.
Finally, a psychoacoustic approach based on the masking of the human ear is exploited in order to mitigate the artifacts resulting from the abovementioned post-filters. Testing indicates that the proposed method significantly reduces the distortion of near-end speech when DT occurs. This makes any audible residual echo sound more natural since it has less musical noise.

[EN] Nature is nonlinear. The linear description of physical phenomena is useful for explain observations with the simplest mathematical models, but they are only accurate for a limited range of input values. In the case of intense acoustics waves, linear models obviate a wide range of physical phenomena that are necessary for accurately describe such high-amplitude waves, indispensable for explain other exotic acoustic waves and mandatory for developing new applied techniques based on nonlinear processes. In this Thesis we study the interactions between nonlinearity and other basic wave phenomena such as non-classical attenuation, anisotropic dispersion and periodicity, and diffraction in specific configurations. First, we present intense strain waves in a chain of cations coupled by realistic interatomic potentials. Here, the nonlinear ionic interactions and lattice dispersion lead to the formation of supersonic kinks. These intrinsically-nonlinear localized dislocations travel long distances without changing its properties and explain the formation of dark traces in mica crystals. Then, we analyze nonlinear wave processes in a system composed of multilayered acoustic media. The rich nonlinear dynamics of this system is characterized by its strong dispersion. Here, harmonic generation processes and the relation with its band structure are presented, showing that the nonlinear processes can be enhanced, strongly minimized or simply modified by tuning the layer parameters. In this way, we show how the dynamics of intense monochromatic waves and acoustic solitons can be controlled by artificial layered materials. In a second part, we include diffraction and analyze four types of singular beams. First, we study nonlinear beams in two dimensional sonic crystals. In this system, the inclusion of anisotropic dispersion is tuned for obtain simultaneous self-collimation for fundamental and second harmonic beams. The conditions for optimal second harmonic generation are presented. Secondly, we present limited diffraction beam generation using equispaced axisymmetric diffraction gratings. The obtained beams are truncated version of zero-th order Bessel beams. Third, the grating spacing can be modified to achieve focusing, where the generated nonlinear beams presents high gain, around 30 dB, with a focal width which is between the diffraction limit and the sub-wavelength regime, but with its characteristic high amplitude side lobes strongly reduced. Finally, we observe that waves diffracted by spiral-shaped gratings generate high-order Bessel beams, conforming nonlinear acoustic vortex. The conditions to obtain arbitrary-order Bessel beams by these passive elements are presented. Finally, the interplay of nonlinearity and attenuation in biological media is studied in the context of medical ultrasound. First, a numerical method is developed. The method solves the constitutive relations for nonlinear acoustics and the frequency power law attenuation of biological media is modeled as a sum of relaxation processes. A new technique for reducing numerical dispersion based on artificial relaxation is included. Second, this method is used to study the harmonic balance as a function of the power law, showing the role of weak dispersion and its impact on the efficiency of the harmonic generation in soft-tissues. Finally, the study concerns the nonlinear behavior of acoustic radiation forces in frequency power law attenuation media. We present how the interplay between nonlinearity and the specific frequency power law of biological media can modify the value for acoustic radiation forces. The relation of the nonlinear acoustic radiation force with thermal effects are also discussed. The broad range of nonlinear processes analyzed in this Thesis contributes to understanding the behavior of intense acoustic waves traveling trough complex media, while its implications for enhancing existent applied acoustics techniques are presented.
