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Load-carrying and energy-dissipation capacities of ultra-high-performance concrete under dynamic loadingBuck, Jonathan J. 06 April 2012 (has links)
The load-carrying and energy-dissipation capacities of ultra-high-performance concrete (UHPC) under dynamic loading are evaluated in relation to microstructure composition at strain rates on the order of 10⁵ s⁻¹ and pressures of up to 10 GPa. Analysis focuses on deformation and failure mechanisms at the mesostructural level. A cohesive finite element framework that allows explicit account of constituent phases, interfaces, and fracture is used. The model resolves essential deformation and failure mechanisms in addition to providing a phenomenological account of the effects of the phase transformation. Four modes of energy dissipation are tracked, including pressure-sensitive inelastic deformation, damage through the development of distributed cracks, interfacial friction, and energy released through phase transformation of the quartz silica constituent. Simulations are carried out over a range of volume fractions of constituent phases to quantify trends that can be used to design materials for more damage-resistant structures. Calculations show that the volume fractions of the constituents have more influence on the energy-dissipation capacity than on the load-carrying capacity, that inelastic deformation is the source of over 70% of the energy dissipation, and that the presence of porosity changes the role of fibers in the dissipation process. The results also show that the phase transformation has a significant effect on the load-carrying and energy-dissipation capacities of UHPC for the conditions studied. Although transformation accounts for less than 2% of the total energy dissipation, the phase transformation leads to a twofold increase in the crack density and yields nearly an 18% increase to the overall energy dissipation. Microstructure-behavior relations are established to facilitate materials design and tailoring for target-specific applications.
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Flow Over A Circular Cylinder With A Flexible Splitter PlateShukla, Sanjay Kumar 05 1900 (has links)
Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate can deform due to the fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted like in the rigid splitter plate case. In particular, we study two kinds of flexible splitter plates. In the first case, the splitter plate is rigid but is flexibly mounted (hinged) to the cylinder, while in the second case, the entire splitter plate is flexible. We are interested in both the dynamics of the splitter plate, if they do vibrate at all, and in the wake dynamics downstream of the flexible splitter plates. The main parameters in the problem are the splitter plate length (L) to cylinder diameter (D) ratio, the relative mass of the plate, the Reynolds number, and the stiffness and internal damping associated with the flexible plate. In our study, we investigate this problem in the limit where the stiffness and internal damping of the plate are negligible and hence are not parameters of interest.
For the hinged-rigid splitter plate case, experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force in this case, and has been seen previously for elastically-mounted cylinders with no restoring force. In the present case, the saturation tip amplitude level can be up to 0.45D,where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter (L/D) ratio is crucial in determining the character and magnitude of the oscillations. For small splitter plate lengths (L/D ≤ 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The non-dimensional oscillation frequencies (fD/U ) on the other hand are found to continuously vary with L/D from fD/U ≈ 0.2at L/D =1 to fD/U ≈ 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D ≥ 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D ≥ 5.0. It appears that the vortex shedding is nearly inhibited for L/D ≥ 4.0 in the present case. This is also supported by measurements of the wake vorticity field from Particle-Image Velocimetry (PIV). The phase-averaged PIV vorticity fields show that the strength of the shed vortices decreases rapidly as the splitter plate length increases. For longer splitter plates, L/D ≥ 4.0, the plate oscillations are no longer periodic, and hence it appears that the wake vortices are not synchronized with the splitter plate motions.
For the entirely-flexible splitter plate case, the splitter plate deformations appear to be in the form of a travelling wave. In this case, the tip amplitudes are significantly larger of the order of 1.1D, and the non-dimensional oscillation frequency (fD/U )is close to 0.2, approximately the same as the Strouhal number for the bare cylinder. In sharp contrast to the hinged-rigid splitter plate case, the non-dimensional amplitude and frequency appear to be nearly independent of the normalized splitter plate length (L/D)even up to L/D =7.0. PIV measurements of the wake vorticity field indicates that there appears to be a nearly continuous sheet of vorticity on both sides of the flexible splitter plate, and the vortex sheet sheds and forms distinct vortices only at the trailing edge of the plate. The strength of these shed vortices appears to be close to that of the bare cylinder at similar Re. The results appear to suggest that in this entirely-flexible case, the vortices form at the same frequency and are of the same strength as in the bare cylinder case, but their formation is just pushed further downstream. This would suggest that in this case, the base suction and drag could be lower than the bare cylinder. Further, the formation of vortices further downstream of the body could imply that this type of flexible splitter plate could be useful to suppress vortex-induced vibrations (VIV).
