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This paper aims to present an elastic, perfectly plastic, constitutive model based on the Hoek-Brown failure criterion and with non-associative plasticity. The objective is to apply the model to the non-linear analysis of geotechnical problems like excavations in rock mass. The computational implementation was carried out with a computational program called ANLOG (Non-Linear Analysis of Geotechnical Problem) system based on a displacement formulation of the finite element method. Due to the non-linear nature of the constitutive model, the study adopts an incremental iterative Newton-Raphson procedure with automatic load increments to guarantee the global level equilibrium. In addition, to guarantee the consistency condition at the local level, the study adopts, for the stress integration, an explicit algorithm with automatic sub-increments of strain. To validate the computational implementation and applicability of the numerical model, the study uses theoretical results to compare with ones obtained with the numerical simulation of cylindrical cavity in rock mass. ResumoEsse artigo apresenta um modelo constitutivo elástico perfeitamente plástico com plasticidade associada e com base no critério de resistência de Hoek-Brown. O objetivo é aplicar esse modelo para análise não linear de problemas geotécnicos como escavações em maciços rochosos. As implementações computacionais foram realizadas no sistema ANLOG (Análise não linear de obras geotécnicas) com base na formulação em deslocamento do método dos elementos finitos. Devido à natureza não linear do modelo constitutivo, o estudo adota um procedimento incremental iterativo do tipo Newton-Raphson com incrementos automáticos de modo a garantir o equilíbrio em nível global. Além disto, para garantir a condição de consistência em nível local, o estudo adota um esquema de explicito de integração de tensão com subincrementos automáticos de deformação. Para validar as implementações computacionais e a aplicabilidade do modelo numérico gerado, o estudo usa os resultados da simulação numérica de uma cavidade cilíndrica em maciços rochosos.

A rigorous analysis for a TM_ mode cylindrical cavity with insertion holes is presented on the basis of the Ritz-Galerkin method to realize accurate measurements of the complex permittivity of liquid. Theeffects of sample insertion holes, a dielectric tube, and air-gaps between a dielectric tube and sample insertion holes are taken into account in this analysis. The validity of this method is verified from measured results of some kinds of liquid., copyright(c)2004 IEICE許諾番号：07RB0174

The dynamics of slender vapor cavities is studied experimentally and with a compressible multi-material Euler equation solver. For the computational study, the cavity was approximated as an infinitely long cylinder. Compressibility is shown to be a controlling factor in the dynamics of the cavity collapse, both as a means to limit the amount of fluid mass accelerated and as a source of radiated energy. As a result, cavities reach an invariant collapse time for fluid domains large enough that acoustic waves traveling outward from the cavity wall are unable to return before collapse. The dynamics of the collapse are studied using an inviscid compressible hydrocode and are compared to those given by the incompressible cylindrical analogue of the Rayleigh-Plesset equation. The incompressible solution is known to depend on the size of the domain due to a logarithmic dependence in the governing equation, predicting a monotonically-increasing collapse time with increasing fluid domain size. Thus, for sufficiently large fluid domains, the analytic incompressible solution greatly over-predicts the cavity collapse time observed in the compressible calculation. Using the results of this study, a compressibility-limited collapse time can be predicted for a cylindrical bubble using the incompressible model, providing a rational upper limit for the effective domain size often used in slender-body approximation models. In the experimental study, supercavitating projectiles with a mass of 55 g, and cavitator radii of 3 and 6 mm were fired vertically into a shallow hydroballistics tank at velocities between 194 and 434 m/s. Cavity morphology and dynamics are extracted from high-speed video footage with two image processing techniques. Resulting cavity radial flow histories are compared to a model adapted from Bergmann et al. (2009). The model uses the volume of the hydroballistics tank as the upper limit for the amount of fluid available for cavity expansion and collapse. It accurately predicts cavity radial dynamics where local three-dimensionality (e.g. surface seal and axial flow) does not dominate the flow. The resulting model is capable of predicting gross cavity behavior and collapse mode. For cavities where the collapse is primarily radial, the model accurately predicts the time and location of collapse. These predictions could facilitate estimates of cavity collapse loading on adjacent structures.

A thin-film grating on a curved substrate functions as a highly reflective and wavelength sensitive mirror for a diverging wave that has the same curvature as the substrate. In this paper we propose a cylindrical cavity surrounded by a curved resonant grating wall, and describe its resonance characteristics. Through finite-difference time-domain (FDTD) simulation we have clarified that this type of cavity supports two resonance modes: one is confined by Fresnel reflection and the other by resonance reflection of the wall. We have also demonstrated that the latter mode exhibits a Q factor several orders of magnitude higher than that of the former mode.