[ES] La Naturaleza es no lineal. La descripción lineal de los fenómenos físicos es de gran utilidad para explicar nuestras observaciones con modelos matemáticos simples, pero éstos sólo son precisos en un limitado rango de validez. En el caso de onda acústica de alta intensidad, los modelos lineales obvian un amplio rango de fenómenos físicos que son necesarios para describir con precisión las ondas de gran amplitud, pero además son necesarios para explicar otros procesos más exóticos e indispensables para desarrollar nuevas aplicaciones basadas en propagación no lineal. En esta Tesis, estudiamos las interacciones entre no linealidad y otros procesos complejos como atenuación no-clásica, dispersión anisotrópica y periodicidad, y difracción en configuraciones específicas. En primer lugar, presentamos ondas de deformación en una cadena de cationes acoplados por potenciales realísticas. Aquí, las interacciones no lineales entre iones, producen la conformación de kinks supersónicos. Estas dislocaciones localizadas intrínsecamente no lineales viajan por la red largas distancias sin variar sus propiedades, y pueden explicar la formación de trazas en minerales como la mica. Aumentando la escala del problema, estudiamos los procesos acústicos no lineales en medios multicapa. La rica dinámica de estos medios está caracterizada por la fuerte dispersión debido a la periodicidad del sistema. Aquí, estudiamos los procesos de generación de harmónicos, mostrando como modificando la estructura podemos potenciar, minimizar, o simplemente modificar artificialmente la transferencia de energía entre las componentes espectrales, y de esta manera controlar la dinámica de las ondas y solitones en el interior de la estructura. En la segunda parte, incluimos difracción y analizamos cuatro tipos de haces singulares. En primer lugar, analizamos haces ultrasónicos no lineales en cristales de sonido bidimensionales. En este sistema, las propiedades de anisotropía del medio son ajustadas para obtener la auto-colimación simultánea del primer y segundo harmónico. Así, se obtiene la propagación no difractiva para las dos componentes. En segundo lugar, presentamos haces de difracción limitada empleando rejillas de difracción axisimétricas. Por último, demostramos la generación de haces de Bessel de orden superior mediante estructuras en espiral. En la última parte, estudiamos la competición entre no linealidad y la atenuación y dispersión observable en medios biológicos en el contexto de las aplicaciones de biomédicas de los ultrasonidos. En primer lugar desarrollamos un nuevo método computacional para la dependencia frecuencial en forma de ley de potencia de la absorción característica de los tejidos. Este método en dominio temporal es usado posteriormente para revisar los procesos básicos no lineales prestando especial interés en el paper de la dispersión del tejido. Por último, la resolución de las ecuaciones constitutivas nos permite abordar la descripción no lineal de la fuerza de radiación acústica producida en tejidos biológicos, y las implicaciones existentes con la deposición de energía y transferencia de momento para ondas ultrasónicas de alta intensidad. El amplio abanico de procesos no lineales analizados en esta tesis contribuye a una mejor comprensión de la dinámica de las ondas acústicas de alta intensidad en medios complejos, donde las implicaciones existentes en cuanto a la mejora de sus aplicaciones prácticas son puestas de manifiesto.
[CAT] La Naturalesa és no lineal. La descripció lineal dels fenòmens físics és de gran utilitat per a explicar les nostres observacions amb models matemàtics simples, però aquests sol són precisos en un limitat rang de validesa. En el cas d'ona acústica d'alta intensitat, els models lineals obvien un ampli rang de fenòmens físics que són necessaris per a descriure amb precisió les ones de gran amplitud, però a més són necessaris per a explicar altres processos més exòtics i indispensables per a desenvolupar noves aplicacions basades en propagació no lineal. En aquesta Tesi, estudiem les interaccions entre no-linealitat i altres processos complexos com atenuació no-clàssica, dispersió anisotròpica i periodicitat, i difracció en configuracions específiques. En primer lloc, presentem ones de deformació en una cadena de cations acoblats per potencials realistes. Ací, les interaccions no lineals entre ions, produeixen la conformació de kinks supersònics. Aquestes dislocacions localitzades intrínsecament no lineals viatgen per la xarxa llargues distàncies sense variar les seues propietats, i poden explicar la formació de traces en minerals com la mica. Augmentant l'escala del problema, estudiem els processos acústics no lineals en mitjans multicapa. La rica dinàmica d'aquests mitjans es caracteritza per la forta dispersió a causa de la periodicitat del sistema. Ací, estudiem els processos de generació d'harmònics, mostrant com modificant l'estructura podem potenciar, minimitzar, o simplement modificar artificialment la transferència d'energia entre les components espectrals, i d'aquesta manera controlar la dinàmica de les ones i solitons a l'interior de l'estructura. En la segona