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Characterization of Hard Metal Surfaces after Various Surface Process TreatmentsHakim, Ali January 2008 (has links)
<p>The aim of this thesis is to investigate how material surfaces are affected by various surface treatments and how this relates to the adhesion of the coating. The materials that were studied were WC-Co and Cermets and the surface treatments used were polishing, grinding with coarser and finer abrasive grains, and finally wet blasting and dry blasting. Focus was on deformations and residual stresses in the surface, surface roughness and cracks. The test methods used for examining the samples included surface roughness measurements, residual stress measurements, adhesion tests using Rockwell indentation and SEM images of the surface and the cross section.<br /><br />The results concluded that polishing gives very good adhesion. Additionally, the adhesion for ground surfaces was good for WC-Co but very poor for Cermets. Furthermore, it was observed that finer abrasive grains did not result in better adhesion. In fact, the coarser grains gave slightly better results. Finally, it was concluded that wet blasting has a clear advantage over dry blasting and results in much better adhesion, especially for the Cermets. The results for the WC-Co were a bit inconsistent and so further research is required.</p>
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Characterization of Hard Metal Surfaces after Various Surface Process TreatmentsHakim, Ali January 2008 (has links)
The aim of this thesis is to investigate how material surfaces are affected by various surface treatments and how this relates to the adhesion of the coating. The materials that were studied were WC-Co and Cermets and the surface treatments used were polishing, grinding with coarser and finer abrasive grains, and finally wet blasting and dry blasting. Focus was on deformations and residual stresses in the surface, surface roughness and cracks. The test methods used for examining the samples included surface roughness measurements, residual stress measurements, adhesion tests using Rockwell indentation and SEM images of the surface and the cross section.<br /><br />The results concluded that polishing gives very good adhesion. Additionally, the adhesion for ground surfaces was good for WC-Co but very poor for Cermets. Furthermore, it was observed that finer abrasive grains did not result in better adhesion. In fact, the coarser grains gave slightly better results. Finally, it was concluded that wet blasting has a clear advantage over dry blasting and results in much better adhesion, especially for the Cermets. The results for the WC-Co were a bit inconsistent and so further research is required.
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Influence of long-term load on the behaviour of reinforced concrete beams strengthened with carbon fibre composite / Ilgalaikės apkrovos įtaka anglies pluoštu sustiprintų lenkiamųjų gelžbetoninių elementų elgsenaiDaugevičius, Mykolas 10 February 2011 (has links)
The influence of long-term load on the reinforced concrete beams strength-ened with a carbon fiber composite layer in the tensioned zone is considered in this dissertation. The evolution of deformations in the layers of the beams and the evolution of beam deflection is analyzed. The load carrying capacities after a long-term load action are also determined herein. The built-up-bars theory for calculation of deflections and the load carrying capacity after a long-term load action is presented in this dissertation. The thesis consists of an introduction, four main chapters, the results and conclusions and a list of used literature. The introduction describes the major objectives of the dissertation. It pre-sents the aims, the methods of research, the scientific novelty and defended pro-positions. The first chapter reviews application of carbon fiber composite polymer in strengthening structures. The influence of a long term load on concrete, polymer matrix, carbon fiber reinforced composite, strengthened concrete beams is also considered. In addition, it considers the calculation methods that evaluate the long term load influence. The second chapter is dedicated to applying of the built-up-bars theory in calculation of deflections and the load carrying capacity, including long term