International audience; When simulating flows in cylindrical rotating cavities a difficulty arises from the singularities appearing on the axis. Its singularities are due to the presence of terms 1/r^n (n = 1, 2) in the Navier-Stokes equations, where r is the radial dis-tance. To avoid evaluating differential equation coefficients which are infinite at that point, the grid must exclude the origin or specific pole conditions must be imposed. An efficient and accurate pseudo-spectral method has been here developed using collocation Chebyshev polynomials in the radial and axial directions and Fourier approximation in the azimuthal direction. To avoid the difficulty on the axis without prescribing any pole conditions, a new approach based on the work of Heinrichs [W. Heinrichs J. Comp. Phys. 199 (2004) 66-86] has been developed. The calculation domain is defined as (r, θ , z) ∈ [−1, 1] × [0, 2π] × [−1, 1] using an even number N of collocation points in the radial direction. Thus, r = 0 is not a collocation point. The clustering of collocation points around the rotation axis is also avoided due to the utilization of a Gauss-Lobatto distribution. The flow being indeed laminar close to the axis in most of the rotating flows. In the azimuthal direction, the overlap in the discretization is avoided by introducing a shift equal to π/2K (K the number of mesh points in θ -direction) for θ > π in the Fourier transform. The accuracy of the method was checked on the exact steady and unsteady analytical solutions and the capability of the method to simulate complex flows is illustrated considering the well documented case of the vortex breakdown phenomenon.

The double cylindrical cavity multiple-device power combiner fabricates with a TM_-mode (n⪰2) oversized cylindrical cavity combiner coupled with a dominant mode combiner through a transmission line. Since the dominant mode combiner as the injection signal source can oscillate only in TM_-mode, injection excitation of the desired mode in the oversized cavity facilitates undesired modes suppression as well as combine the available power of all the devices in both cavities. To study the operating characteristics of this combiner, it is necessary to understand the coupling field in the cavities and construct suitable equivalent circuit model. In this paper, axial symmetric FEM field analysis is applied on the reduced and loss free double cylindrical cavity eliminating the active devices and the output probes. Then the configurations of the coupling circuit are discussed.

Aerodynamically generated noise sources are multiple for an airplane. During the landing phase, airframe noise is the main source. At the instigation of Airbus, the project AEROCAV (Aeroacoustics of cavities) deals with the noise produced by cylindrical burst-disk cavities located under the wings. An intense tonal noise is emitted. Numerical simulations of the noise generated by these cylindrical cavities are performed to investigate the noise source mechanisms by using Direct Noise Computation. Such simulations require high-accuracy numerical algorithms in order to compute the fine-scale turbulence together with the very weak associated noise radiation. An overset grid method is developed to tackle the complex geometry of interest. The main point is to choose an interpolation method preserving the high-accuracy of the numerical schemes in order to ensure the communication between the different grids. Turbulent inflow methods based on synthetic turbulence, recycling techniques, or bypass transition are investigated to reproduce the flow conditions of the wind tunnel. Two Large Eddy Simulations are conducted for a cavity with a diameter and a height of 100 mm, and a freestream velocity of 70 m/s, with the turbulent inflow method for one of these computations. The characteristics of the flow and noise, as measured in the AEROCAV experimental campaign, are satisfactorily reproduced by the direct noise computations., Les sources de bruit d'origine aérodynamique sont multiples pour un avion. A l'atterrissage, la source prépondérante est le bruit dû à l'écoulement autour de la voilure, du fuselage et du train d'atterrissage. Sous l'impulsion d'Airbus, le projet AEROCAV (Aéroacoustique des cavités) s'intéresse au bruit généré par des cavités cylindriques qui se situent sous les ailes des avions pour évacuer un éventuel surplus de carburant. Elles émettent un rayonnement acoustique intense et très marqué en fréquence. Afin d'étudier les mécanismes de génération sonore, des simulations numériques du rayonnement acoustique dû à l'écoulement affleurant une cavité cylindrique sont réalisées par calcul direct du bruit. Ce type de simulation requiert des algorithmes numériques de haute précision afin de résoudre la turbulence fine échelle et le rayonnement acoustique associé de faible amplitude. Afin de gérer la géométrie complexe, une technique de recouvrement de maillages a été développée. Le point principal est le choix d'une interpolation compatible avec ces schémas de haute précision pour la communication entre les différentes grilles. Un travail spécifique est réalisé sur les méthodes de génération d'une condition d'entrée turbulente afin de reproduire de façon réaliste les conditions de la soufflerie. Deux Simulations des Grandes Échelles sont réalisées pour une cavité de diamètre et profondeur de 100 mm et une vitesse amont de 70 m/s, l'un avec la nouvelle condition d'entrée turbulente et l'autre sans. Ils permettent de reproduire les principales caractéristiques de l'écoulement et du champ acoustique mesurées durant la campagne expérimentale du projet AEROCAV.

