Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios.

Cette thèse est une contribution expérimentale à l’étude des résonances aéroacoustiques des jets sous-détendus : le Screech. Diverses méthodes expérimentales sont utilisées à ces fins, telles que la mesure de pression acoustique, la strioscopie et Vélocimétrie par Image des Particules, et associées à des techniques classiques de post-traitement comme les décompositions en mode de Fourier et aux valeurs propres. Ces Techniques permettent d’évaluer les effets d’épaisseur de la lèvre de la buse sur l’écoulement, et fournissent des informations sur les différences de comportement d’un même jet montrant des modes oscillatoires différents. Enfin, on entreprend d’étudier la présence de divers mécanismes de fermeture de la boucle de résonance pour divers modes de screech. La présence d’ondes intrinsèques du jet, se propageant vers l’aval pour les modes axisymétrique (A2) et hélicoïdal (C) suggèrent que ces ondes puissent jouer un rôle dans la résonance. La signature de ces ondes n’est en revanche pas attestée pour les modes battants (B). Ces résultats semblent donc indiquer que plusieurs mécanismes de rétroaction différents puissent être à l’oeuvre dans la résonance du jet sous-détendus. / This work provides an experimental contribution to the study of the Screech phenomenon. Various experimental techniques such as microphones array, Schlieren and Particle Image Velocimetry (PIV) together with advanced post-processing techniques like azimuthal Fourier decomposition and Proper Orthogonal Decomposition (POD) are employed. These techniques enable the evaluation of the lip thickness effects on the jets generated by two different round nozzles. The differences on the flow aerodynamics and acoustics are discussed. Then, we carry out experiments to analyse the effects of the different dominant Screech modes (B and C) on the flow characteristics. No noticeable differences are found in the mean fields. However, the fluctuation fields shows the contrary: B mode has larger fluctuation. In the last part, we investigate the Screech closure mechanism. The signature of upstream jet waves is revealed in the axisymmetric (A2) and helical (C) mode. However, the mode B does not present evidence of this instability in the flow, indicating that its closure mechanism may be bonded to another kind of waves. The conclusion from the results is that the Screech phenomenon seems be driven by different closure mechanisms.