load action. Also, variation of concrete and carbon fiber composite contact stiff-ness is presented in this chapter. Chapter three presents the carried out experiments. It describes the experi-mental... [to full text] / Disertacijoje nagrinėjama lenkiamųjų gelžbetoninių sijų, tempiamojoje zo-noje sustiprintų anglies pluošto kompozitu, elgsena esant ilgalaikiam statinės apkrovos poveikiui. Disertacinio darbo tikslas – atlikti eksperimentinius tyrimus ir nustatyti ilgalaikės apkrovos poveikį sijos laikomajai galiai bei įlinkių vysty-muisi; apskaičiuoti sijos įlinkį pagal sudėtinių strypų teoriją įvertinant ilgalaikės statinės apkrovos poveikį bei betono ir anglies pluošto kompozito jungties stan-dumo pokytį dėl šlyties valkšnumo deformacijų prieaugio. Disertaciją sudaro: įvadas, keturi pagrindiniai skyriai, rezultatų apibendri-nimas ir išvados, naudotos literatūros sąrašas, autoriaus publikacijų disertacijos tema sąrašas. Įvadiniame skyriuje nagrinėjama tiriamoji problema ir darbo aktualumas, nurodytas tyrimų objektas, suformuluoti darbo tikslai ir uždaviniai, pateikta ty-rimų metodika, aptarta darbo svarba ir praktinė rezultatų reikšmė, pristatyti gi-namieji teiginiai. Pirmajame skyriuje atlikta literatūros apžvalga. Čia nagrinėjamas ilgalaikės apkrovos ir aplinkos poveikis anglies pluošto kompozitui, kompozito ir betono jungčiai bei gelžbetoninių sijų elgsenai. Pateikiami sustiprintų sijų elgsenos eks-perimentinių tyrimų, veikiant trumpalaike ir ilgalaike apkrova, rezultatai. Apta-riamos skaičiavimo metodikos, vertinančios ilgalaikį apkrovos poveikį. Antrajame skyriuje pateikiama skaičiavimo metodika, grindžiama sudėtinių strypų teorija. Skaičiavimo metodika skirta sijų, sustiprintų anglies... [toliau žr. visą tekstą]
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Mechanical modeling of brain and breast tissueOzan, Cem 28 April 2008 (has links)
We propose a new approach for defining mechanical properties of the brain tissue in-vivo by taking MRI or CT images of a brain response to ventriculostomy operation, i.e., the relief of the elevated pressure in the ventricular cavities. Then, based on 3-D image analysis, the displacement fields are recovered from these images. Constitutive parameters of the brain tissue are determined using inverse analysis and a numerical method allowing for computations of large strain deformations. We tested this approach in controlled laboratory experiments with silicone brain models mimicking brain geometry, mechanical properties, and boundary conditions. The ventriculostomy was simulated by inflating and deflating internal cavities that model cerebral ventricles. Subsequently, the silicone brain model was described by a hyperelastic (neo-Hookean) material. The obtained mechanical properties have been verified with direct laboratory tests. Properties of real brain tissue are more complicated, but the proposed approach requires only conventional medical images collected before and after ventriculostomy.
Breast cancer is the second most prevalent cancer in women, and an operative mastectomy is frequently a part of the treatment. Women often choose to follow a mastectomy with a reconstruction surgery using a breast implant. Furthermore, there is a growing demand for breast augmentation for the sake of aesthetic improvement. In this dissertation, we also developed a quantitative large-strain 3-D mechanical model of female breast deformation. The results show that the stiffness of skin and the constitutive parameters of the breast tissue are important factors affecting breast shape. Our results also suggest that the published Mooney-Rivlin parameters of breast tissue are underestimated by at least one or two orders of magnitude. Scale analysis, representing female breast as a cantilever beam, confirms these conclusions.
Subdural hematoma (tearing and bleeding between scull and brain) is one of the major complications of the ventriculostomy operations. Understanding the mechanism of subdural hematoma is critically important for development of more effective medical treatments. In this work, we developed a simple, spherically-symmetrical poroelastic model of the ventriculostomy operation and studied brain response to the pressure change in the ventricles. The observed effect of the material properties on the occurrence of subdural hematoma may be useful for making clinical decisions.