SİLİNDİRİK BOŞLUK İÇEREN ÖNGERİLMELİ ANİZOTROP KALIN PLAĞIN STATİK VE DİNAMİK ANALİZİMatematik Yük. Müh. ve Fizikçi Ülkü (BABUŞCU) YEŞİLMatematik Mühendisliği Anabilim DalıDoktora TeziTez Danışmanı: Prof. Dr. Nazmiye YAHNİOĞLUBu tez kapsamında, silindirik boşluk içeren öngerilmeli, basit mesnetli dikdörtgen plak için bazı statik ve dinamik problemlerin matematiksel formülasyonu ve çözüm metodu; anizotrop malzemeler için üç boyutlu nonlineer elastisite teorisinin kesin denklemleri çerçevesinde önerilmiştir. Bahsedilen çözüm metodu 3 boyutlu sonlu elemanlar modellemesi kullanılarak geliştirilmiştir.Silindirik boşluğun etrafında statik ve dinamik gerilme yığılmasına problem parametrelerinin etkisini gösteren sayısal sonuçlar, aynı zamanda doğal frekans değerleri sunulmuş ve tartışılmıştır.Tez altı bölüm ve Kaynaklardan oluşmaktadır. Birinci bölümünde, konuyla ilgili genel bilgiler, tezin amaç ve kapsamı verilmiştir.İkinci bölümde, ele alınan problemlerin matematiksel modellemesinde kullanılan Lineerize Edilmiş Üç Boyutlu Elastisite Teorisinin denklem ve ifadeleri elde edilmiştir.Üçüncü bölümde, üzerinde çalışılan plakta statik gerilme yığılması problemi araştırılmıştır. Ek yükleme altında öngerilmeli dikdörtgen plakta silindirik boşluk etrafındaki gerilme yığılmalarına ait problemlerin sonlu eleman modellemesi ve sayısal sonuçlar verilmiştir. Ayrıca ele alınan problem için sonlu eleman modellemesinde özel durumlar ayrıntılı olarak verilmiştir.Dördüncü bölümde, silindirik boşluk içeren öngerilmeli dikdörtgen plağın doğal titreşim problemine ait matematiksel formülasyon, sonlu eleman modellemesi ve sayısal sonuçlar verilmiştir. Sayısal sonuçların analizinden, ele alınan plağın doğal titreşim frekanslarına plağın çeşitli geometrik ve malzeme parametreleri ile silindirik boşluk ve öngerilmenin önemli ölçüde etki gösterdiği belirlenmiştir.Beşinci bölümde, silindirik boşluk içeren öngerilmeli dikdörtgen plağın zorlanmış titreşim problemine ait matematiksel formülasyon, sonlu eleman modellemesi ve sayısal sonuçlar verilmiştir. Sayısal sonuçların analizinden, zamana göre harmonik değişen ilave dış yükleme altında plağın içerdiği silindirik boşluk civarında oluşan gerilme yığılmasına, plağın çeşitli geometrik ve malzeme parametreleri ile silindirik boşluk ve öngerilmenin önemli ölçüde etki gösterdiği belirlenmiştir.Son bölümde, tez çerçevesinde yapılan araştırmaların değerlendirmesi sunulmuştur.Anahtar Kelimeler: silindirik boşluk, öngerilme, gerilme yığılması, doğal titreşim, zorlanmış titreşim, dikdörtgen plak, 3B SEY. STATİC AND DYNAMİC ANALYSIS OF INITIALLY ANISOTROPIC THICK PLATE CONTAINING A CYLINDRICAL HOLEMSc Mat.Eng. and Physicist Ulku (BABUSCU) YESILDepartment of Mathematical EngineeringPhD. ThesisAdvisor: Prof. Dr. Nazmiye YAHNIOGLUIn the scope of this thesis, the mathematical formulations and method of solution to some static and dynamic problems for the initially stressed simply supported rectangular plate which contains a cylindrical hole are proposed in the framework of the exact equations of the three dimensional geometrically non-linear theory of elasticity for anisotropic bodies. The mentioned method of solution is developed by employing the 3D finite element modeling.Numerical results on the influence of the problem parameters on the static and dynamic stress concentration around the cylindrical hole, as well as on the values of the natural frequencies are presented and discussed.The Thesis consists of six chapters and References. In the first chapter, the general information on the subject, the aim and the scope of the thesis are given.In the second chapter, the equations and expressions of the Three-Dimensional Linearized Theory of Elasticity which is used for the mathematical modeling of the considered problems, is derived.In the third chapter, the problem on the static stress concentration in the plate under consideration is studied. The finite element modeling and the numerical results on the concentration of the stresses around the cylindrical hole within the initially stressed rectangular plate under the additional static loading are presented. Moreover the special cases in the finite element modeling for the considered problems are provided in detail.In the fourth chapter, the mathematical formulation, the finite element modeling and the numerical results for the problem of the natural vibration of the initial stressed rectangular plate containing a cylindrical hole are presented. From the analysis of the numerical results it is established that various geometrical and material parameters of the plate as well as the cylindrical hole and the initial stresses significantly affect the fundamental frequencies of the considered plate.In the fifth chapter, the mathematical formulation, the finite element modeling and the numerical results for the problem of the forced vibration of the initial stressed rectangular plate containing a cylindrical hole are presented. From the analysis of the numerical results it is established that the various geometrical and material parameters of the plate as well as the cylindrical hole and the initial stresses significantly affect the concentration of the stresses around the cylindrical hole containing the considered plate under the time harmonic additional forces.In the final chapter, the conclusions of the results of the considered investigations in the thesis are presented.Keywords: cylindrical hole, initial stress, concentration of stress, natural vibration, forced vibration, rectangular plate, 3D FEM 126

