Dans le cadre des applications sans fil à 60GHz, l’amplificateur de puissance reste un des composants les plus compliqués à implémenter en technologie CMOS. Des modulations à enveloppe non constante obligent à concevoir des circuits hautement linéaires, conduisant à une consommation statique importante. La recherche de topologies et de techniques de linéarisation viables aux fréquences millimétriques fait l’objet de cette thèse. Dans un premier temps, un état de l’art des différents amplificateurs de puissance à 60GHz est dressé, afin d’en extraire l’ensemble des verrous technologiques limitant leurs performances. Suite à l’analyse des phénomènes physiques impactant les composants passifs, plusieurs structures d’amplificateurs élémentaires sont conçues dans les technologies 65nm et 28nm Bulk. Les topologies les plus pertinentes sont déduites de cette étude. Enfin, deux amplificateurs intégrant des techniques de combinaison de puissance et de linéarisation sont implémentés dans les technologies 65nm et 28nm FD-SOI. Ces deux circuits présentent les plus hauts facteurs de mérite ITRS publiés à ce jour. Le circuit en 28nm FD-SOI atteint en outre le meilleur compromis linéarité/consommation de l’état de l’art. / The CMOS 60GHz power amplifier (PA) remains one of the most design-challenging components. Indeed, a high linearity associated with a large back-off range are required due to complex modulated signals.In this context, this work focuses on the design of architectures and linearization techniques which are usable at millimeter-wave frequencies. First, a CMOS PA state of the art is presented to define all bottlenecks. Then, the physical phenomena impacting on passive device performances are described. Elementary PAs are implemented in CMOS 65nm and 28nm Bulk and the most suitable topologies are selected. Finally, two highly linear circuits are designed in 65nm Bulk and 28nm FD-SOI. They achieve the highest ITRS figures of merit reported to this day. In addition, the 28nm FD-SOI PA exhibits the best linearity/consumption tradeoff.

Accurate determination of the pressure losses at the bit is very important for drilling practices in petroleum industry. In the literature, there are several studies on determination of the pressure losses. Major focus is concentrated on single phase drilling fluids, which is far from accurate estimation of pressure losses for multiphase fluids, i.e., fluids including a liquid and a gas phase, at the bit. Some of these models are valid for multiphase fluids, however, they are either valid for very high gas flow rates, or developed using very strong assumptions. This study presents a mathematical model for calculating bit hydraulics for gasified drilling fluids. The theory, which is valid for both sonic (critical) and subsonic (sub-critical) regimes, is based on the solution of the general energy equation for compressible fluid flow. The model is sensitive to changes in internal energy, temperature and compressibility. In addition, the model uses &ldquo / mixture sound velocity&rdquo / approach. A computer program is developed based on the proposed mathematical model. The program calculates pressure drop through a nozzle in subsonic flow region, and suggest flow rate if the calculated pressure drop values is in the sonic flow pressure ranges. The program has been run at reasonable field data. The results of the models have been compared with the results of existing models in the literature. The results show that the pressure losses through the bit can be estimated with a variation less than 9%. Also, it has been observed that bottom hole pressure, velocity of the liquid phase and nozzle size have a strong influence on bit pressure drop.

This diploma thesis is about creating a program to model turbulent cells of different sizes on the chosen transmission path. The initial part of the work is devoted to the formation of atmospheric turbulence and the mathematical description of the extent of turbulence and its effect on optical waves. The methods of the turbulence generation and their physical description of formation are described below. The practical part is devoted to the created program in the MATLAB.