part, incloem difracció i analitzem quatre tipus de feixos singulars. En primer lloc, analitzem feixos ultrasònics no lineals en cristalls de so bidimensionals. En aquest sistema, les propietats d'anisotropia del medi són ajustades per a obtenir l'acte-col·limació simultània del primer i segon harmònic. Així, s'obté la propagació no difractiva per a les dues components. En segon lloc, presentem feixos de difracció limitada emprant reixetes de difracció axisimètriques. Per últim, vam demostrar la generació de feixos de Bessel d'ordre superior mitjançant estructures en espiral. En l'última part, estudiem la competició entre no linealitat i l'atenuació i dispersió observable en medis biològics en el context de les aplicacions biomèdiques dels ultrasons. En primer lloc desenvolupem un nou mètode computacional per a la dependència freqüencial en forma de llei de potència de l'absorció característica dels teixits biològics. Aquest mètode en domini temporal és usat posteriorment per a revisar els processos bàsics no lineals prestant especial interés en el paper de la dispersió del teixit. Per últim, la resolució de les equacions constitutives ens permet abordar la descripció no lineal de la força de radiació acústica produïda en teixits biològics, i les implicacions existents amb la deposició d'energia i transferència de moment per a ones ultrasòniques d'alta intensitat. L'ampli ventall de processos no lineals analitzats en aquesta tesi contribueix a una millor comprensió de la dinàmica de les ones acústiques d'alta intensitat en medis complexos, on les implicacions existents quant a la millora de les seues aplicacions practiques són posades de manifest.
Jiménez González, N. (2015). Nonlinear Acoustic Waves in Complex Media [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/53237
TESIS
Premiado

Conventional contact ultrasonic methods suffer from large variability, which is known to originate from a number of sources such as coupling variability, and the surface roughness at the transducer/specimen interface. The inherently small higherharmonic signals can be significantly influenced by the changes in contact conditions, especially in nonlinear ultrasonic measurements. For this reason, the noncontact generation and detection techniques are very attractive. This research first focuses on the optical generation of tone-burst surface acoustic waves in a metallic specimen. Two methods that use laser light as an optical source are compared for generating surface acoustics waves in the 5 MHz range. Both the shadow mask and diffraction grating are used to convert a laser pulse to a tone-burst signal pattern on the specimen. The generated signals are detected by a wedge transducer at a fixed location and then the harmonic contents in the generated signals and the repeatability of the methods are evaluated. Finally, the developed method is used to characterize the material nonlinearity of aluminum (Al 6061) and steel (A36). The results showed repeatable measurements for ablative signal excitation on aluminum.

Thesis (M.S.)--School of Mechanical Engineering, Georgia Institute of Technology, 2005. Directed by David Trivett.
Trivett, David, Committee Chair ; Berthelot, Yves, Committee Member ; Rogers, Peter, Committee Member. Includes bibliographical references.

The Underwater Acoustic (UWA) channel has been an area of interest for many researchers and engineers, but also a very challenging area. Compared to the over-the-air radio frequency (RF) channel, the underwater acoustic channel causes multiple distortions – due to multipath, frequency selectivity, noise, and Doppler – some of which are more severe. The increased distortion causes many techniques and assumptions made for typical RF communication systems to break down. One of the assumptions that breaks down is that the Doppler effect that the signal undergoes can be modelled with a simple shift in frequency, since the signals used to communicate in a UWA channel are effectively wideband. In this work the Doppler Effect that a signal undergoes is modelled as a nonlinear time warp. A procedure is developed to estimate the parameters of the time warp from the observed signal. These time warp parameters are then used to reverse the effect of the time warp. Two different methods for estimating the time warp parameters and correcting the Doppler are compared. The first technique uses sinusoids placed at the beginning and end of the signal to estimate the parameters of the warp that the signal undergoes. The second technique uses sinusoids that are present during the signal to estimate and correct for the warp. The frequencies of the sinusoids are outside of the frequency range used for the transmitted data signal, so there is no interference with the information that is being sent. The transmitted data signal uses Orthogonal Frequency Division Multiplexing (OFDM) to encode the data symbols, but the Doppler Correction technique will in principle work for other kinds of wideband signals as well. The results, which include MATLAB based simulations and over-the-air experiments, show that performance improvements can be realized using the time warp correction model.