Збудовано розв’язок оберненої задачі на основі розв’язку прямої задачі про дослідження нестаціонарних коливань пружної ізотропної середи з циліндричною порожниною. Поширення осесиметричних деформаційних хвиль зумовлено завданням переміщень на поверхні порожнини у пружному тілі. Приведено числовий приклад розрахунку оберненої задачі., Построено решение обратной задачи на основе прямой задачи об исследовании нестационарных колебаний упругой изотропной среды с цилиндрической полостью. Распространение осесимметричнных деформационных волн обусловлено заданием перемещений на поверхности полости в упругом теле. Представлен численный пример расчета обратной задачи., The inverse problems solution based on the direct problem of non-stationary vibrations of an elastic isotropic medium with a cylindrical cavity is considered. Distribution of axisymmetric deformation waves which are caused by displacements on the surface of an elastic body. A numerical calculations’ example for the inverse problem are presented.

Cavity noise is a very frequent phenomenon in air transport. It occurs in particular during landing approaches, where airframe-flow interactions are responsible for strong tonal emissions. Accordingly, it turns to be a non negligible source of acoustic pollution for populations living near airport areas. Numerical and experimental studies reported in the literature tackle essentially the case of rectangular cavities. Nevertheless, cavities may often exhibit more complex shapes in practice. When subject to aerodynamic excitations, and because of their geometrical specificity, these cavities may have acoustic responses which can be rather far from estimations resulting from academic models designed for rectangular cavities. Only asmall number of studies tackle the case of cylindrical cavities.The present work requested by Airbus is dedicated to the study of aeroacoustics in cylindrical cavities. This work was been supported by the Fondation de Recherche pour l'Aéronautique& l'Espace (FRAE) under contract reference AEROCAV. It aims at discerning the mechanisms responsible for strong and tonal acoustic emissions for the studied configurations.Experimental data resulting from measurements performed in the anechoic wind-tunnel of the Centre Acoustique at 'Ecole Centrale de Lyon are presented in a first part. A semi-empirical model based on the hypothesis of a shear-layer driven acoustic resonance is constructed from the Elder model (1978). The model provides an estimation of the frequences which are likely to be predominant in the far-field acoustics, given the mean streamwise velocity field, currently measured in the flow plane by Particle Image Velocimetry (PIV).A second part deals with the direct computation of the noise radiated by a laminar or turbulent grazing flow over a standard cylindrical cavity. The method consists in the calculationof the acoustic field directly from the resolution of the tridimensional Navier-Stokes equations. The Alesia solver is presented in a modified form, adapted to the implementationof a high-order chimera method involving several overlapping grids. Interpolation techniques have been specifically developed to achieve a bidirectional communication between the meshes in spite of strong geometrical constraints. A flow excitation model has also been constructed in order to obtain fluctuations into the incoming flow in the turbulent case. These two last points make the present computations original. The simulations, which are performed on a cavity of geometric ratio taken as 1 and subject to a grazing flow of Mach 0.2, reveal that it is possible to retrieve the radiated noise numerically with high fidelity. They indicate the presence of two large amplifying vortices in the shearlayer. These vortices go with strong velocity fluctuations giving rise to an inflow of fluid at the cavity mouth which excites the cavity acoustically. A forced acoustic resonance occurs into the cavity, then destabilises the shear layer near the separation point. This self-sustained coupling is responsible for strong tonal radiations from the cavity. The frequency of the radiated noise is close to the one predicted by the semi-empirical model., Le bruit de cavité est un phénomène très fréquent dans le domaine des transports aériens.Il survient notamment lors de l'approche à l'atterrissage, où des interactions entre la cellule de l'aéronef et l'écoulement sont à l'origine de fortes émissions tonales. Il devient dès lors une source de pollution acoustique non-négligeable pour les populations résidant à proximité de zones aéroportuaires. Les études numériques et expérimentales décrites jusqu'à présent dans la littérature abordent essentiellement le cas des cavités rectangulaires. Pourtant, les cavités rencontrées en pratique dans l'industrie aéronautique impliquent des géométries souvent plus complexes. Lorsque ces cavités sont soumises à une excitation de nature aérodynamique, leur spécificité géométrique conduit le plus souvent à des réponses acoustiques assez éloignées des estimations issues de modèles académiques construits sur l'observation de cavités rectangulaires. Quelques travaux seulement abordent le cas des cavités cylindriques.Ce travail est consacré à l'étude aéroacoustique des cavités cylindriques, à l'initiative d'Airbus. Il s'inscrit dans le cadre du projet AEROCAV soutenu par la Fondation de Recherche pour l'Aéronautique & l'espace (FRAE). Son objectif est de déterminer les mécanismes impliqués dans les émissions acoustiques intenses et tonales pour les configurations étudiées.Une première partie présente les résultats expérimentaux issus des campagnes de mesures menées dans la soufflerie anéchoïque du Centre Acoustique du LMFA et de l'école Centrale de Lyon. Un modèle semi-empirique, reposant sur l'hypothèse d'une résonance acoustique pilotée par les instabilités présentes dans la couche de cisaillement à l'ouverture de la cavité,est construit à partir du modèle d'Elder (1978). Le modèle permet d'estimer les fréquences susceptibles de dominer l'acoustique rayonnée en champ lointain à partir de la donnée du champ moyen de vitesse longitudinale, que l'on mesure dans le plan de l'écoulement par Vélocimétrie par Imagerie des Particules (PIV).Une seconde partie est destinée au calcul direct du bruit rayonné par un écoulement laminaire ou turbulent affleurant une cavité cylindrique de référence. Il consiste à calculer le champ acoustique directement à partir de la résolution des équations tridimensionnelles de la mécanique des fluides. Le solver Alesia est présenté dans une version modifiée et adaptée à la mise en oeuvre d'une approche multidomaine d'ordre élevé faisant intervenir plusieurs maillages se recouvrant. Des techniques d'interpolation sont spécifiquement développées en vue d'assurer une communication bidirectionnelle entre les différents maillages, malgré des contraintes géométriques fortes. Un modèle d'excitation de l'écoulement est aussi développé afin de disposer de fluctuations dans l'écoulement incident, pour le cas turbulent. Ces deux points font l'originalité des calculs réalisés.Les simulations, menées sur une cavité de rapport d'aspect géométrique égal à 1 et soumise à un écoulement incident à Mach 0.2, montrent que le rayonnement acoustique peut être fidèlement reproduit numériquement. La couche de cisaillement est caractérisée par la présence de deux larges structures tourbillonnaires s'amplifiant lors de leur convection. Leur présence s'accompagne de fortes fluctuations de vitesse à l'origine d'un débit aérodynamique de fluide à l'ouverture qui excite la cavité acoustiquement. Une résonance forcée s'établit dans celle-ci, excitant la couche de mélange au voisinage du point de séparation. Ce couplage auto-entretenu est à l'origine du rayonnement acoustique intense et fortement tonal de la cavité. Il s'établit à une fréquence proche de la fréquence prédite par le modèle semi-empirique développé.