On s'intéresse à la localisation de l'axe du cône de Mach lié au déplacement supersonique d'un source acoustique en milieu réverbérant à l'aide d'un nombre limité de microphones. L'application faisant l'objet du financement doctoral est la localisation de tireurs embusqués, dans le cadre de la protection du combattant. Le principe du retournement temporel stipule que, lors de la réémission des mesures renversées dans le temps depuis leurs positions respectives, tout se passe comme si le champ de pression acoustique se propageait en remontant le temps et focalisait à l'endroit de la distribution de sources. Cette focalisation est d'autant plus efficace que les positions de capteurs ont tendance à former une surface fermée autour des sources. On considère une distribution discrète de microphones à hauteur constante dans une rue rectiligne. Dans une première approche, le déplacement supersonique est modélisé selon le principe de Huygens-Fresnel comme une sommation de sources monopolaires. Cela permet une formulation analytique du problème direct pouvant être résolue par des simulations numériques simples en accord avec un montage expérimental de synthèse de cône de Mach au moyen d'une ligne de haut-parleurs. La résolution du problème inverse se fait en calculant numériquement le champ rétropropagé depuis les positions des microphones jusque dans des tranches verticales disposées le long de la rue. L'utilisation d'un critère statistique d'ordre supérieur permet de réduire la contribution des termes de sources dans le champ rétropropagé, à l'origine d'une divergence du champ de pression autour des positions de microphones. L'axe du cône de Mach peut alors être localisé avec une bonne précision angulaire. Dans une deuxième approche, on considère un front d'onde conique réel en déplacement supersonique. Les temps d'arrivée obéissent à des lois de retard bien précises. Notre modèle de réverbération permet de prédire la plupart des pics correspondant à l'arrivée au point de mesure des signaux impulsionnels réfléchis. La réverbération n'a pas un effet aussi bénéfique dans le cadre d'une source supersonique réelle que dans le cas d'une source statique, ni même que dans celui de la ligne de haut-parleurs, car la source supersonique présente des contraintes géométriques particulières dont le retournement temporel ne tient pas compte, étant donnée la différence de géométrie des ondes directe (un cône) et retournée dans le temps (une superposition d'ondes sphériques). Cependant, la focalisation autour du passage de l'axe est observée dans les tranches horizontales, avec une qualité dépendant fortement de l'agencement de l'antenne de microphones. / We are interested into the localisation of the Mach cone --- created by the supersonic motion of an acoustic source into a reverberant medium --- by means of a limited amount of microphones. The application concerns sniper localisation, hence protection of the soldier. Theory of time-reversal states that when reemitting measures reversed in time from their respective positions, everything happens as if the pressure field were propagating travelling backwards in time and focused on the source distribution. This result is enhanced when the microphone distribution over space forms a closed surface surrounding the sources, according to Kirchhoff-Helmholtz formula. Aiming at a physically and technologically implementable method, we consider a discrete distribution of microphones, disposed at a constant height in a reverberating area reproducing the geometry of a straight narrow street.The problem shows specific constraints due to its specific geometry that we aim to use sparsely. In a first approach, we consider the supersonic displacement from the viewpoint of Huygens-Fresnel principle as a discrete sum of monopolar sources, which allows an analytical formulation of the direct problem solvable by simple numerical simulations. This model is in agreement with an experimental framework, were the Mach cone is synthesized by means of a loudspeaker array. The resolution of the inverse problem is made by computing the time-reversed pressure field into vertical slices disposed along the street. The use of a fourth-order spatiotemporal statistical criterion (kurtosis) allows to reduce unwanted contribution of source term causing a divergence around microphone positions. A maximum of kurtosis is observed around the intersection between the time-reversal slice and the Mach cone axis, allowing localisation of the latter with good angular precision. In a second approach, we investigate the previous method on a real Mach cone. It is necessary to adopt the point of view of dynamical space-time geometry to understand the behaviour of the times of arrival of the different image sources. It is also necessary to take into account the finiteness of the reberberating walls. Our geometrical theory of reverberation allows a modelisation of the direct problem in good agreement with experimental measurements. We show that the effect of reverberation does not enhance time-reversed focalisation as well as it does with a static source. This is mainly due to geometric constraints that are not reproduced in the time-reversed wavefront superposition. The resolution of the inverse problem strongly depends on the disposition of the microphone set: on the 9 configurations, only one allows detection of the axis.