O desenvolvimento deste trabalho foi motivado pela alta demanda de novas aplicações para o mercado do consumidor que necessitam de sistemas de transmissão e recepção de dados sem fio trabalhando na região de ondas milimétricas (mmW - entre 30 GHz e 300 GHz). Para estes tipos de sistemas, os defasadores são cruciais por definir o custo e o tamanho do dispositivo final. A pesquisa bibliográfica mostra que a melhor opção são os defasadores passivos do tipo linha carregada que utilizam Sistemas Microeletromecânicos (MEMS) como elemento de ajuste para a mudança de fase. Por esse motivo neste trabalho foi feito o estudo de diferentes tecnologias para o desenvolvimento de defasadores baseados em MEMS distribuídos e linhas de transmissão com efeito de ondas lentas de tipo shielded-CoPlanar Stripline (S-CPS) e shielded-Coplanar Waveguide (S-CPW). Foram estudadas três diferentes tecnologias: a tecnologia CMOS; a tecnologia dedicada desenvolvida pelo Laboratoire d\'électronique des technologies de l\'information (CEA-Leti) e a tecnologia in-house desenvolvida no Laboratório de Microeletrônica da Universidade de São Paulo. Utilizando a tecnologia CMOS foram fabricadas linhas de transmissão de tipo S-CPS utilizando a tecnologia de 250 nm da IHP (Innovations for High Performance Microelectronics) e a tecnologia de 0,35 µm da AMS (Austria Micro Systems). A tecnologia de 0,35 µm da AMS foi utilizada também para o desenvolvimento de defasadores de 2-bits e 3-bits baseados em linhas de transmissão de tipo S-CPW. Para estes defasadores foi definido um processo de liberação da camada de blindagem, reprodutível, que permitiu a atuação do dispositivo. Outros defasadores baseados em S-CPW que foram desenvolvidos anteriormente com a tecnologia dedicada CEA-LETI, foram modelados eletrostaticamente utilizando o Comsol MultiPhysics e o Ansys Workbench. Os modelos desenvolvidos permitiram entender o comportamento eletromecânico do defasador e foram utilizados reprojetar o defasador com um desempenho otimizado. Finalmente, visando o desenvolvimento dos dispositivos otimizados utilizando a tecnologia in house com os materiais e métodos disponíveis no Laboratório de Microeletrônica da USP (LME-USP), foram estudadas algumas etapas críticas do processo de fabricação. / The development of this work is motivated by the high demand for new applications for the consumer market that require wireless systems for data transmission and reception working in the millimeter wave region (mmW - between 30 GHz and 300 GHz). For these kinds of systems, the phase shifter are crucial to define the cost and size of the final device. The bibliographical research shows that the best option are the passive load line-type phase shifters using Microelectromechanical Systems (MEMS) as tuning element. Therefore, in this work, the study of different technologies for the development of phase shifter based on distributed MEMS and slow-wave transmission lines. The two types of transmission lines considered were the shielded-CoPlanar Stripline (S-CPS) and shielded-Coplanar Waveguide line (S-CPW). Three different technologies were studied: CMOS technology; the dedicated technology developed by the Laboratoire d\'électronique des technologies de l\'information (CEA-Leti) and the in-house technology developed at the Microelectronics Laboratory of the University of São Paulo. Using the CMOS technology, S-CPS-type transmission lines were fabricated using IHP\'s 250 nm CMOS technology and AMS\'s 0.35 µm CMOS technology. AMS\'s 0.35 µm technology has also been used for the development of 2-bit and 3-bit phase-shifters based on S-CPW type transmission lines. For these phase shifters, a reproducible shielding layer release process was defined that allowed the device to operate. Also, another phase shifter based in S-CPW-type transmission lines that were previously developed with dedicated CEA-LETI technology was electrostatically modeled using Comsol MultiPhysics and Ansys Workbench. The developed models allowed to understand the electromechanical behavior of the phase shifter and was used for a new design of the phase shifter with an optimized performance. Finally, in order to develop the optimized devices using the in-house technology with the materials and methods available at the USP Microelectronics Laboratory (LME-USP), some critical stages of the fabrication process were studied.