Made available in DSpace on 2014-06-11T19:25:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-08-20Bitstream added on 2014-06-13T19:32:32Z : No. of bitstreams: 1 jordam_a_me_bauru.pdf: 3535049 bytes, checksum: a22a97d375d5d91449be8bd46442ee9e (MD5) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) A fluidodinâmica computacinal (CFD) tem sido utilizada, estudadda e implementada ao longa das duas últimas décadas na solução dos mais diversos problemas de engenharia. O princípio básico desta ciência é a aplicação de métodos numéricos em problemas que envolvam mecânica dos fluidos. Nesse contexto, este trabalho utiliza essa técnica para analisar o comportamento de um fluido incompreensível, que se encontra numa cavidade cilíndrica fechada onde as faces inferior e superior são adiabáticas e as superfícies laterais se encontram em diferentes temperaturas. Os perfis de velocidade e temperatura resultantes - ocasionados pela convecção natural - serão avaliados em todo o domínio do problema. Existe uma série de técnicas para a solução de problemas envolvendo escoamentos, sendo as mais comuns as que se utilizam do Esquema de Passo Fracionado proposto por Chorin no final da década de 60. Dentre as diversas soluções que se utilizam desta técnica, este trabalho optou pelo uso do método das características e do algoritmo CBS de solução proposto por Zienkiewicz e Codina (1995). Para a implementação do algoritmo de solução do problema proposto foi realizada uma discretização geral através do método dos elementos finitos usando-se de uma malha formada por elementos bilineares. A solução foi obtida a partir de um ambiente matemático adequado, a GNU-Octave (2008). Os resultados foram analisados para diferentes razões de curvatura, números de Rayleigh e métodos de solução, sendo plotados para as suas diversas variáveis buscando descrever o comportamento do fenônemo The Computational Fluid Dynamics (CFD) has been used, studied and performed through the last two decades to solve the series of problems in Engineering. The most basic aim of this science is the appliance of numerical methods in cases that envolve fluid mechanics. In this context, this work uses this technic to analyze the behaviour of an incompressible fluid, which is found in a closed cylindrical cavity, a place where the inferior and superior surfaces are adiabatic and the lateral surfaces are shown in different temperatures. The resultant profiles of speed and temperature - induced by the free convection - are going to be appraised in all the dominion of the problem. There is a set of technics to solve the problems which involve the drainage, but the most usual are those which use the techic Fractional Step Method offered by Chorin in the final of 60s. Among the several solutions that are solved through this technic, this research used the characteristics method and of the CBS algorthm, offered by Zienkiewicz e Codina (1995). For the implementation of the algorithm, it was realized a general discretization through the finite elements method, making use of a loop formed by bilinear elements. The resolution was obtained from an adequated mathematical ambient, the GNU-Octave (2008). The results were analysed for different curvature ratios, Rayleigh numbers and methods of solution, being plotted for its different variables searching to describe the behavior of the phenomenon