Master of Science

This thesis examines the nonlinear behaviour of thermoacoustic systems by using approaches from the field of nonlinear dynamics. The underlying behaviour of a nonlinear system is determined by two things: first, by the type and form of the attractors in phase space, and second, by the mechanism that the system transitions from one attractor to another. For a thermoacoustic system, both of these things must be understood in order to define a safe operating region in parameter space, where no high-amplitude oscillations exist. Triggering in thermoacoustics is examined in a simple model of a horizontal Rijke tube. A triggering mechanism is presented whereby the system transitions from a stable fixed point to a stable limit cycle, via an unstable limit cycle. The practical stability of the Rijke tube was investigated when the system is forced by stochastic noise. Low levels of noise result in triggering much before the linear stability limit. Stochastic stability maps are introduced to visualise the practical stability of a thermoacoustic system. The triggering mechanism and stochastic dependence of the Rijke tube match extremely well with results from an experimental combustor. The most common attractors in thermoacoustic systems are fixed points and limit cycles. In order to define the nonlinear behaviour of a thermoacoustic system, it is therefore important to find the regions of parameter space where limit cycles exist. Two methods of finding limit cycles in large thermoacoustic sytems are presented: matrix-free continuation methods and gradient methods. Continuation methods find limit cycles numerically in the time domain, with no additional assumptions other than those used to form the governing equations. Once the limit cycles are found, these continuation methods track them as the operating condition of the system changes. Most continuation methods are impractical for finding limit cycles in large thermoacoustic systems because the methods require too much computational time and memory. In the literature, there are therefore only a few applications of continuation methods to thermoacoustics, all with low-order models. Matrix-free shooting methods efficiently calculate the limit cycles of dissipative systems and have been demonstrated recently in fluid dynamics, but are as yet unused in thermoacoustics. These matrix-free methods are shown to converge quickly to limit cycles by implicitly using a 'reduced order model' property. This is because the methods preferentially use the influential bulk motions of the system, whilst ignoring the features that are quickly dissipated in time. The matrix-free methods are demonstrated on a model of a ducted 2D diffusion flame, and the safe operating region is calculated as a function of the Peclet number and the heat release parameter. Both subcritical and supercritical Hopf bifurcations are found. Physical information about the flame-acoustic interaction is found from the limit cycles and Floquet modes. Invariant subspace preconditioning, higher order prediction techniques, and multiple shooting techniques are all shown to reduce the time required to generate bifurcation surfaces. Two types of shooting are compared, and two types of matrix-free evaluation are compared. The matrix-free methods are also demonstrated on a model of a ducted axisymmetric premixed flame, using a kinematic G-equation solver. The methods find limit cycles, period-2 limit cycles, fold bifurcations, period-doubling bifurcations and Neimark-Sacker bifurcations as a function of two parameters: the location of the flame in the duct, and the aspect ratio of the steady flame. The model is seen to display rich nonlinear behaviour and regions of multistability are found. Gradient methods can also efficiently calculate the limit cycles of large systems. A scalar cost function is defined that describes the proximity of a state to a limit cycle. The gradient of the cost function is used in an optimisation routine to iteratively converge to a limit cycle (or fixed point). The gradient of the cost function is found with a forwards-backwards process: first, the direct equations are marched forwards in time, second, the adjoint equations are marched backwards in time. The adjoint equations are derived by partially differentiating the direct governing equations. The gradient method is demonstrated on a model of a horizontal Rijke tube. This thesis describes novel nonlinear analysis techniques that can be applied to coupled systems with both advanced acoustic models and advanced flame models. The techniques can characterise the rich nonlinear behaviour of thermoacoustic models with a level of detail that was not previously possible.

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.