O desenvolvimento deste trabalho foi motivado pela alta demanda de novas aplicações para o mercado do consumidor que necessitam de sistemas de transmissão e recepção de dados sem fio trabalhando na região de ondas milimétricas (mmW - entre 30 GHz e 300 GHz). Para estes tipos de sistemas, os defasadores são cruciais por definir o custo e o tamanho do dispositivo final. A pesquisa bibliográfica mostra que a melhor opção são os defasadores passivos do tipo linha carregada que utilizam Sistemas Microeletromecânicos (MEMS) como elemento de ajuste para a mudança de fase. Por esse motivo neste trabalho foi feito o estudo de diferentes tecnologias para o desenvolvimento de defasadores baseados em MEMS distribuídos e linhas de transmissão com efeito de ondas lentas de tipo shielded-CoPlanar Stripline (S-CPS) e shielded-Coplanar Waveguide (S-CPW). Foram estudadas três diferentes tecnologias: a tecnologia CMOS; a tecnologia dedicada desenvolvida pelo Laboratoire d\'électronique des technologies de l\'information (CEA-Leti) e a tecnologia in-house desenvolvida no Laboratório de Microeletrônica da Universidade de São Paulo. Utilizando a tecnologia CMOS foram fabricadas linhas de transmissão de tipo S-CPS utilizando a tecnologia de 250 nm da IHP (Innovations for High Performance Microelectronics) e a tecnologia de 0,35 µm da AMS (Austria Micro Systems). A tecnologia de 0,35 µm da AMS foi utilizada também para o desenvolvimento de defasadores de 2-bits e 3-bits baseados em linhas de transmissão de tipo S-CPW. Para estes defasadores foi definido um processo de liberação da camada de blindagem, reprodutível, que permitiu a atuação do dispositivo. Outros defasadores baseados em S-CPW que foram desenvolvidos anteriormente com a tecnologia dedicada CEA-LETI, foram modelados eletrostaticamente utilizando o Comsol MultiPhysics e o Ansys Workbench. Os modelos desenvolvidos permitiram entender o comportamento eletromecânico do defasador e foram utilizados reprojetar o defasador com um desempenho otimizado. Finalmente, visando o desenvolvimento dos dispositivos otimizados utilizando a tecnologia in house com os materiais e métodos disponíveis no Laboratório de Microeletrônica da USP (LME-USP), foram estudadas algumas etapas críticas do processo de fabricação. / The development of this work is motivated by the high demand for new applications for the consumer market that require wireless systems for data transmission and reception working in the millimeter wave region (mmW - between 30 GHz and 300 GHz). For these kinds of systems, the phase shifter are crucial to define the cost and size of the final device. The bibliographical research shows that the best option are the passive load line-type phase shifters using Microelectromechanical Systems (MEMS) as tuning element. Therefore, in this work, the study of different technologies for the development of phase shifter based on distributed MEMS and slow-wave transmission lines. The two types of transmission lines considered were the shielded-CoPlanar Stripline (S-CPS) and shielded-Coplanar Waveguide line (S-CPW). Three different technologies were studied: CMOS technology; the dedicated technology developed by the Laboratoire d\'électronique des technologies de l\'information (CEA-Leti) and the in-house technology developed at the Microelectronics Laboratory of the University of São Paulo. Using the CMOS technology, S-CPS-type transmission lines were fabricated using IHP\'s 250 nm CMOS technology and AMS\'s 0.35 µm CMOS technology. AMS\'s 0.35 µm technology has also been used for the development of 2-bit