The numerical simulation of laminar natural convection in a vertical cylindrical cavity is proposed. The cavity is insulated at the bottom, laterally heated at a uniform heat flux and cooled by a non uniform evaporative heat flux at the top surface obeying the Hashemi–Wesson's law. The equations of mass conservation, momentum and energy are resolved with finite-volume method in fully implicit form. The influence of the characteristic parameters (10 3 ≤ Ra ≤ 10 5 , Pr = 2, 1/3 ≤ Al ≤ 1) on the thermal and dynamic behavior at steady state is analysed and discussed. In particular, the study describes the solutions at Ra = 10 5 and Pr = 2 for various aspect ratios. The evaporative heat flux is computed for all the parameters and it is found that its maximum is localized near the lateral wall whereas its minimum is at the free surface center.

The growth of thermal convection out of different perturbations of the conductive base state is investigated using a spectral element time-stepping code. The fluid is subject to a vertical heat transfer in a cylindrical cavity with an upper free surface corresponding to the so-called Rayleigh-Bénard-Marangoni situation and the heat exchange through the free surface is evaluated via the Biot number. The results of the stability diagrams show that the evolution of the primary thresholds are largely influenced by the Biot number, the Marangoni number, and the aspect ratio of the cavity. Flow transitions are elucidated in quantitative detail as a function of the Rayleigh number for different Biot numbers in the tension free limit Ma = 0. The results shown are obtained by solving the full nonlinear field equations numerically among a continuation method. When an axisymmetric m = 0 Fourier mode is obtained at onset, the non-linear evolution shows the coexistence of different convective structures, the axisymmetric structures with up-ow or down-ow at the center and mixed-mode structures which appear on secondary subcritical branches. The action of a constant magnetic field is then considered for melts in the same type of configuration with an upper free surface. We show the global stabilizing effect of the magnetic field on the primary bifurcation thresholds and the selective effect on the different instability modes. We also analyze the evolution of the convective structures above the thresholds and show how the magnetic field modifies the transitions between these structures. When applying a magnetic body forcing in the azimuthal direction (RMF), one can damp the unavoidable thermal fluctuations inside the melt and delay the transition to the Rayleigh-Bénard instability (for rigid-rigid circular plates at top and bottom). The rotation effect also changes the transitions from steady to oscillatory, except for the m = 0 Fourier mode where the transitionis first steady until a critical Taylor number and then becomes oscillatory. The dynamics of the transitions to the axisymmetric flow, below and above this value of critical magnetic Taylor number, is particularly interesting and will be described., Nous présentons dans cette étude le développement de la convection à partir de différentes perturbations de l'état conductif d'une couche fluide confinée dans une cavité cylindrique, chauffée par le bas et avec une surface supérieure libre. La discrétisation spatiale du domaine repose sur la méthode des éléments spectraux et les itérations temporelles sont assurées par une méthode splitting.Au déclenchement de la convection, les structures convectives correspondent à des modes de Fourier, et les seuils critiques dépendent du rapport de forme de la cavité, et des nombres de Biotet de Marangoni qui caractérisent la surface libre. Les transitions d'écoulements au-delà du seuil primaire sont caractérisées quantitativement en fonction du nombre de Rayleigh pour différentes valeurs du nombre de Biot et Ma = 0. Les résultats présentés sont obtenus en résolvant l'ensemble des équations non-linéaires de conservation à travers une méthode de continuation. Lorsque la convection se déclenche sous la forme d'un mode axisymétrique m = 0, l'évolution non-linéaire montre la coexistence de différentes structures convectives, des structures axisymétriques avec écoulement montant ou descendant au centre de la cavité et des structures correspondant à des combinaisons de modes qui apparaissent sur des branches secondaires sous-critiques.L'action d'un champ magnétique constant est ensuite étudiée pour des fluides conducteurs dans une même configuration comprenant une surface supérieure libre. Nous montrons l'effet stabilisateur du champ magnétique sur les seuils primaires ainsi que son action sélective sur les différents modes de convection. Nous analysons l'évolution des structures convectives au delà de ces seuils et montrons comment le champ magnétique modifie les transitions entre ces structures.En soumettant le bain fondu à un champ magnétique tournant, le mouvement de rotation du fluide se superpose aux mouvements de convection thermique et on observe une diminution des fluctuations de température et un retard du déclenchement de l'instabilité de Rayleigh-Bénard(lorsque les deux parois haut/bas du bain sont rigides). La rotation influe sur ce déclenchement qui de stationnaire devient oscillatoire, à l'exception du mode m = 0 de Fourier, pour qui la transition reste stationnaire jusqu'à une certaine valeur critique du nombre de Taylor magnétique.La dynamique de l'écoulement axisymétrique de part et d'autre de cette valeur critique sera étudiée en détail.

