En sciences et dans l’industrie pour limiter le nombre de maquettes expérimentales dans les projets R&D afin de mieux comprendre et de bien interpréter les phénomènes ultrasonores complexes observés sur site, des simulations de contrôles ultrasonores sont effectuées. Ces simulations sont d’autant plus réalistes que la description des structures à contrôler est précise, en particulier au niveau des constantes d’élasticité et d’atténuation intrinsèque. Les objectifs de cette étude sont d’améliorer d’une part les connaissances sur l’influence des caractéristiques métallurgiques des matériaux anisotropes et hétérogènes sur la propagation ultrasonore et d’autre part les performances des codes de calcul (logiciel ATHENA d’EDF) qui nécessitent de disposer des données d’entrée pertinentes, notamment en ce qui concerne les constantes d’élasticité et l’atténuation ultrasonore. Cette étude est dédiée à la caractérisation des matériaux à gros grains, comme les aciers austéno-ferritiques moulés par centrifugation et les soudures en acier inoxydable austénitique ou en alliages à base nickel. Un système expérimental unique permettant de mesurer les constantes d’élasticité et l’atténuation en incidence oblique à été mis au point. Le point fort de ce dispositif est qu’il permet de travailler au-delà de l’angle critique longitudinal et donc de mesurer les propriétés d’atténuation des ondes transversales. Les constantes d’élasticité sont déduites des vitesses ultrasonores à partir d’un processus d’optimisation basé sur la résolution de problème inverse. Nous avons montré les potentialités d’algorithmes d’optimisation globaux tels que les algorithmes génétiques moins susceptibles de converger vers des minima locaux de la fonction à minimiser. Les résultats obtenus à partir des mesures expérimentales sont en accord avec la littérature. Des résultats de l’atténuation des ondes longitudinales et transversales par décomposition du faisceau en spectre d’ondes planes sont présentés. / In industry, to limit the number of experimental models in R&D projects, to better understand and to well interpret the complex ultrasonic phenomena observed du ring controls on site, simulations of ultrasonic controls are carried out. These simulations are all the more realistic as the description of structures to control is accurate, especially in terms of elastic constants, and intrinsic attenuation. The objectives of this study are firstly to improve knowledge about the influence of the metallurgical properties of anisotropie and heterogeneous materials on the ultrasonic propagation and secondly the performance of the computation codes (software ATHENA EDF) which need to have the relevant inputs, particularly as regards the elastic constants and ultrasonic attenuation. This study is dedicated to the characterization of coarse materials such as austenitic-ferritic steel centrifugally cast and the welding in steel austenitic stainless or in alloy nickel-based. A unique experimental system for measuring the elastic constants and attenuation at oblique incidence has been developed. The strong point of this device is that it can work beyond the longitudinal critical angle and thus to measure the attenuation properties of transversal waves. The elastic constants are deduced from ultrasonic speed from an optimization process based on the resolution of Inverse problems. We have shown the potential of global optimization algorithms such as genetic algorithms Jess likely to converge to local minima of the function to minimize. The results obtained from experimental measurements are in agreement with literature. Results of the attenuation of the longitudinal and transverse waves by beam decomposition into spectrum of plane waves are represented.

[pt] Os efeitos das variações laterais de um terreno irregular na propagação de ondas eletromagnéticas são considerados pela representação dos campos vetoriais em termo de dois potenciais escalares Hertzianos em coordenadas esféricas. A combinação da equação parabólica para esses potenciais com uma condição de contorno de impedância para o solo, seguida por uma transformação de variáveis, define um problema de condição de contorno caracterizado por equações exibindo coeficientes que dependem da função altura do terreno e de suas derivadas parciais. A solução do problema através do esquema de Crank-Nicolson leva a um sistema esparso de equações lineares que é resolvido por um método direto. O modelo numérico resultante é aplicado a terrenos irregulares, representando configurações tridimensionais hipotéticas. / [en] The effects from lateral variations of irregular terrain on the propagation of radio waves are considered by the representation of the vector fields in terms of two scalar Hertz potentials in spherical coordinates. The combination of three-dimensional parabolic equations for these potentials with an impedance boundary condition for the ground, followed by a transformation of variables, will define a boundary-condition problem characterized by equations displaying coefficients that depend on the terrain height function and its partial derivatives. The problem solution through the Crank-Nicolson scheme will lead to a sparse system of linear equations, which will be solved by a direct method. The resulting numerical model will be applied to irregular terrain, representing hypothetical three-dimensional configurations.