The natural dynamics are not ideal or linear. To understand their complex behavior, we needs to study the nonlinear dynamics in more simple models. This thesis is consist of two main setups. Both setups are simplified models for the behavior occurs in the complex systems. We studied in both systems the same nonlinear dynamics such as higher-harmonics, sub-harmonics, solitary waves,...etc. In Chapter (2), the propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly in influenced by dispersion. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of FPU equation, describing a chain of masses connected by nonlinear quadratic springs. The results can be extrapolated to other systems described by this equation. We studied theoretically and experimentally the generation and propagation of kinks in the system. We excite pulses at one boundary of the system and demonstrate the existence of kinks, whose properties are in very good agreement with the theoretical predictions, that is the equation that approaches, under the conditions of our experiments, the one corresponding to full model describing a chain of masses connected by magnetic forces. The results can be extrapolated to other systems described by this equation. Also, In the case of a lattice of finite length, where standing waves are formed, we report the observation of subharmonics of the driving wave. In chapter (3), we studied the propagation of intense acoustic waves in a multilayer crystal. The medium consists in a structured fluid, formed by a periodic array of fluid layerswith alternating linear acoustic properties and quadratic nonlinearity coefficient. We presents the results for different mathematicalmodels (NonlinearWave Equation,Westervelt Equation and Constitutive equations). We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media. In chapter (4), the oscillatory behavior of a microbubble is investigated through an acousto-mechanical analogy based on a ring-shaped chain of coupled pendula. Observation of parametric vibration modes of the pendula ring excited at frequencies between 1 and 5 Hz is considered. Simulations have been carried out and show spatial mode, mixing and localization phenomena. The relevance of the analogy between a microbubble and the macroscopic acousto-mechanical setup is discussed and suggested as an alternative way to investigate the complexity of microbubble dynamics.
La dinámica natural no es ideal ni lineal. Para entender su comportamiento complejo, necesitamos estudiar la dinámica no lineal en modelos más simples. Esta tesis consta de dos configuraciones principales. Ambas configuraciones son modelos simplificados de el comportamiento que se produce en los sistemas complejos. Estudiamos en ambos sistemas la misma dinámica no lineal como son la generación de armónicos superiores, los sub-armónicos, las ondas solitarias, etc. En elCapítulo (2), se estudia, tanto teórica comoexperimentalmente, la propagación de ondas no lineales en sistemas periodicos de partículas acopladas mediante fuerzas repulsivas. Se propone una configuración experimental simple, que consiste en una matriz de dipolos magnéticos acoplados. Inyectando armónicamente la señal en un extremo, excitamos ondas de propagación y demostramos diferentes regímenes de conversión de modos en armónicos, fuertemente influenciados por la dispersión. También se predice y se discute el fenómeno de dilatación acústica de la cadena. Los resultados se comparan con las predicciones teóricas de la ecuación FPU, describiendo una cadena de masas conectadas por muelles cuadráticos no lineales. Los resultados pueden ser extrapolados a otros sistemas descritos por esta ecuación. Estudiamos también teórica y experimentalmente la generación y propagación de kinks. Excitamos pulsos en la frontera del sistema y demostramos la existencia de kinks cuyas propiedades están en muy buen acuerdo con las predicciones teóricas, es decir, con la ecuación que aproxima bajo las condiciones de nuestros experimentos la correspondiente al modelo completo que describe un cadena de masas conectadas por fuerzas magnéticas. Los resultados pueden ser extrapolados a otros sistemas descritos por esta ecuación. Además, en el caso de una red finita, donde se forman ondas estacionarias, describimos la observación de subarmónicos del armónico principal. En el capítulo (3), estudiamos la propagación de ondas acústicas intensas en un cristal multicapa. El medio consiste en un fluido estructurado, formado por un conjunto periódico de capas fluidas con propiedades acústicas lineales alternas y coeficiente de no linealidad cuadrática. Presentamos los resultados de diferentes modelos matemáticos (ecuación de ondas no lineal, ecuación de Westervelt y ecuaciones constitutivas). Mostramos que la interacción entre la fuerte dispersión y la no linealidad conduce a nuevos escenarios de propagaciónde ondas. El proceso de distorsión de la onda clásica, típico de las ondas acústicas intensas en medios homogéneos, puede ser alterado de forma importante cuando los armónicos generados no linealmente se encuentran dentro o cerca del gap. Esto permite la posibilidad de diseñar un medio con el fin de obtener una forma de onda en particular. Ejemplos de esto incluyen el diseño demedios con no linealidad efectiva (por ejemplo, cúbica) o medios extremadamente lineales. En el capítulo (4), el comportamiento oscilatorio de una microburbuja se investiga a través de una analogía acusto-mecánica basada en una cadena en forma de anillo de péndulos acoplados. Se estudian los modos de vibración paramétrica del anillo pendular excitado a frecuencias entre 1 y 5 Hz. Se han llevado a cabo simulaciones que muestran la presencia de modos espaciales, mixtos y fenómenos de localización. Se discute la relevancia de la analogía entre una microburbuja y la configuración macroscópica acústico-mecánica y se sugiere como una vía alternativa para investigar la complejidad de la dinàmica de microburbujas.