Η παρούσα διπλωματική εργασία αποτελεί βιβλιογραφική έρευνα πάνω στο επιστημονικό αντικείμενο της Ακουστικής Εκπομπής (ΑΕ) σαν μια από τις μεθόδους του Μη Καταστροφικού Ελέγχου (ΜΚΕ) και υλοποίηση της μεθόδου εντοπισμού της θέσης πηγής ΑΕ στο προγραμματιστικό περιβάλλον Matlab. Στην εργασία γίνεται αναφορά στις πιο διαδεδομένες μεθόδους του ΜΚΕ, στα πλεονεκτήματα της ΑΕ έναντι των άλλων μεθόδων. Γίνεται παρουσίαση των τεχνικών της ΑΕ, με βάση την ιστορική εξέλιξή της, από την συμβατική τεχνική που αξιοποιεί κάποιες παραμέτρους του σήματος, για την «ποιοτική» εκτίμηση της καταπόνησης του υλικού, μέχρι τις σύγχρονες τεχνικές που αξιοποιούν τις υπολογιστικές ικανότητες που προσφέρουν οι Θ/Τ δίνοντας τη δυνατότητα για μια περισσότερο «ποσοτική» εκτίμηση του μεγέθους και του είδους της αστοχίας. Γίνεται αναφορά στη θεωρία της διάδοσης των κυμάτων σε λεπτές πλάκες, ακρογωνιαίο λίθο της επεξεργασίας των σημάτων με πιο εξελιγμένες υπολογιστικές μεθόδους στο πεδίο του χρόνου και της συχνότητας. Παρουσιάζεται η εφαρμογή της θεωρίας της διάδοσης των κυμάτων στα σύνθετα υλικά, των προβλημάτων που παρουσιάζει η τεχνική της ΑΕ σε αυτά, καθώς και η αξιοποίηση των νευρωνικών δικτύων, στην χωρίς επίβλεψη αναγνώριση του είδους της αστοχίας σε σύνθετα υλικά. Γίνεται αναφορά στον μετασχηματισμό κυματιδίου σαν τεχνική ανάλυσης των κυματομορφών της ΑΕ. Τέλος παρουσιάζεται το πρόβλημα του εντοπισμού της θέσης της πηγής της ΑΕ, όπου υλοποιείται η μέθοδος που αξιοποιεί τους χρόνους άφιξης του σήματος στους αισθητήρες για τον υπολογισμό της θέσης της πηγής. Αναφέρονται οι σημαντικότερες και πιο πρόσφατες εργασίες της διεθνούς βιβλιογραφίας και σχολιάζονται οι τεχνικές που χρησιμοποιούνται για την εξαγωγή συμπερασμάτων για το είδος και την θέση της αστοχίας. / The thesis is a search about the techniques of acoustic emission. It refers to algorithms for finding the source location af acoustis emission. Finally, a new algorithm made on MATLAB environment is introduced.

This thesis presents an investigation of the factors controlling the performance of two forms of active vibration control applied to lattice structures, such as those used for space applications. The structure considered is based on a lattice structure assembled by NASA in 1984. It consists of a satellite boom with 93 aluminium members connected rigidly through 33 spherical joints. The structure has two distinct forms of motion which are categorized in terms of short and long wavelength modes. The short wavelength modes occurs when the length of the individual members is a multiple of half wavelength of bending waves. The second category, named long wavelength modes occur when the length of the whole structure is a multiple of half wavelength of waves propagating by longitudinal motion in the structure. Simple expressions are derived to identify the factors that control the frequency bands where short and long wavelength modes occur. It is possible to alter the dynamic behaviour of the system by changing some of the factors in these expressions and thus study the active and passive control of vibration in a variety of such structures. The two strategies of active control considered in the thesis are feedforward control and integral force feedback control. Feedforward control usually requires deterministic forms of disturbance sources while feedback control can be applied to random disturbances. It has been found that short wavelength modes can reduce the performance in the feedback control strategy, while the results of feedforward control are not affected so much. To support this analysis, the energy dissipation and power flow mechanisms in the structure are studied. The results in this thesis are based on numerical simulations and experimental tests which have been used to validate the mathematical model of the structure.