International audience; The propagation of elastic surface waves, guided by the free surface of an infinitely long cylinder of arbitrary cross section, is formulated as an eigenvalue problem for an unbounded self-adjoint operator. We prove the existence of a hierarchy of guided modes. Two of them propagate for any value of the wave number, whereas all of the others only exist beyond a cut-off wave number. For any fixed value of the wave number, only a finite number of modes propagate.

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2006, Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2006, İkiz dairesel boşluk içeren yarım uzayın harmonik iç basınç altındaki davranışı bu çalışmanın konusu olmuştur. Her iki oyuk ta kendi yerel eksen takımı ile tariflenmiştir. Oyukların ekseni boyunca malzeme özellikleri, ortamın geometrisi ve zorlama değişmemektedir. Böylece problem bir düzlem şekildeğiştirme problemi olarak göz önüne alınmıştır. Hareket denklemi olarak yerdeğiştirmeler cinsinden Navier denklemi alınmıştır. Helmholtz yerdeğiştirme potansiyellerinin kullanılmasıyla hareket denklemi kutupsal koordinatlarda iki adet dalga denklemine indirgenmiştir. İndirgenmiş dalga denklemleri iki ayrı yerel eksen takımında Bessel – Trigonometrik çarpım serileri yardımıyla analitik olarak çözülmüştür. Çözüm sonunda ortaya çıkan bilinmeyen sabitler oyuk yüzeyleri ve serbest yüzey üzerinde yazılan sınır koşulları yardımıyla hesaplanmıştır. Her iki oyuğun yerel eksenleri arasındaki dönüşümde Graff Ekleme Teoremi bağıntılarından yararlanılmıştır. Böylece oyuk yüzeylerinde sınır koşulları kesin olarak sağlatılmıştır. Serbest yüzeyde incelenen bölgenin uç ve orta kesimlerinde yoğunlaşmış nokta seçimiyle, yüzey boyunca gerilme bileşenleriyle ilgili koşullar yaklaşık olarak sağlatılmıştır., The response of twin circular cylindrical cavities to disturbances harmonically inner pressures an elastic half – space is subject of this study. The cavities are treated in the local coordinate systems. The geometry, material properties of the medium and the excitation have not changed through the axis of cavities. Thus, the problem is considered the plane strain case. Navier’s equation in terms of displacements has been received as the equations of motion. Using Helmholtz’ displacement potentials, governing equation is reduced into two wave equations in polar coordinates. These reduced wave equations are solved in two local coordinates by using the Bessel – Trigonometric multiplication series. Unknown coefficients appeared at the end of solution are calculated by applying boundary conditions on the cavities and free surface. Transformation of the local coordinate systems of between the cavities is benefited Graff’ Addition Theorem. Thus, Boundary conditions on the cavity surface are satisfied exactly. Conditions related to the components of stress on the surface are approximately provided by concentrated point selection in the middle and the tip of the investigated part on the free surface., Yüksek Lisans, M.Sc.

DAB applications demand the realization of band-pass filters with very stringent characteristics. In this paper this requirements have been fulfilled by designing and realizing a four-pole elliptic transfer function by means of a Dual-Mode Circular Waveguide Filter (DMCWF). This design has been performed by adopting a conventional synthesis strategy. The most critical aspect of this structure, that is its difficult tunability, has been overcome by experimentally adjusting the filter dimensions following a CAD procedure extensively described in the paper.

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2002, Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2002, Bu çalışmada, harmonik kısmi iç basınçla zorlanan ve bu yüklemenin limit hali olan harmonik tekil kuvvet zorlaması için homogen, izotrop ve lineer elastik, silindirik boşluklu yarım uzayın davranışı incelendi. Silindirik boşluğun ekseni boyunca geometri, malzeme özellikleri ve zorlamanın değişmemesi nedeniyle düzlem şekil değiştirme hali göz önüne alındı. Kuple hareket denklem takımı, Helmholtz yerdeğiştirme potansiyelleri kullanılarak çözülmüş ve kutupsal koordinatlarda iki adet indirgenmiş dalga denklemi elde edilmiştir. İndirgenmiş dalga denklemleri Bessel – trigonometrik fonksiyon serileri yardımıyla analitik olarak çözülmüştür. Çözüm sonunda ortaya çıkan bilinmeyen sabitler delik yüzeyi ve serbest yüzey üzerinde yazılan sınır koşulları yardımıyla hesaplanmıştır. Oyuk yüzeyinde sınır koşullarının tam olarak sağlatılmasıyla bilinmeyen sabitlerin yarısı diğer yarısı cinsinden elde edilmiştir. Geri kalan bilinmeyenler, serbest yüzey üzerindeki gerilme bileşenlerinin sıfır olması koşulunun “En Küçük Kareler Yöntemi” kullanılarak yaklaşık olarak sağlatılması ile elde edilmiştir., In this study, response of a homogeneous, isotropic and linear elastic semi-infinite medium, which includes a cylindrical cavity, is investigated when subjected to harmonic partial inner pressure and to the harmonic point load, which is simply the limit of the same inner pressure. Because of the geometry, material properties of the medium and the forcing function have never changed through the axis of cylindrical cavity, the plane strain case is used. Coupled equation of motions is reduced into two wave equations by use of Helmholtz potentials in polar coordinates. These reduced wave equations are solved by using the multiplication series of the Bessel and the trigonometric functions. Unknown coefficients are calculated by applying boundary conditions on the cavity and free surface conditions. Boundary conditions on the cavity surface are satisfied exactly. Using these conditions, half of the unknown coefficients are calculated in terms of the others. The stress components on the free surface must be zero. Using the Least Square Technique, these conditions have been satisfied approximately., Yüksek Lisans, M.Sc.