<p>This thesis deals with the electromagnetic compatibility (EMC) problems of distributed electrical networks, especially that caused by lightning to electrified railway. Lightning transients were found to damage important devices that control train movements, causing traffic stoppage and delays. This thesis attempts to develop computational models for identification of parameters influencing the coupling phenomena between those devices and lightning. Some supporting experimental investigations are also carried out. This thesis forms the groundwork on the subject of lightning interaction with the electrified railway networks.</p><p>Lightning induces transient overvoltages in railway conductor systems such as tracks, overhead wires, and underground cables, either due to direct lightning strike to the system or due to the coupling of electromagnetic fields from remote strikes. Models based on multiconductor transmission line theory were developed for calculating the induced voltages and currents. A transmission line return stroke model, that can predict the remote electromagnetic fields comparable to experimental observations, is also developed. </p><p>Earlier works on modeling earth return impedances for transient studies in power distribution systems are not readily applicable for railways for lightning transients, in cases of low earth conductivities found in Sweden and for large variation in conductor heights. For the wires above ground, the ground impedance models were modified for wide range of frequencies, soil conductivities and wide spread of conductor heights. Influences of pole insulator flashovers, pole-footing soil ionizations and interconnections between the conductors on the lightning surge propagation are studied. Wave propagation in buried shielded and unshielded cables with ground return is studied. Simplified, valid and computationally efficient ground impedance expressions for buried and on-ground wires are proposed. A model for the coupling phenomena (transfer impedance) through multiple cable shields with multiconductor core is also proposed. Besides, experimental studies on lightning induced transients entering a railway technical house, failure modes of relay and rectifier units used in the train position/signaling applications for lightning transients are performed. A high frequency circuit model for the booster transformer for lightning interaction studies is developed. The simulation models are being converted to user-friendly software for the practicing engineers of the railway industry.</p>

In der Arbeit wird gezeigt, wie man die Bodensteifigkeit bei sehr kleinen Dehnungen sowie die Abnahme der Steifigkeit mit zunehmender Scherdehnung in Labor- und Feldversuchen ermitteln kann. Dazu werden typische Eigenschaften mineralischer und organischer Böden einschließlich Korrelationen zusammengestellt und wesentliche Unterschiede zum Bodenverhalten bei großen Dehnungen, insbesondere hinsichtlich der Steifigkeit und der Spannungsabhängigkeit aufgezeigt. Weiterhin wird dargelegt, wie man mit dem hypoplastischen Stoffgesetz mit intergranularen Dehnungen das Bodenverhalten bei kleinen Dehnungen wirklichkeitsnah erfassen kann und wie die Stoffparameter zu bestimmen sind. Für die realistische Erfassung des Bodenverhaltens infolge zyklischer Belastung einschließlich der Ausbildung von Hystereseschleifen wird eine Modifizierung des hypoplastischen Stoffgesetzes unter Einführung eines zusätzlichen Stoffparameters vorgenommen. Es wird gezeigt, wie dieser Parameter in zyklischen Laborversuchen bestimmt werden kann und wie damit die Akkumulation von Dehnungen bei drainierten Bedingungen bzw. von Porenwasserdrücken bei undrainierten Bedingungen zuverlässig prognostiziert werden kann. Anhand der dynamischen Beanspruchung eines Eisenbahndammes auf weichem, organischem Untergrund wird das modifizierte hypoplastische Stoffgesetz mit intergranularen Dehnungen für ein bodendynamisches Randwertproblem angewendet und gezeigt, dass damit das Bodenverhalten realistisch abgebildet werden kann. Die Berechnungsergebnisse zeigen eine gute Übereinstimmung mit Ergebnissen von Schwingungsmessungen und Langzeitverformungsmessungen. Es werden bodendynamische Berechnungen zur Wellenausbreitung sowohl eindimensional als auch im Halbraum mit unterschiedlichen Stoffgesetzen geführt und Vergleiche mit analytischen Lösungen vorgenommen. Dazu wird gezeigt, welche Anforderungen an numerische Berechnungen zur Wellenausbreitung, insbesondere hinsichtlich Wahl der Zeitschritte, Elementgröße bzw. Knotenabstände, Größe des FE-Netzes und Modellierung der FE-Ränder erforderlich sind. / In this thesis it is shown how to determine the soil stiffness at very small strains, as well as the decrease in stiffness with increasing shear strain amplitude in laboratory and field tests. Typical properties and empirical correlations of coarse-, fine-grained and organic soils are collected and significant differences in soil stiffness and stress-dependence at small strains compared to large strains are shown. Further it is shown how one can realistically reproduce the soil behaviour at small strains with the hypoplastic constitutive model with intergranular strains and how the material parameters are determined. For a realistic prediction of soil behaviour due to cyclic loading including hysteresis loops in the stress-strain relationship, a modification of the hypoplastic constitutive model is made by using an additional material parameter. It is shown how this additional parameter can be determined in cyclic laboratory tests and how the accumulation of strains in drained conditions and excess pore pressures built up in undrained conditions can be realistically reproduced. Based on the dynamic load on a railway embankment on soft marshy ground, the modified hypoplastic constitutive model with intergranular strains is applied for a boundary value problem. It is demonstrated, that the soil behaviour can be reproduced realistically. Numerical results show a good agreement with results of vibration measurements and measurements of permanent displacements. A dynamical numerical analysis is performed for both one-dimensional and half-space conditions. Different constitutive models have been applied and compared with analytical solutions. The results demonstrate requirements on numerical analysis of wave propagation, in particular with regards to time steps, element size, node spacing, size of the FE mesh and boundary conditions.