La dinàmica natural no és ideal ni tampoc lineal. Per entendre el seu comportament complex, es necessita estudiar la dinàmica no lineal dels models més simples. Aquesta tesi consisteix en l'estudi de dues configuracions principals, que són models simplificats del comportament que es produeix en els sistemes complexos. Estudiem en ambdós sistemes la mateixa dinàmica no lineal, com és la generació d'harmònics superiors, sub-harmònics, ones solitàries, etc. En el capítol (2), estudiem, tant teòrica com experimentalment, la propagació de les ones no lineals en sistemes periòdics de partícules acoblades mitjançant forces repulsives. Es proposa una configuració experimental simple, que consisteixen en una matriu de dipols magnètics acoblats. En conduint harmònicament la xarxa en un límit, excitemla propagació de les ones i demostrem diferents règims de conversió de modes en harmònics més alts, força influenciada per la dispersió. El fenomen de la dilatació acústica de la cadena també es prediu i es discuteix. Els resultats es comparen amb les prediccions teòriques que descriu una cadena de masses conectades per molls quadràtics no lineals. Els resultats es poden extrapolar a altres sistemes descrits per aquesta equació. Hem estudiat teòrica i experimentalment la generació i propagació de Kinks. Excitem polsos a la frontera del sistema i demostrem l'existència d'Kinks, les propietats desl quals estan en molt bon acord amb les prediccions teòriques, és a dir, de l'equació que aproxima sota les condicions dels nostres experiments la corresponent al model complet que descriu un cadena demasses connectades per forcesmagnètiques. Els resultats es poden extrapolar a altres sistemes descrits per aquesta equació. A més, en el cas d'una xarxa finita, on es formen ones estacionàries, descrivim l'observació de subarmónicos de l'harmònic principal. En el capítol (3), s'estudia la propagació d'ones acústiques intenses en un medi multicapa. El medi consisteix en un fluid estructurat, format per una matriu periòdica de capes de fluid amb l'alternança de propietats acústiques lineals i coeficient de no linealitat de segon grau. Es presenten els resultats per a diferents models matemàtics no lineals (equació d'ones no lineal, equació de Westervelt i les equacions constitutives). Es demostra que la interacciò entre la forta dispersió i no linealitat condueix a nous escenaris de propagació de l'ona. El procés de distorsió en formad'ona clàssica, típica de les ones acústiques intenses en medis homogenis, es pot alterar de manera significativa quan els harmònics generats de forma no lineal es troben dins o a prop del gap. Això obri la possibilitat de dissenyar unmedi per tal d'obtenir una forma d'ona particular. Exemples d'això inclouen el disseny delsmedis amb una no linealitat efectiva (per exemple cúbica), o medis extremadament lineals. En el capítol (4), el comportament oscilatori d'una micro-bombolla és investigat a través d' una analogia acústica-mecànica basada en una cadena en forma d'anell de pèndols acoblats. Es considera l'observació dels modes de vibració paramètriques de l'anell pendular excitat amb freqüències entre 1 i 5 Hz. S'han dut a terme simulacions que mostren la presència de moes espacilas, mixtes i fenòmens de localització. Es discuteix la relevància de l'analogia entre les microbambolles i la configuració macroscòpica acústica-mecànica i es suggereix una formaalternativa per a investigar la complexitat de la dinàmica demicrobombolles.