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2002, Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2002, Bu çalışmada, elastik yarım uzay içinde bulunan silindirik boşluğun yüzeyinde harmonik zorlama etkisi göz önüne alınmıştır. Bu harmonik zorlama üniform yayılı kayma gerilmesi şeklindedir. Yarı sonsuz düzlemdeki malzeme lineer elastik, homojen ve izotrop olarak göz önüne alınmıştır. Silindirik boşluğun ekseni boyunca geometri, malzeme özellikleri ve zorlamanın değişmemesi nedeniyle düzlem şekil değiştirme hali göz önüne alındı. Kuple hareket denklem takımında, Helmholtz yerdeğiştirme potansiyelleri kullanılarak kutupsal koordinatlarda iki adet indirgenmiş dalga denklemi elde edilmiştir. İndirgenmiş dalga denklemleri Bessel – trigonometrik fonksiyon serileri yardımıyla analitik olarak çözülmüştür. Çözüm sonunda ortaya çıkan bilinmeyen sabitler delik yüzeyi ve serbest yüzey üzerinde yazılan sınır koşulları yardımıyla hesaplanmıştır. Oyuk yüzeyinde sınır koşullarının tam olarak sağlatılmasıyla bilinmeyen sabitlerin yarısı diğer yarısı cinsinden elde edilmiştir. Geri kalan bilinmeyenler, serbest yüzey üzerindeki gerilme bileşenlerinin sıfır olması koşulunun “En Küçük Kareler Yöntemi” kullanılarak yaklaşık olarak sağlatılması ile elde edilmiştir., In this study, the behaviour of the half space with cylindrical cavity under the harmonic forcing has been examined. The harmonic forcing is an uniformly distributed shearing stress. Material is linear elastic, homogeneous and isotropic. Because of the geometry, material properties of the medium and the forcing function have never changed through the axis of cylindrical cavity, the plane strain case is used. Coupled equations of motion are reduced into two wave equations by use of Helmholtz potentials in polar coordinates. These reduced wave equations are solved by using the multiplication series of the Bessel and the trigonometric functions. Unknown coefficients are calculated by applying boundary conditions on the cavity and free surface. Boundary conditions on the cavity surface are satisfied exactly. Using these conditions, half of the unknown coefficients are calculated in terms of the others. The stress components on the free surface must be zero. Using the Least Square Technique, these conditions have been satisfied approximately., Yüksek Lisans, M.Sc.

The dynamic behavior of a dry long bone considered as a piezoelectric cylinder of crystal class 6 with arbitrary cross-section is presented. For the solution of the wave propagation problem we follow the procedure proposed in a previous work (D.I, Fotiadis, G. Foutsitzi, C.V. Massalas, Wave propogation modeling in human long bones, Acta Mechanica 137 (1-2) (1999) 65-82). The boundary conditions on the inner and outer lateral surface of the cylinder, which is of irregular shape, are satisfied by using the Fourier expansion collocation method. The obtained dispersion relation is solved numerically and results are presented for various cross-sections and geometrical parameters of the system. (C) 2000 Elsevier Science Ltd. All rights reserved. International Journal of Engineering Science

The dynamic behavior of a dry long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated. The solution for the wave propagation problem is expressed in terms of a potential function which satisfies an eighth-order partial differential equation, whose solutions lead to the derivation of the explicit solution of the wave equation. The mechanical boundary conditions correspond to those of stress free lateral surfaces, while the electrical boundary conditions correspond to those of short circuit. The satisfaction of the boundary conditions leads to the dispersion relation which is solved numerically. The frequencies obtained are presented as functions of various parameters and they compare well with other researchers' theoretical results. Acta Mechanica

In this paper, we present a novel miniaturized MNG (-negative) metamaterial loaded cylindrical cavity resonator based on the existence of surface waves at the interface between a metamaterial and an ordinary medium. First, we formulate the general dispersion relation for such a resonator and we show that this configuration may in principal provide the miniaturization possibility. A category of settings which provide maximum degree of miniaturization are determined. Quality factor variations are also calculated theoretically and finally a design example with the resonant frequency of about 1.39GHz, 94% miniaturization, and a relatively high quality factor of about 4500, comparing with the other miniaturized metamaterial resonators, is presented and also numerically simulated. The simulated results verify the accuracy of analytical calculations.