This thesis deals with the electromagnetic compatibility (EMC) problems of distributed electrical networks, especially that caused by lightning to electrified railway. Lightning transients were found to damage important devices that control train movements, causing traffic stoppage and delays. This thesis attempts to develop computational models for identification of parameters influencing the coupling phenomena between those devices and lightning. Some supporting experimental investigations are also carried out. This thesis forms the groundwork on the subject of lightning interaction with the electrified railway networks. Lightning induces transient overvoltages in railway conductor systems such as tracks, overhead wires, and underground cables, either due to direct lightning strike to the system or due to the coupling of electromagnetic fields from remote strikes. Models based on multiconductor transmission line theory were developed for calculating the induced voltages and currents. A transmission line return stroke model, that can predict the remote electromagnetic fields comparable to experimental observations, is also developed. Earlier works on modeling earth return impedances for transient studies in power distribution systems are not readily applicable for railways for lightning transients, in cases of low earth conductivities found in Sweden and for large variation in conductor heights. For the wires above ground, the ground impedance models were modified for wide range of frequencies, soil conductivities and wide spread of conductor heights. Influences of pole insulator flashovers, pole-footing soil ionizations and interconnections between the conductors on the lightning surge propagation are studied. Wave propagation in buried shielded and unshielded cables with ground return is studied. Simplified, valid and computationally efficient ground impedance expressions for buried and on-ground wires are proposed. A model for the coupling phenomena (transfer impedance) through multiple cable shields with multiconductor core is also proposed. Besides, experimental studies on lightning induced transients entering a railway technical house, failure modes of relay and rectifier units used in the train position/signaling applications for lightning transients are performed. A high frequency circuit model for the booster transformer for lightning interaction studies is developed. The simulation models are being converted to user-friendly software for the practicing engineers of the railway industry.

A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure.The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.