and 3-bit phase-shifters based on S-CPW type transmission lines. For these phase shifters, a reproducible shielding layer release process was defined that allowed the device to operate. Also, another phase shifter based in S-CPW-type transmission lines that were previously developed with dedicated CEA-LETI technology was electrostatically modeled using Comsol MultiPhysics and Ansys Workbench. The developed models allowed to understand the electromechanical behavior of the phase shifter and was used for a new design of the phase shifter with an optimized performance. Finally, in order to develop the optimized devices using the in-house technology with the materials and methods available at the USP Microelectronics Laboratory (LME-USP), some critical stages of the fabrication process were studied.

L’objectif de ce travail est de concevoir et de caractériser un front-end millimétriqueutilisant des lignes de propagation à ondes lentes S-CPW optimisées en technologies CMOS avancées.Ces lignes présentant des facteurs de qualité 2 à 3 fois supérieurs à ceux des lignes classiques de typemicroruban ou CPW.Dans le premier chapitre, l’impact de l’évolution des noeuds technologiques CMOS sur lesperformances des transistors MOS aux fréquences millimétriques et sur les lignes de propagation ainsiqu’un état de l’art concernant les performances des front-end sont présentés. Le deuxième chapitreconcerne la réalisation des lignes S-CPW dans différentes technologies CMOS et la validation d’unmodèle phénoménologique électrique équivalent. Le troisième chapitre est dédié à la conceptiond’amplificateurs de puissance à 60 GHz utilisant ces lignes S-CPW en technologies CMOS 45 et65 nm. Cette étude a permis de mettre en évidence l’apport des lignes à ondes lentes aux performancesdes amplificateurs de puissance fonctionnant dans la gamme des fréquences millimétriques. Uneméthode de conception basée sur les règles d’électro-migration et permettant une optimisation desperformances a été développée. Finalement, un amplificateur faible bruit et un commutateur d’antennetravaillant à 60 GHz et à base de lignes S-CPW ont été conçus en technologie CMOS 65 nm afin degénéraliser l’impact de ce type de lignes sur les performances des front-end millimétriques. / The objective of this work is to design and characterize a millimeter-wave front-end usingthe optimized slow-wave transmission lines S-CPW in advanced CMOS technologies. The qualityfactor of these transmission lines is twice to three times higher than that of the conventionaltransmission lines such as microstrip lines and coplanar waveguides.In the first chapter, the influence of CMOS scaling-down on the performance of transistors atmillimeter-wave frequencies and on the transmission lines was studied. In addition, a state of the artwith regard to the performance of the front-end was presented. The second chapter concerns about therealization of the S-CPW lines in different CMOS technologies and the validation of an electricalequivalent model. The third chapter is dedicated to the design of 60-GHz power amplifiers using theseS-CPW lines in CMOS 45 and 65 nm technologies. This study highlighted the performanceenhancement of power amplifiers operating at millimeter-wave frequencies by using the slow-wavetransmission lines. A design method based on the electro-migration rules was also developed. Finally,a low noise amplifier and an antenna switch operating at 60 GHz were designed in CMOS 65 nm inorder to generalize the impact of such transmission lines on the performance of the millimeter-wavefront-end.