The focus of this thesis is on the prediction of sound attenuation through a lined duct, based on a mathematical model. Ducts with a single section as well as multi-segmented sections are discussed. The duct of interest has a rectangular cross-section as normally used for ventilation purposes. The mean flow in a ventilation duct is very low and can be neglected. In this thesis, two-dimensional analytical models are developed for sound transmission in a series of different duct configurations. Two models of the lining behaviour are considered, either locally-reacting or bulk-reacting. The models are used first to obtain the transverse and axial wavenumbers of various modes of the duct. The required finite numbers of wavenumbers are tracked using Müller’s method. The wavenumbers are traced from a very low frequency to high frequency using small frequency steps. It is found that, for a duct with a bulk-reacting lining, the number of modes with a transverse wavenumber below a particular value may exceed the corresponding number of modes in a duct with a locally-reacting lining. These additional modes are termed lining modes. The number of lining modes depends on the lining thickness. Dispersion curves are presented for both types of lining. The transmission of sound through the duct is then calculated using the mode-matching technique. The mode-matching model allows analysis of multi-modal wave propagation in the duct. The model is first developed for an infinitely long rigid duct with a finite length of lined insert. The estimation from the locally reacting model, that is widely available in the literature, is compared with the estimation from the newly developed bulk-reacting model. Although the locally reacting model often overestimates the performance of a bulk-reacting lining it is found that this is not always the case, especially for a small lining thickness and at lower frequencies where the locally reacting model may under-estimate the performance. The analytical model is then extended to a multi-segmented lining where the lined section is uniformly segmented with rigid walled sections in a periodic manner. For a bulk-reacting lining, the segmented arrangement renders the lining more similar to the behaviour of a duct with a locally-reacting lining and improves the peak attenuation. Little improvement is found in the case of a multi-segmented locally-reacting lining. The effect of duct height, lining thickness and lining flow resistivity on sound attenuation is studied using the analytical model. Experiments are presented which validate the analytical model.

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Vibration-based energy harvesting devices have received much attention over the past few years due to the need to power wireless devices in remote or hostile environments. To date, resonant linear generators have been the most common type of generators used in harvesting energy for such devices. Simple tuning and modelling methods make it a more favourable solution theoretically if not practically. This thesis considers the limitations of resonant linear devices and investigates two non-linear generators to see if they can outperform the linear devices in certain situations. So far, in most of the literature, the energy harvester is assumed to be very small dynamically compared to the source so the source is not aected by the presence of the device. This thesis considers how the dynamics of the source is aected by the device if its impedance is signicant compared to the source. A tuning condition for maximum power transfer from the source to the device is derived. This tuning condition converges to the one presented in most of the literature when the impedance of the device is assumed to be very small compared to that of the source i.e. tuned so that the natural frequency of the device equals the excitation frequency. For the case when the impedance of the device has a negligible eect on the source, the performance of the device is only limited to a narrow frequency band and drops o rapidly if mistuned. To accommodate the mistuning limitations, new types of generators are proposed mainly by using a non-linear mechanism. These mechanisms are made up of a non-linear spring connected together with a mass and a linear viscous damper i.e. the energy harvesting component. The analysis of the fundamental performance limit of any non-linear device compared to that of a tuned linear device is carried out using the principal of conservation of energy. The analysis reveals that the performance of a non-linear device in terms of the power harvested is at most 4= greater than that of a tuned linear system and is strongly dependent upon the type of the non-linearity used. Two types of non-linear mechanisms are studied in this thesis. The rst one is a non-linear bi-stable mechanism termed a snap-through mechanism which rapidly moves the mass between two stable states. The aim is to steepen the displacement response curve as a function of time which results in the increase of velocity for a given excitation, thus increasing the amount of power harvested. This study reveals that the performance of the mechanism is better than a linear system when the natural frequency of the system is much higher than the excitation frequency. The study also shows that the power harvested by this mechanism rolls o at a slower rate compared to that of the linear system. Another non-linear mechanism described in this thesis uses a hardening-type spring. The aim of this mechanism is to provide a wider bandwidth over which the power can be harvested. This thesis presents numerical solutions and approximate analytical solutions for the bandwidth and eective viscous damping of a non-linear device employing a hardening-type stiness. Unlike the linear system, in which the bandwidth is only dependent on the damping ratio, it is found that the bandwidth of the nonlinear device depends on both the strength of the nonlinearity and the damping ratio. Experimental results are presented to validate the theoretical results. This thesis also investigates the benets of the non-linear device for a low frequency and high amplitude application using the measured vibration inputs from human motion such as walking and running. The eect of harmonics on the power harvested is also studied. Numerical simulations are carried out using measured input vibrations from human motion to study the best placement of the natural frequency of the device across the range of harmonics.

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