Die zerstörungsfreie Ultraschallprüfung von akustisch anisotropen Werkstoffen stellt auch heute noch eine Herausforderung dar. Die Gefügestruktur in solchen Materialien beeinflusst die Wellenausbreitung derart, dass es zum einen zu starken Streuungen durch die großflächigen Korngrenzen und zum anderen, aufgrund der akustischen Anisotropie, zu einer Richtungsabhängigkeit der Schallgeschwindigkeiten kommt. In den vergangenen Jahren wurden bereits Lösungsansätze zur mathematischen Modellierung der Schallausbreitung in anisotropen Materialien vorgestellt. Diese basieren in der Regel auf FEM- bzw. FIT- Algorithmen, die durch die Diskretisierung des gesamten Volumens einen hohen Rechenaufwand erfordern und in der täglichen Prüfpraxis aufgrund ihrer Komplexität bei der Parametrierung nur bedingt einsetzbar sind. Aus diesem Grund wird hier ein Ansatz zur Schallfeldberechnung gewählt, der auf die praktische Anwendung von Gruppenstrahler-Prüfköpfen zugeschnitten ist. Während sich andere Verfahren auf einzelne Wellenanteile und monofrequente Lösungen beschränken, um den Rechenaufwand zu reduzieren, können mit diesem Ansatz die reale Signalform des Prüfkopfes sowie alle auftretenden Wellenanteile in homogenen transversalisotropen Medien berücksichtigt werden. Durch entsprechende Optimierungen im Berechnungsalgorithmus lässt sich das gesamte vierdimensionale Schallfeld eines Gruppenstrahler-Prüfkopfes im Halbraum in kürzester Zeit berechnen. Die analytische Lösung der Wellengleichung für den Halbraum in Form einer Greenschen Funktion wird dabei in eine Gleichung umgeformt, die hier als vierdimensionale Punktrichtwirkung bezeichnet wird. Dieser Modellansatz ermöglicht es, die Parameter eines Gruppenstrahlersystems in der praktischen Anwendung zu überprüfen und durch iterative Rechnungen zu optimieren. Mit Hilfe einer einfach zu handhabenden Visualisierungstechnik ist es möglich diesen Modellansatz mit realen Schallfeldmessungen zu vergleichen. Dazu werden mit elektrodynamischen Sonden die einzelnen Komponenten des dreidimensionalen Vektors der Teilchenverschiebung an der Oberfläche von Festkörpern abgetastet. Die an den Messpunkten ermittelten Zeitfunktionen des Verschiebungsvektors werden dann dem berechneten Zeitverlauf der Wellenausbreitung gegenübergestellt. Die berechneten und gemessenen Schallfelder stimmen in der Phasenlage und im Amplitudenverlauf gut überein. Die Ergebnisse zeigen, dass mit dem verwendeten Rechenmodell alle in der Realität auftretenden Wellenanteile vollständig berücksichtigt werden und dreidimensionale Problemstellungen aus der Praxis mit diesem Modell korrekt berechnet werden können. / The non-destructive ultrasonic testing of acoustic anisotropic materials is an important challenge. The texture of these materials causes a strong scattering of the sound wave by the extensive grain boundaries and a direction dependent sound velocity by the acoustic anisotropy. Several approaches for the modelling of the sound propagation in anisotropic materials were presented in the last years. These approaches are normally based on FEM or FIT algorithms using a discretisation of the complete volume. Their calculation needs extensive time and a very complex parameterisation. Thus these algorithms are not suitable in practice of ultrasonic testing. In this work an approach is presented that is optimised for the application of phased array transducers. The new approach considers the real frequency spectrum of the transducer as well as all occurring wave modes in homogeneous transversely isotropic media, whereas other approaches are limited to solutions for single wave modes and single frequencies to reduce the calculation effort. The appropriate optimisations of the mathematical algorithm allow the fast calculation of the complete four-dimensional transient wave field of a phased array transducer in the half-space. The Green’s functions are derived by an analytical solution of the elastodynamic wave equation for the half-space. These functions will be transformed into an equation which will be referred to in this work as four-dimensional directivity pattern. This approach allows the verification of the parameters of a phased array system and their optimisation by iterative calculations in the practical application. To get accurate results in these calculations, the experimental verification of the applied mathematical model for the wave propagation is an essential task. The technique presented in this work applies electrodynamic probes, which provides a simple use. The probes can detect the particle displacement at a solid surface in all three spatial directions. The measured time-functions of the wave field will be compared with the calculated time-functions. They show a good accordance in the phase and the amplitude. This confirms that the applied mathematical model considers completely all in practice occurring wave modes. The results further show that three-dimensional problems in practice can be calculated correctly with this model.