Ce travail de thèse s’inscrit dans la recherche des solutions économiquementviables pour des réseaux personnels à hauts débits (plusieurs Gbps à plusieursdizaines de Gbps) opérationnels en bande millimétrique autour de 60 GHz. Aucas où ces réseaux servent un nombre élevé d’utilisateurs, ils comprendront unemultitude d’antennes afin d’assurer l’accès sans fil rapide. Afin de réduire aumaximum le coût d’un module d’antenne, les réseaux doivent fournir un signalanalogue à des porteuses millimetriques. Une solution prometteuse pour les systèmesde distribution qui correspond à ces besoins sont des structures à fibreoptique, laquelle permet une transmission à faibles pertes et à haute bande passante.On parle de l’approche "radio-sur-fibre" (en anglais, radio-over-fiber). Laproblématique est de pouvoir générer et moduler un signal aux fréquences millimétriqueslors de la transmission optique - et ce avec des composant bas coûts.La technique utilisée dans le cadre de cette thèse est l’emploi des diodes laser àverrouillage de modes. Ces derniers vont pouvoir générer des hautes fréquencestout en ne nécessitant qu’une alimentation continue, et ils peuvent être modulésde manière directe ou externe. Les lasers à semi-conducteurs employés ici sontd’une génération encore à l’état d’étude puisqu’il s’agit des lasers à boites (ouîlots) quantiques. Ces lasers ont montrés de très bonnes capacités à générer dessignaux électriques aux fréquences autour de 60 GHz, bien qu’ayant encore, pourl’instant, à une stabilité de fréquence (ou de phase) limitée. Dans le cadre des systèmesde communication opto/micro-ondes, peu de travaux approfondis ont étémenés sur ces structures.Au cours de cette thèse, plusieurs études ont été effectuées. La première portesur les propriétés générales d’un système construit à partir de ce type de laser(puissances disponibles, figure de bruit, linéarité etc.). Une deuxième étude aété consacrée aux effets de la propagation des signaux dans les systèmes baséssur les lasers à verrouillage de modes, notamment de la dispersion chromatiquelaquelle a un effet considérable sur les distances de transmission. Les deux étudesmettent en avant l’importance d’une limitation du nombre de modes générés parla diode laser afin d’optimiser non seulement le gain du lien et la puissance RFrécupérée, mais aussi la figure de bruit du système. Lors d’une troisième étude, lastabilité en fréquence/phase s’est révélée critique, car le bruit de fréquence/phaselimite la qualité de la transmission en introduisant un plancher d’erreur mêmepour des rapports signal-a-bruit très élevés. Des différentes générations de lasersà boites (îlots) quantiques et à verrouillage de modes ont été testées. Le problèmedu bruit de fréquence et de phase persiste et ne peut pas être résolu en utilisantles techniques classiques comme les boucles à verrouillage de phase conventionnelles.Une solution pour ce problème a été développée pour les systèmes detransmission; elle permet simultanément un ajustement de fréquence supérieure(précision de quelques Hz à quelques kHz) à celle donnée par le processus de fabricationdes diodes lasers (précision de quelques GHz), ainsi qu’une stabilisationde fréquence et de phase. / This dissertation is related to the search for an economically sustainable solutionfor high data rate (several Gbps to several tens of Gbps) personal area networksoperating in the millimeter-wave region around 60 GHz. If such networks supplya large number of users, they need to encompass a multitude of antenna pointsin order to assure wireless access to the network. With the aim of reducing thecost of an antenna module, the networks should at best provide quasi "readyto-radiate" signals to the modules, i.e. at millimeter-wave carrier frequencies.Thanks to their low transmission loss and their high bandwidth, optical fiber distributionarchitectures represent a promising solution. The technique is referredto as the so-called "radio-over-fiber" approach whereby the analog radio signalwill be transported to the access point by an optical wave. The challenge herebyis the generation and modulation of an optical signal by a millimeter-wave radiosignal using preferably cost-efficient system components. The technique proposedherein is based on the use of mode-locked laser diodes which can generatesignals at very high frequencies under the condition of continuous current supply.Mode-locked laser diodes can be modulated both directly and externally. Thediodes employed in this work are based on so-called quantum dots (or quantumdashes); these are material structures