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Dynamic mechanical behavior and high pressure phase stability of a zirconium-based bulk metallic glass and its composite with tungstenMartin, Morgana 04 March 2008 (has links)
An investigation of the high-strain-rate mechanical properties, deformation
mechanisms, and fracture characteristics of a Zr-based bulk metallic glass (BMG) and its composite with tungsten was conducted through the use of controlled impact experiments and constitutive modeling. The overall objective of this research was to determine the high-strain-rate deformation and failure mechanisms of a BMG and its composite as a function of stress state and strain rate, and
describe the mechanical behavior over a range of loading conditions. The research involved performing controlled impact experiments on BMG
composites consisting of an amorphous Zr57Nb5Cu15.4Ni12.6Al10 (LM106) with
crystalline tungsten reinforcement particles. Monolithic LM106 was also examined to aid in the understanding of the composite. The mechanical
behavior of the composite was investigated over a range of strain rates (10^3 s^-1 to 10^6 s^-1), stress states (compression, compression-shear,
tension), and temperatures (RT to 600 C) to determine the dependence of mechanical properties and deformation and failure modes (i.e., homogeneous deformation vs. inhomogeneous shear banding) on these parameters. Mechanical
testing in the quasi-static to intermediate strain rate regimes was performed using an Instron, Drop Weight Tower, and Split Hopkinson Pressure
Bar, respectively. High-strain-rate mechanical properties of the BMG-matrix composite and monolithic BMG were investigated using dynamic compression (reverse Taylor) and dynamic tension (spall) impact experiments performed using a gas gun instrumented with velocity interferometry and high-speed digital photography. These experiments provided information about dynamic strength and deformation modes, and allowed for validation of constitutive models via comparison of experimental and simulated transient deformation profiles and free surface velocity traces. Hugoniot equation of state measurements were performed on the monolithic BMG to investigate the high
pressure phase stability of the glass and the possible implications of a high pressure phase transformation on mechanical properties. Specimens were recovered for post-impact microstructural and thermal analysis to gain information about the mechanisms of dynamic deformation and fracture, and to examine for possible shock-induced phase transformations of the amorphous phase.
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Nage par flambage de coque sphérique / Swimming through spherical shell bucklingDjellouli, Abderrahmane 15 June 2017 (has links)
Les micronageurs et parmi eux les microangeurs artificiels sont en général, limités à exister dans des écoulements dominés par des forces visqueses. Ces écoulements sont caractérisés par un bas nombre de Reynolds (Re). Cela impacte la stratégie de nage et plus particulièrement les séquences de forme possibles, qui doivent nécessairement être non-réciproques dans l'espace de déformation pour espérer induire un déplacement net non-nul. De plus, due aux forts effets de traînée, les vitesses de nage sont limités à des valeurs faibles.Dans cette thèse, on examine la possibilité d'utiliser un mécanisme de nage basé sur l'instabilité de flambage d'une sphère creuse. Cette instabilité est provoquée en soumettant la sphère à une onde de pression. La particularité de ce mécanisme est qu'il satisfait par construction la condition nécessaire de nage à bas Reynolds exposée précédemment. De plus, la rapidité de la déformation lors de l'instabilité pousse à prévoir l'apparition d'effets inertiels, et ce même à l'échelle microscopique.Une étude expérimentale a été conduite à l'échelle macroscopique dans le but de comprendre la dynamique de l'instabilité et son impact sur le fluide qui entoure la coque creuse. Ces expériences nous permettent de montrer qu'un déplacement net non-nul est produit pour tous les régimes d'écoulements.On met en évidence le rôle de paramètres géométriques, des propriétés du matériau composant la coque creuse et de la rhéologie du fluide sur l'efficacité de la nage.On montre l'existence d'un optimum de déplacement net pour des valeurs intermédiaires du nombre de Reynolds. Pour expliquer cela, on se sert de mesures de PIV résolues temporellement pour mettre en évidence la présence d'effets d'histoire non-triviaux qui augmentent le déplacement net.On dérive un simple modèle en se basant sur les observations expérimentales pour montrer que ce régime optimal de nage est atteignable pour des sphères microscopiques, ceci est possible grâce l'activation rapide de l'instabilité. Cette propriété permet aussi une excitation à haute fréquence en utilisant des ultrasons. Une étude d'échelle nous permet de prédire une vitesse de nage de 1 cm/s pour un micro-robot contrôlé à distance. Cet ordre de grandeur de vitesse est idéal pour des applications biologiques comme la distribution ciblée de médicaments. / Microswimmers, and among them aspirant microrobots, are generally bound to cope with flows where viscous forces are dominant, characterized by a low Reynolds number (Re). This implies constraints on the possible sequences of body motion, which have to be nonreciprocal. Furthermore, the presence of a strong drag limits the range of resulting velocities.Here, we propose a swimming mechanism which uses the buckling instability triggered by pressure waves to propel a spherical hollow shell. The particularity of this mechanism is that it fulfills naturally the necessary condition of swimming at low Re. In addition, the swiftness of the instability might produce inertial effects even at the microscopic scale.With a macroscopic experimental model we show that a net displacement is produced at all Re regimes. We put in evidence the role of geometrical parameters, shell material properties and rheology of the surrounding fluid on the swimming efficiency.An optimal displacement is reached at intermediate Re. Using time-resolved PIV measurements, we explain that non-trivial history effects take place during the instability and enhance net displacement.Using a simple model, derived from the study of shell dynamics, we show that due to the fast activation induced by the instability, this regime is reachable by microscopic shells. The rapid dynamics would also allow high frequency excitation with standard traveling ultrasonic waves. Scale considerations predict a swimming velocity of order 1 cm/s for a remote controlled microrobot, a suitable value for biological applications such as drug delivery.