Στην παρούσα εργασία παρουσιάζεται μια μέθοδος για την αριθμητική προσομοίωση δισδιάστατης, μη συνεκτικής ροής με ελεύθερη επιφάνεια, που προκύπτει από τη διάδοση κυμάτων βαρύτητας πάνω από πυθμένα με τυχαία μορφολογία. Η μέθοδος βασίζεται στην αριθμητική επίλυση των εξισώσεων Euler, που υπόκεινται σε πλήρως μη γραμμικές οριακές συνθήκες ελεύθερης επιφάνειας και κατάλληλες οριακές συνθήκες πυθμένα, εισόδου και εξόδου, χρησιμοποιώντας ένα υβριδικό σχήμα πεπερασμένων διαφορών και ψευδό-φασματικής μεθόδου. Οι εξισώσεις ροής μετασχηματίζονται έτσι ώστε τα όρια του υπολογιστικού πεδίου να είναι ανεξάρτητα του χρόνου. Η επαλήθευση της μεθόδου επίλυσης γίνεται με την εφαρμογή της στο πρόβλημα της κατανομής θερμοκρασίας σε λεπτή ορθογωνική πλάκα, υπό σταθερές συνθήκες. Για την ελαχιστοποίηση της ανάκλασης χρησιμοποιείται ζώνη απορρόφησης στην περιοχή απορροής. Η αποτελεσματικότητα της ζώνης απορρόφησης τεκμηριώνεται με την παρουσίαση αποτελεσμάτων προσομοίωσης διάδοσης γραμμικών κυματισμών σε πυθμένα σταθερού βάθους. Προκύπτει ότι η ζώνη απορρόφησης που βασίζεται στην επιβολή εξωτερικής δυναμικής πίεσης στην ελεύθερη επιφάνεια εμφανίζει την ελάχιστη ανάκλαση. Αποτελέσματα παρουσιάζονται για την προσομοίωση ροής με ελεύθερη επιφάνεια πάνω από πυθμένα σταθερής κλίσης 1:10 και 1:50, για διαφορετικά μήκη και ύψη κυμάτων εισόδου. Ο μετασχηματισμός των γραμμικών κυμάτων πάνω από την περιοχή σταθερής κλίσης συμφωνεί με τη θεωρία γραμμικής διασποράς για ροή με μικρά ύψη κύματος. Για μη γραμμικούς κυματισμούς, το μήκος κύματος μειώνεται πάνω από την περιοχή σταθερής κλίσης, ενώ η ανύψωση της ελεύθερης επιφάνειας αποκλίνει από την αρχική ημιτονοειδή μορφή και το ύψος κύματος αυξάνει λόγω της ρήχωσης. / A method for the numerical simulation of two-dimensional, inviscid, free-surface flow resulting from the propagation of regular gravity water waves over topography with arbitrary bottom shape is presented. The method is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid scheme of finite-differences and pseudo-spectral method. The formulation includes a boundary-fitted transformation. The validation of the pressure solver is accomplished by applying it to the two-dimensional, temperature, steady problem, under differing boundary conditions. For the free-surface flow, a wave absorption zone is attached at the outflow domain in order to minimize reflection effects. The absorption zone effectiveness is validated by the simulation of linear waves propagation over constant-depth bottom. Minimal reflection occurs when an appropriate external dynamic pressure is imposed on the free surface of the absorption zone. Results are presented for cases of wave propagation over constant slope bottom, with slopes 1:10 and 1:50, for various incoming wavelengths and wave heights. Over the bottom slope, lengths of waves in the linear regime are modified according to linear theory dispersion. For waves in the nonlinear regime, wave lengths are becoming shorter, while the free surface elevation deviates from its initial sinusoidal shape and the wave height increases due to shoaling.

This thesis focuses on the development of tools and methods dedicated for ultra wide band (UWB) localization systems in indoor environment. The thesis work was conducted within the European FP7 project Where2, about the cooperative localization in cellular networks. Data from a measurement campaign conduct during the project are used to validate the proposed algorithms. This thesis is divided in four parts : The first part is focused on the description of an original raytraing tool based on a graph description. In order to be compliant with the requirement of a mobile simulation, a new concept of rays signature enabling incremental computation, and a vectorized formalism for processing rays are described and implemented. The second part is focused on the indoor localization techniques, where a novel technique based on interval analysis approaches is presented and compared to alternative techniques. Advantageously using this approach, a specific processing based on an hypothesis testing method using received power observations to resolve ambiguities appearing in under determined localization problems is described. A third part describes different aspects of the dynamic platform. In particular a realistic mobility model based on ''steering behaviors'', a graph description of the network scene and an inter agents communication protocol are detailed. The fourth section uses measured data obtained from an heterogeneous measurement campaign to validate both the developed software platform and the proposed localization algorithms.

In this work passive piezoelectric devices for vibration damping are studied. It is developed the basic idea of synthesizing electrical wave guides to obtain an optimal electro-mechanical energy exchange and therefore to dissipate the mechanical vibrational energy in the electric form. Modular PiezoElectroMechanical (PEM) structures are constituted by continuous elastic beams (or bars) coupled, by means of an array of PZT transducers, to lumped dissipative electric networks. Both refined and homogenized models of those periodic systems are derived by an energetic approach based on the principle of virtual powers. Weak and strong formulation of the dynamical problem are presented having in mind future studies involving the determination of numerical solutions. In this framework the effectiveness of the proposed devices for the suppression of mechanical vibrations is investigated by a wave approach, considering both the extensional and flexural oscillations. The optimal values of the electric parameters for a fixed network topology are derived analytically by a pole placement technique. Their sensitivities on the dimensions of the basic cell of the periodic system and on the design frequency are studied. Moreover the dependence of damping performances on the frequency is analyzed. Comparing the performances of different network topological configurations, the advantages of controlling a mechanical structure with an electric analog are shown. As a consequence of those results, new interconnections of PZT transducers are proposed. An experimental setup for the validation of the analytical and numerical results is proposed and tested. A classical experience on resonant shunted PZT is reproduced. Future experimental work is programmed.