which are themselves still subject to intensivephysical research. Signals at millimeter-wave frequencies (around 60 GHz)can easily be generated by such lasers. However, their frequency and phase stabilityis as yet limited. In the context of radio-over-fiber communication systems,these structures have not yet been studied in detail.In the course of this dissertation, several aspects are considered. A first systemstudy treats the basic properties of a system built from this type of laser source(available signal power, system noise figure, linearity etc.). A second study isdevoted to an investigation of propagation effects like dispersion, which considerablyinfluence the attainable transmission distances. An essential result of bothstudies is the importance of limiting the laser spectrum to a small number of lasermodes for an optimization of link gain, generated RF power, and system noisefigure. A third study deals with the limited frequency and phase stability whichturn out to be critical factors for transmission quality. The study of several generationsof quantum dot/dash lasers has revealed that the problems of frequencyand phase noise persist and cannot be solved using classical techniques involvinge.g. conventional phase-locked loops. In this dissertation, a solution is presentedwhich not only allows a more precise adjustment of the laser frequency (precisionin the order of Hz to kHz) than that given by the manufacturing process of thelaser (precision in the order of GHz), but also enables a stabilization of frequencyand phase. / Die vorliegende Dissertation steht im Zusammenhang mit der Suche nach wirtschaftlichtragfähigen Lösungen zum Aufbau hochdatenratiger Heimnetzwerke(einige Gbps bis einige zehn Gbps), so genannter Personal area-Netzwerke imMillimeterwellenbereich um 60 GHz. Sollen diese Netze eine große Anzahl vonNutzern versorgen, wird eine Vielzahl von Zugangspunkten - also Antennenmodulen- benötigt, um den drahtlosen Netzanschluss zu ermöglichen. Um dieKosten eines Antennenmoduls soweit wie möglich zu senken, sollen die Netzequasi "abstrahlfertige" Signale an die Module liefern, d. h. auf Trägerfrequenzenim Millimeterwellenbereich. Glasfaserbasierte Verteilsysteme werden dankihrer geringen Leitungsverluste und ihrer hohen Bandbreite diesem Anspruchgerecht. Man spricht hier vom so genannten Radio-over-fiber-Ansatz, wobei dasanaloge Signal von einer optischen Welle zum Zugangspunkt transportiert wird.Die Herausforderung liegt hierbei in der Generierung und Modulation eines optischenSignals mit einem Nutzsignal imMillimeterwellenbereich - und das unterVerwendung möglichst kostengünstiger Komponenten. Die hier vorgeschlageneTechnik basiert auf der Nutzung von modengekoppelten Laserdioden, welcheallein bei Gleichstromversorgung Signale bei hohen Frequenzen erzeugen undsowohl direkt als auch extern moduliert werden können. Die Dioden, welche hierzur Verwendung kommen, basieren auf so genannten Quantenpunkten (englisch:quantum dot/quantum dash); es sind Strukturen, die selbst noch Gegenstand intensiverphysikalischer Forschung sind. Signale bei Frequenzen um 60 GHz könnenleicht von diesen Lasern erzeugt werden, wenn auch bisher nur bei begrenzterFrequenz- und Phasenstabilität. Im Kontext von Radio-over-fiber-Systemenwurden diese Strukturen noch nicht untersucht.Im Rahmen dieser Dissertation wurden mehrere Aspekte betrachtet. Eine ersteSystemstudie behandelt die grundlegendenEigenschaften eines Systems, welchesauf dieser Art von Lasern basiert (verfügbare Leistung, Rauschzahl, Linearitätusw.). Eine zweite Untersuchung ist der Erforschung von Ausbreitungseffektenwie etwa Dispersion gewidmet, welche die erreichbaren Entfernungen maßgeblichbeeinflusst. Ein wesentliches Ergebnis beider Studien ist die Relevanzeiner Begrenzung des Laserspektrums auf wenige Moden zur Optimierung vonGewinn, Hochfrequenz-Leistung und Rauschzahl. Eine dritte Studie untersuchtdie Frequenz-und die Phasenstabilität, welche sich als kritisch für die Übertragungsqualitäterweisen. Die Untersuchung von mehreren Generationen von modengekoppeltenQuantenpunktlasern hat ergeben, dass das Problem des FrequenzundPhasenrauschens fortbesteht und nicht auf konventionellem Weg wie z.B.durch die Verwendung von klassischen Phasenregelkreisen gelöst werden kann.Im Rahmen der Arbeit wurde eine Lösung für dieses Problem gefunden, welcheerstens eine bessere Feineinstellung der Frequenz erlaubt (Genauigkeit von Hzbis kHz), als sie durch den Laserfertigungsprozess gegeben ist (Genauigkeit vonGHz), und zweitens eine Stabilisierung von Frequenz und Phase ermöglicht.