Mehrem Issa Mohamed Mehrem, A. (2017). Nonlinear acoustics in periodic media: from fundamental effects to applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/80289
TESIS

Ces dernières années, les métamatériaux acoustiques sont largement étudiés pour leur intérêt dans la réalisation de divers types de contrôle des ondes à une échelle sub-longueur d’onde. En particulier, les métasurfaces acoustiques ont montré leur capacité à manipuler des ondes en limites de milieux de propagation via les processus de réflexion, de transmission et de réfraction. Contrairement au régime linéaire qui concerne l’immense majorité des travaux sur les métamatériaux acoustiques, les études sur les propriétés non linéaires des métamatériaux, de surcroit des métasurfaces, restent peu nombreuses, malgré la possibilité de générer des phénomènes acoustiques riches et variés. Les principaux freins au développement des métamatériaux non linéaires sont l'efficacité généralement faible de la réponse non linéaire et le manque de contrôle sur cette non-linéarité. Les travaux de recherche présentés ici ont donc pour objectif de concevoir des architectures de métasurfaces élastiques, permettant un contrôle des ondes acoustiques dans le régime non linéaire. En particulier l’effet de conversion d’une onde fondamentale vers son deuxième harmonique est étudié dans le processus de réflexion et de transmission unidirectionnelle. Cela nécessite le design de la non-linéarité élastique, qui est réalisé à base de modélisations discrètes de systèmes masses-ressorts et d'architectures composées d'éléments tournants. Les métasurfaces ainsi conçues, résonantes et à non-linéarité contrôlée, permettent de générer des effets non linéaires acoustiques inhabituels, potentiellement intéressants pour la manipulation d'ondes acoustiques
In recent years, acoustic metamaterials have proven to be of great interest for their ability to achieve a variety of wave control at sub-wavelength scale. In particular, acoustic metasurfaces have shown their ability to manipulate waves from the boundaries of propagation media, via the reflection, transmission and refraction processes. Unlike the linear regime which has been extensively investigated in acoustic metamaterials, studies of the nonlinear acoustic properties of metamaterials, especially nonlinear acoustic metasurfaces, are quite scarce, despite the possibility to lead to a rich and diverse set of non-trivial acoustic phenomena. The key limitations in the development of nonlinear acoustic metamaterials are the typically weak efficiency of their nonlinear response together with the lack of control on this nonlinearity. This PhD research is thus dedicated to the design of nonlinear elastic metamaterial and metasurface architectures, enabling acoustic wave control in the nonlinear regime. Specifically, the conversion effect from a fundamental wave to its second harmonic is studied through the one-dimensional scattering process (reflection and transmission) by metasurfaces. This requires the elastic nonlinearity management, realized via the discrete modeling of lumped-element systems and architectures made of rotating units. Such designed metasurfaces, resonating and with harnessed nonlinearity, can create unusual nonlinear acoustic effects, potentially interesting for wave control. This research open the path to a more systematic study of nonlinear acoustic wave manipulation by metamaterials

Surface acoustic wave (SAW) technology has been in use for well over one century. In the last few decades, due to its low cost and high performance, this technology has been widely adopted in modern wireless communication systems, to build filtering devices at radio frequency (RF). SAW filters and duplexers can be virtually found inside every mobile handset. SAW devices are traditionally recognized as passive devices with high linear signal processing behavior. However, recent deployments of third generation (3G) and fourth generation (4G) mobile networks require the handsets to handle an increasing number of frequency bands with more complex modulation /demodulation schemes and higher data rate for more subscribers. These requirements directly demand more stringent linearity specifications on the front end devices, including the SAW duplexers. In the past, SAW duplexer design was based on empirically obtained design rules to meet the linearity specifications. Lack of predictability and an understanding of the root cause of the nonlinearity have limited the potential applications of SAW duplexers. Therefore, research on the nonlinearity characterization and an accurate modeling of SAW nonlinearity for mobile device applications are very much needed. The Ph.D. work presented here primarily focuses on developing a general nonlinear model for SAW resonators/duplexers. Their nonlinear characteristics were investigated by measuring the harmonic and intermodulation distortions