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Lien entre structure et propriétés électroniques des moirés de graphène étudié par microscopie à effet tunnel / Link between structural and electronic properties of moirés of graphene studied by scanning tunneling microscopyHuder, Loïc 29 November 2017 (has links)
Les dernières années ont vu l'avènement des couches cristallines bidimensionnelles, appelées matériaux 2D. L'exemple le plus connu est le graphène, d'autres étant le nitrure de bore hexagonal isolant et le diséléniure de niobium supraconducteur. Ces matériaux 2D peuvent être empilés de manière contrôlée sous la forme d'hétérostructures de van der Waals pour obtenir les propriétés électroniques désirées. L’une des plus simples hétérostructures de van der Waals est l'empilement de deux couches de graphène tournées. Cet empilement donne naissance à un moiré qui peut être vu comme un potentiel superpériodique dépendant de l'angle entre les deux couches. Les propriétés électroniques des couches tournées de graphène sont intimement liées à ce moiré.Le sujet de cette thèse est l'étude expérimentale du lien entre la structure et les propriétés électroniques des couches tournées de graphène par Microscopie et Spectroscopie à effet tunnel à basse température.Alors que l'effet de l'angle entre les couches sur les propriétés électroniques a déjà été étudié en détail, la modification de celles-ci par une déformation des couches n'a été envisagée que récemment. La première partie de ce travail expérimental étudie la modification par la déformation des propriétés électroniques de couches de graphène tournées d'un angle de 1.26° crûes sur carbure de silicium. La déformation en question est différente dans les deux couches et son effet apparait clairement dans la densité locale d'états électroniques du moiré. Contrairement à une déformation appliquée identiquement aux deux couches, une différence de déformations entre les couches (déformation relative) modifie fortement la structure de bandes même à faibles valeurs de déformations. Alors que la déformation relative était spontanément présente, la deuxième partie de cette thèse s'intéresse à l'effet d'une déformation appliquée directement aux couches de graphène. Cette déformation vient d'une interaction induite par l'approche de la pointe STM vers la surface de graphène. La modification active de la densité d'états qui en résulte dépend de la position de la pointe dans le moiré avec l'apparition d'instabilités périodiques lorsque la distance entre la pointe et l'échantillon est très faible.La troisième partie de cette thèse concerne l'étude d'un autre type de modification des propriétés électroniques consistant en l'induction de supraconductivité dans les couches de graphène. Cette modification est effectuée par une croissance du graphène en une seule étape sur du carbure de tantale supraconducteur. Les résultats montrent la formation d'une couche de carbure de tantale de grande qualité sur laquelle les couches de graphène forment des moirés. La mesure à basse température de la densité d'états de ces moirés montre la présence d'un effet de proximité supraconducteur induit par le carbure de tantale. / Recent years have seen the emergence of two-dimensional crystalline layers, called 2D materials. Examples include the well-known graphene, insulating hexagonal boron nitride and superconducting niobium diselenide. The stacking of these 2D materials can be controlled to achieve desirable electronic properties under the form of van der Waals heterostructures. One of the simplest van der Waals heterostructures is the misaligned stacking of two graphene layers. Twisted graphene layers show a moiré pattern which can be viewed as a superperiodic potential that depends on the twist angle. The electronic properties of the twisted graphene layers are strongly linked to this moiré pattern.The subject of the present thesis is the experimental study of the link between the structural and the electronic properties of twisted graphene layers by means of low-temperature Scanning Tunneling Microscopy and Spectroscopy (STM/STS).While the effect of the twist angle has already been studied in great details, the modulation of the electronic properties by the deformation of the layers has been explored only recently. In the first part of this experimental work, a strain-driven modification of the electronic properties is probed in graphene layers with a twist angle of 1.26° grown on silicon carbide. The determined strain is found to be different in the two layers leading to a clear signature in the local electronic density of states of the moiré even