Dans ce travail, nous avons introduit le concept sous-jacent de PUFEM et la formulation de base lié à l'équation de Helmholtz dans un domaine borné. Le processus d'enrichissement de l'onde plane de variables PUFEM a été montré et expliqué en détail. L'idée principale est d'inclure une connaissance a priori sur le comportement local de la solution dans l'espace des éléments finis en utilisant un ensemble de fonctions d'onde qui sont des solutions aux équations aux dérivées partielles. Dans cette étude, l'utilisation des ondes planes se propageant dans différentes directions a été favorisée car elle conduit à des algorithmes de calcul efficaces. En outre, nous avons montré que le nombre de directions d'ondes planes dépend de la taille de l'élément PUFEM et la fréquence des ondes à la fois en 2D et 3D. Les approches de sélection de ces ondes planes sont également illustrés. Pour les problèmes 3D, nous avons étudié deux systèmes de distribution des directions d'ondes planes qui sont la méthode du cube discrétisé et la méthode de la force de Coulomb. Il a été montré que celle-ci permet d'obtenir des directions d'onde espacées de façon uniforme et permet d'obtenir un nombre arbitraire d'ondes planes attachées à chaque noeud de l'élément de PUFEM, ce qui rend le procédé plus souple.Dans le chapitre 3, nous avons étudié la simulation numérique des ondes se propageant dans deux dimensions en utilisant PUFEM. La principale priorité de ce chapitre est de venir avec un schéma d'intégration exacte (EIS), résultant en un algorithme d'intégration rapide pour le calcul de matrices de coefficients de système avec une grande précision. L'élément 2D PUFEM a ensuite été utilisé pour résoudre un problème de transmission acoustique impliquant des matériaux poreux. Les résultats ont été vérifiés et validés par la comparaison avec des solutions analytiques. Les comparaisons entre le régime exact d'intégration (EIS) et en quadrature de Gauss ont montré le gain substantiel offert par l'EIE en termes de temps CPU.Une 3D exacte Schéma d'intégration a été présenté dans le chapitre 4, afin d'accélérer et de calculer avec précision (jusqu'à la précision de la machine) des intégrales très oscillatoires découlant des coefficients de la matrice de PUFEM associés à l'équation 3D Helmholtz. Grâce à des tests de convergence, un critère de sélection du nombre d'ondes planes a été proposé. Il a été montré que ce nombre ne pousse que quadratiquement avec la fréquence qui donne lieu à une réduction drastique du nombre total de degrés de libertés par rapport au FEM classique. Le procédé a été vérifié pour deux exemples numériques. Dans les deux cas, le procédé est représenté à converger vers la solution exacte. Pour le problème de la cavité avec une source de monopôle située à l'intérieur, nous avons testé deux modèles numériques pour évaluer leur performance relative. Dans ce scénario, où la solution exacte est singulière, le nombre de directions d'onde doit être choisie suffisamment élevée pour faire en sorte que les résultats ont convergé.Dans le dernier chapitre, nous avons étudié les performances numériques du PUFEM pour résoudre des champs sonores intérieurs 3D et des problèmes de transmission d'ondes dans lequel des matériaux absorbants sont présents. Dans le cas particulier d'un matériau réagissant localement modélisé par une impédance de surface. Un des critères d'estimation d'erreur numérique est proposé en considérant simplement une impédance purement imaginaire qui est connu pour produire des solutions à valeur réelle. Sur la base de cette estimation d'erreur, il a été démontré que le PUFEM peut parvenir à des solutions précises tout en conservant un coût de calcul très faible, et seulement environ 2 degrés de liberté par longueur d'onde ont été jugées suffisantes. Nous avons également étendu la PUFEM pour résoudre les problèmes de transmission des ondes entre l'air et un matériau poreux modélisé comme un fluide homogène équivalent. / In this work, we have introduced the underlying concept of PUFEM and the basic formulation related to the Helmholtz equation in a bounded domain. The plane wave enrichment process of PUFEM variables was shown and explained in detail. The main idea is to include a priori knowledge about the local behavior of the solution into the finite element space by using a set of wave functions that are solutions to the partial differential equations. In this study, the use of plane waves propagating in various directions was favored as it leads to efficient computing algorithms. In addition, we showed that the number of plane wave directions depends on the size of the PUFEM element and the wave frequency both in 2D and 3D. The selection approaches for these plane waves were also illustrated. For 3D problems, we have investigated two distribution schemes of plane wave directions which are the discretized cube method and the Coulomb force method. It has been shown that the latter allows to get uniformly spaced wave directions and enables us to acquire an arbitrary number of plane waves attached to each node of the PUFEM element, making the method more flexible.In Chapter 3, we investigated the numerical simulation of propagating waves in two dimensions using PUFEM. The main priority of this chapter is to come up with an Exact Integration Scheme (EIS), resulting in a fast integration algorithm for computing system coefficient matrices with high accuracy. The 2D PUFEM element was then employed to solve an acoustic transmission problem involving porous materials. Results have been verified and validated through the comparison with analytical solutions. Comparisons between the Exact Integration Scheme (EIS) and Gaussian quadrature showed the substantial gain offered by the EIS in terms of CPU time.A 3D Exact Integration Scheme was presented in Chapter 4, in order to accelerate and compute accurately (up to machine precision) of highly oscillatory integrals arising from the PUFEM matrix coefficients associated with the 3D Helmholtz equation. Through convergence tests, a criteria for selecting the number of plane waves was proposed. It was shown that this number only grows quadratically with the frequency thus giving rise to a drastic reduction in the total number of degrees of freedoms in comparison to classical FEM. The method has been verified for two numerical examples. In both cases, the method is shown to converge to the exact solution. For the cavity problem with a monopole source located inside, we tested two numerical models to assess their relative performance. In this scenario where the exact solution is singular, the number of wave directions has to be chosen sufficiently high to ensure that results have converged. In the last Chapter, we have investigated the numerical performances of the PUFEM for solving 3D interior sound fields and wave transmission problems in which absorbing materials are present. For the specific case of a locally reacting material modeled by a surface impedance. A numerical error estimation criteria is proposed by simply considering a purely imaginary impedance which is known to produce real-valued solutions. Based on this error estimate, it has been shown that the PUFEM can achieve accurate solutions while maintaining a very low computational cost, and only around 2 degrees of freedom per wavelength were found to be sufficient. We also extended the PUFEM for solving wave transmission problems between the air and a porous material modeled as an equivalent homogeneous fluid. A simple 1D problem was tested (standing wave tube) and the PUFEM solutions were found to be around 1% error which is sufficient for engineering purposes.