of resonators. A nonlinear Mason model is developed and the characterization results are integrated into SAW duplexer design flows to help to simulate the nonlinear effects accurately and improve the linearity performance of the products. In this dissertation, first, a novel nonlinear Mason equivalent circuit model including a third order nonlinear coefficient in the wave propagation is presented. Next, the nonlinear distortions of SAW resonators are analyzed by measuring large-signal harmonic and intermodulation spurious emission on resonators using a wafer probe station. The influence of the setups on the measurement reliability and reproducibility is discussed. Further, the nonlinear Mason model is validated by comparing its simulation results with harmonic and intermodulation measurements on SAW resonators and a WCDMA Band 5 duplexer. The Mason model developed and presented here is the first and only nonlinear physical model for SAW devices based on the equivalent circuit approach. By using this new model, good simulation measurement agreements are obtained on both harmonic and intermodulation distortions for SAW resonators and duplexers. These outcomes demonstrate the validity of the research on both the characterization and modeling of SAW devices. The result obtained confirms that the assumption of the representation of the 3rd order nonlinearity in the propagation by a single coefficient is valid.
Ph.D.
Doctorate
Electrical Engineering and Computer Science
Engineering and Computer Science
Electrical Engineering

Basing on recent solar models, the excitation of ion-acoustic turbulence in the weaklycollisional, fully and partially-ionized regions of the solar atmosphere is investigated. Within the frame of hydrodynamics, conditions are found under which the heating of the plasma by ion-acoustic type waves is more effective than the Joule heating. Taking into account wave and Joule heating effects, a nonlinear differential equation is derived, which describes the evolution of nonlinear ion-acoustic waves in the collisional plasma.

This thesis is motivated by the need for noise control in aircraft engine with orifices and perforated liner. The presence of high-level acoustic excitation, different flow situations either bias flow, grazing flow or any combination in the aircraft engine, makes the acoustic behavior complex due to the interaction between sound and flow over the lined wall. Both systematic acoustic prediction of aircraft engines and liner optimization necessitate progress in impedance measurement methods by including the effect of the complex flow situations. The aim of the present thesis is to experimentally study the change in acoustic properties of orifices and perforated liners under bias or grazing flow. In order to study the effect of different combinations of bias flow and high-level acoustic excitation, an in-duct orifice has been investigated with finely controlled acoustic excitation levels and bias flow speeds. This provides a detailed study of the transition from cases when high-level acoustic excitation causes flow reversal in the orifice to cases when the bias flow maintains the flow direction. Nonlinear impedance is measured and compared, and a scattering matrix and its eigenvalues are investigated to study the potentiality of acoustic energy dissipation or production. A harmonic method is proposed for modelling the impedance, especially the resistance, which captures the change in impedance results at low frequencies compared with experimental results. The presence of grazing flow can increase the resistance of acoustic liners and shift their resonator frequency. So-called impedance eduction technology has been widely studied during the past decades, but with a limited confidence due to the interaction of grazing flow and acoustic waves. A comparison has been performed with different test rigs and methods from the German Aerospace Center (DLR). Numerical work has been performed to investigate the effect of shear flow and viscosity. Our study indicates that the impedance eduction process should be consistent with that of the code of wave propagation computation, for example with the same assumption regarding shear flow and viscosity. A systematic analysis for measurement uncertainties is proposed in order to understand the essentials for data quality assessment and model validation. The idea of using different Mach numbers for wave dispersion and in the Ingard-Myers boundary condition has been tested regarding their effect on impedance eduction. In conclusion, a local Mach number based on friction velocity is introduced and validated using both our own experimental results and those of previous studies.

QC 20150522

Thesis (M.S. in Physics) Naval Postgraduate School, December 1996.
Thesis advisor(s): A. Larraza and B.C. Denardo. "December 1996." Includes bibliographical references (p. 41-42). Also available online.