at low strain magnitudes. Contrary to a strain applied in the two layers, this difference of strain between the layers (relative strain) modifies strongly the electronic band structure even at low strain magnitudes. While this relative strain is natively present, the second part of the work explores the effect of an applied strain in the layers. This is realized by approaching the STM tip to the graphene surface to trigger an interaction between the two. The resulting active modification of the density of states is shown to depend on the position on the moiré, leading to periodic instabilities at very low tip-sample distances.In the third part of the work, another type of modification of the electronic properties is studied when superconductivity was induced in the graphene layers. This is done by growing graphene on superconducting tantalum carbide in a single-step annealing. The results show the formation of a high-quality tantalum carbide layer on which graphene layers form moiré patterns. The low-temperature density of states of these moirés show evidence of a superconducting proximity effect induced by the tantalum carbide.
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Modélisation et analyse du comportement dynamique nonlinéaire des rotors / Modeling and Analysis of Nonlinear Dynamic Behavior of RotorsShad, Muhammad rizwan 17 March 2011 (has links)
L'objectif de ce travail de thèse est d'étudier analytiquement et numériquement le comportementdynamique non-linéaire des rotors, en prenant en compte des effets significatifs comme les grandesdéformations en flexion, les non-linéarités géométriques et le cisaillement. Le manuscrit est diviséen trois parties principales. Dans la première partie, le principe de Hamilton est utilisé pour formulerles équations du mouvement qui prennent en compte un ensemble d’effets non-linéaires comme desdéformations d'ordre supérieur en flexion et le cisaillement. De plus, si les supports du rotor nepermettent pas à l'arbre de se déplacer dans la direction axiale, il y a alors une force dynamiqueharmonique agissant axialement sur le rotor en fonctionnement. Ces modèles se composentd’équations différentielles non-linéaires du deuxième et du quatrième ordre.Les deux parties suivantes sont consacrées à la résolution des différents modèles non-linéairesdéveloppés dans la première partie. Des méthodes analytiques et numériques sont appliquées afin detraiter les équations non-linéaires du mouvement. Une méthode basée sur des développementsasymptotiques, la méthode des échelles multiples (MEM) est utilisée. Les courbes de réponse sonttracées pour différentes résonances possibles et l'effet de la non-linéarité est discuté par rapport àl'analyse linéaire. La réponse forcée du système provoquée par un balourd est également présentéepour plusieurs configurations du rotor. Lorsque les déformations de cisaillement sont prises encompte, l'analyse est effectuée pour différents élancements afin de mettre en évidence cet effet sur ladynamique d’un système arbre-disque / The objective of the present work is to investigate the nonlinear dynamic behavior of the rotorsystems analytically and numerically, taking into account the significant effects, for example, higherorder large deformations in bending, geometric nonlinearity and shear effects.This thesis is dividedinto two major parts. In the first part, Hamilton’s principle is used to derive the equations of motionwhich take into account various effects, for example, nonlinearity due to higher order largedeformations in bending and shear effects. In addition, if the supports of the rotor do not allow theshaft to move in the axial direction, then there will be a dynamical force acting axially on the rotoras it operates. The mathematical models are composed of coupled nonlinear differential equations ofthe 2nd and the 4th order.In the second part, the resolution of various nonlinear models developed in the first part isaddressed. Analytical and numerical methods are applied for treating the nonlinear equations ofmotion. A method based on asymptotic developments, the method of multiple scales (MMS) is used.The response curves are plotted for different possible resonance conditions and the effect ofnonlinearity is discussed with respect to the linear analysis. The forced response of the system due toa mass unbalance is also presented for various configurations of the rotor. When shear deformationsare taken into account, the analysis is performed for various slenderness ratios to highlight sheareffects on the dynamics of the shaft-disk rotor systems
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