Wave propagation is a phenomenon resulting from high transient loadings where the duration of the load is in µ seconds range. In aerospace and space craft industries it is important to gain knowledge about the high frequency characteristics as it aids in structural health monitoring, wave transmission/attenuation for vibration and noise level reduction. The wave propagation problem can be approached by the conventional Finite Element Method(FEM); but at higher frequencies, the wavelengths being small, the size of the finite element is reduced to capture the response behavior accurately and thus increasing the number of equations to be solved, leading to high computational costs. On the other hand such problems are handled in the frequency domain using Fourier transforms and one such method is the Spectral Finite Element Method(SFEM). This method is introduced first by Doyle ,for isotropic case and later popularized in developing specific purpose elements for structural diagnostics for inhomogeneous materials, by Gopalakrishnan. The general approach in this method is that the partial differential wave equations are reduced to a set of ordinary differential equations(ODEs) by transforming these equations to another space(transformed domain, say Fourier domain). The reduced ODEs are usually solved exactly, the solution of which gives the dynamic shape functions. The interpolating functions used here are exact solution of the governing differential equations and hence, the exact elemental dynamic stiffness matrix is derived. Thus, in the absence of any discontinuities, one element is sufficient to model 1-D waveguide of any length. This elemental stiffness matrix can be assembled to obtain the global matrix as in FEM, but in the transformed space. Thus after obtaining the solution, the original domain responses are obtained using the inverse transform. Both the above mentioned manuscripts present the Fourier transform based spectral finite element (FSFE), which has the inherent aliasing problem that is persistent in the application of the Fourier series/Fourier transforms. This is alleviated by using an additional throw-off element and/or introducing slight damping in to the system. More recently wave let transform based spectral finite element(WSFE) has been formulated which alleviated the aliasing problem; but has a limitation in obtaining the frequency characteristics, like the group speeds are accurate only up-to certain fraction of the Nyquist(central frequency). Currently in this thesis Laplace transform based spectral finite elements(LSFE) are developed for sandwich members. The advantages and limitations of the use of different transforms in the spectral finite element framework is presented in detail in Chapter-1. Sandwich structures are used in the space craft industry due to higher stiffness to weight ratio. Many issues considered in the design and analysis of sandwich structures are discussed in the well known books(by Zenkert, Beitzer). Typically the main load bearing structures are modeled as beam sand plates. Plate structures with kh<1 is analysed based on the Kirch off plate theory/Classical Plate Theory(CPT) and when the bending wavelength is small compared to the plate thickness, the effect of shear deformation and rotary inertia needs to be included where, k is the wave number and h is the thickness of the plate. Many works regarding the wave propagation in sandwich structures has been published in the past literature for wave propagation in infinite sandwich structure and giving the complete description of dispersion relation with no restriction on frequency and wavelength. More recently exact analytical solution or simply supported sandwich plate has been derived. Also it is seen by comparison of dispersion curves obtained with exact (3D formulation of theory of elasticity) and simplified theories (2D formulation as generalization of Timoshenko theory) made on infinite domain and concluded that the simplified theory can be reliably used to assess the waveguide properties of sandwich plate in the frequency range of interest. In order to approach the problems with finite domain and their implementation in the use of general purpose code; finite degrees of freedom is enforced. The concept of displacement based theories provides the flexibility in assuming different kinematic deformations to approach these problems. Many of the displacement based theories incorporate the Equivalent Single Layer(ESL) approach and these can capture the global behavior with relative ease. Chapter-2 presents the Laplace spectral finite element for thick beams based on the First order Shear Deformation Theory (FSDT). Here the effect of different choices of the real part of the Laplace variable is demonstrated. It is shown that the real part of the Laplace variable acts as a numerical damping factor. The spectrum and dispersion relations are obtained and the use of these relations are demonstrated by an example. Here, for sandwich members based on FSDT, an appropriate choice of the correction factor ,which arises due to the inconsistency between the kinematic hypothesis and the desired accuracy is presented. Finally the response obtained by the use of the element is validated with experimental results. For high shock loading cases, the core flexibility induces local effects which are very predominant and this can lead to debonding of face sheets. The ESL theories mentioned above cannot capture these effects due to the computation of equivalent through the thickness section properties. Thus, higher order theories such as the layer-wise theories are required to capture the local behaviour. One such theory for sandwich panels is the Higher order Sandwich Plate theory (HSaPT). Here, the in-plane stress in the core has been neglected; but gives a good approximation for sandwich construction with soft cores. Including the axial inertial terms of the core will not yield constant shear stress distribution through the height of the core and hence more recently the Extended Higher order Sandwich Plate theory (EHSaPT) is proposed. The LSFE based on this theory has been formulated and is presented in Chapter-4. Detailed 3D orthotropic properties of typical sandwich construction is considered and the core compressibility effect of local behavior due to high shock loading is clearly brought out. As detailed local behavior is sought the degrees of freedom per element is high and the specific need for such theory as compared with the ESL theories is discussed. Chapter-4 presents the spectral finite element for plates based on FSDT. Here, multi-transform method is used to solve the partial differential equations of the plate. The effect of shear deformation is brought out in the spectrum and dispersion relations plots. Response results obtained by the formulated element is compared and validated with many different experimental results. Generally structures are built-up by connecting many different sub-structures. These connecting members, called joints play a very important role in the wave transmission/attenuation. Usually these joints are modeled as rigid joints; but in reality these are flexible and exhibits non-linear characteristics and offer high damping to the energy flow in the connected structures. Chapter-5 presents the attenuation and transmission of wave energy using the power flow approach for rigid joints for different configurations. Later, flexible spectral joint model is developed and the transmission/attenuation across the flexible joints is studied. The thesis ends with conclusion and highlighting futures cope based on the developments reported in this thesis.