The diploma work deals with a mathematical description of vibration and its generation when machining. Moreover, some techniques of modal parameters measurement in the theoretical part are included. The practical part is designed and based on the measured natural frequencies of the machine with specific tool and materials. In conclusion, a lobe diagram stability for semiautomatic lathe SPN 12 CNC and selected machining operation is specified by means of apparatus.

Ion traps can easily be miniaturized to become portable mass spectrometers. Trapped ions can be ejected by adjusting voltage settings of the radiofrequency (RF) signal applied to the electrodes. Several ion trap designs include the quadrupole ion trap (QIT), cylindrical ion trap (CIT), linear ion trap (LIT), rectilinear ion trap (RIT), toroidal ion trap, and cylindrical toroidal ion trap. Although toroidal ion traps are being used more widely in miniaturized mass spectrometers, there is a lack of fundamental understanding of how the toroidal electric field affects ion motion, and therefore, the ion trap's performance as a mass analyzer. Simulation programs can be used to discover how traps with toroidal geometry can be optimized. Potential mapping, field calculations, and simulations of ion motion were used to compare three types of toroidal ion traps: a symmetric and an asymmetric trap made using hyperbolic electrodes, and a simplified trap made using cylindrical electrodes. Toroidal harmonics, which represent solutions to the Laplace equation in a toroidal coordinate system, may be useful to understand toroidal ion traps. Ion trapping and ion motion simulations were performed in a time-varying electric potential representing the symmetric, second-order toroidal harmonic of the second kind—the solution most analogous to the conventional, Cartesian quadrupole. This potential distribution, which we call the toroidal quadrupole, demonstrated non-ideal features in the stability diagram of the toroidal quadrupole which were similar to that for conventional ion traps with higher-order field contributions. To eliminate or reduce these non-ideal features, other solutions to the Laplace equation can be added to the toroidal quadrupole, namely the toroidal dipole, toroidal hexapole, toroidal octopole, and toroidal decapole. The addition of a toroidal hexapole component to the toroidal quadrupole provides improvement in ion trapping, and is expected to play an important role in optimizing the performance of all types of toroidal ion trap mass spectrometers.The cylindrical toroidal ion trap has been miniaturized for a portable mass spectrometer. The first miniaturized version (r0 and z0 reduced by 1/3) used the same central electrode and alignment sleeve as the original design, but it had too high of capacitance for the desired RF frequency. The second miniaturized version (R, r0, and z0 reduced by 1/3) was designed with much less capacitance, but several issues including electrode alignment and sample pressure control caused the mass spectra to have poor resolution. The third miniaturized design used a different alignment method, and its efficiency still needs to be improved.

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Dans le cadre du Projet National SOLCYP, le présent travail avait pour but d'étudier la réponse des pieux sous chargements axiaux pour les phases avant, pendant et après cycles. Pour atteindre cet objectif, une étude expérimentale étendue a donc été réalisée par le moyen de deux compagnes d'essais de chargements cycliques sur différents types de pieux instrumentées (battus, forés, vissés) dans deux sites expérimentaux : le site de Merville dans l'argile surconsolidée des Flandres et le site de Loon-Plage près de Dunkerque dans les sables denses des Flandres. Les essais cycliques comportaient des essais en compression, en traction et alternés avec des séries de cycles à forte amplitude conduisant à la rupture cyclique et des séries d'amplitude modérée à très grands nombres de cycles (N>5 000 cycles).L'interprétation de ces essais a englobé, d'une part, une analyse globale du comportement des pieux sous chargements cycliques notamment (i) la réduction de la capacité du pieu; (ii) le nombre de cycles que le pieu peut support avant la rupture (iii) l'évolution du déplacement en tête des pieux (rigidité cyclique). D'autre part, elle a intégré une étude locale en particulier sur la dégradation du frottement latéral et l'évolution de la résistance de pointe du pieu. Cette thèse, basée sur l'étude expérimentale, a permis la formulation des conclusions pratiques sur le comportement des pieux sous chargements cycliques axiaux et a proposé des perspectives pour bien cerner cette problématique / As part of the French National research project SOLCYP, the purpose of this work was study the behavior of the piles under axial loadings for the phases before, during and after cycles.To achieve this objective, an extensive series of static and cyclic axial pile load tests have been carried out in two experimental sites of the North of France: the overconsolidated Flandrian clays (Merville experimental site) and in dense Flandrian sands (Loon-Plage experimental site). Tests were performed on driven closed-ended pipe piles, bored piles and screwed. All piles were instrumented with retrievable extensometers for measuring the load distribution along the pile wall.Cyclic load tests were composed of series of cycles of constant load amplitude. A large range of load histories were applied including series of small amplitude cycles and great number of cycles (N > 5000) and series of large amplitude cycles leading to cyclic failure after a small number of cycles..A large volume of data has been interpreted to describe the effects of axial cyclic loads on the behavior of the piles. The interpretation of these tests included, on the one hand, a global analysis focusing on (i) the potential reduction on the ultimate axial capacity; (ii) the number of load cycles of a given load that the pile can sustain before cyclic failure and (iii) the evolution of displacements of the pile head during cyclic loading (pile stiffness). In addition, it integrated a local study in particular on shaft friction degradation along the pile wall and evolution of the resistance of point of the pile.This thesis, based on the experimental study, allowed the formulation of the practical conclusions on the behavior of the piles under axial cyclic loadings and proposed prospects for determining these problems well

Ce mémoire concerne la modélisation mathématique de l’érythropoïèse, à savoir le processus de production des érythrocytes (ou globules rouges) et sa régulation par l’érythropoïétine, une hormone de contrôle. Nous proposons une extension d’un modèle d’érythropoïèse tenant compte du vieillissement des cellules matures. D’abord, nous considérons un modèle structuré en maturité avec condition limite mouvante, dont la dynamique est capturée par des équations d’advection. Biologiquement, la condition limite mouvante signifie que la durée de vie maximale varie afin qu’il y ait toujours un flux constant de cellules éliminées. Par la suite, des hypothèses sur la biologie sont introduites pour simplifier ce modèle et le ramener à un système de trois équations différentielles à retard pour la population totale, la concentration d’hormones ainsi que la durée de vie maximale. Un système alternatif composé de deux équations avec deux retards constants est obtenu en supposant que la durée de vie maximale soit fixe. Enfin, un nouveau modèle est introduit, lequel comporte un taux de mortalité augmentant exponentiellement en fonction du niveau de maturité des érythrocytes. Une analyse de stabilité linéaire permet de détecter des bifurcations de Hopf simple et double émergeant des variations du gain dans la boucle de feedback et de paramètres associés à la fonction de survie. Des simulations numériques suggèrent aussi une perte de stabilité causée par des interactions entre deux modes linéaires et l’existence d’un tore de dimension deux dans l’espace de phase autour de la solution stationnaire. / This thesis addresses erythropoiesis mathematical modeling, which is the process of erythrocytes production and its regulation by erythropeitin. We propose an erythropoiesis model extension which includes aging of mature cells. First, we consider an age-structured model with moving boundary condition, whose dynamics are represented by advection equations. Biologically, the moving boundary condition means that the maximal lifespan varies to account for a constant degraded cells flux. Then, hypotheses are introduced to simplify and transform the model into a system of three delay differential equations for the total population, the hormone concentration and the maximal lifespan. An alternative model composed of two equations with two constant delays is obtained by supposing that the maximal lifespan is constant. Finally, a new model is introduced, which includes an exponential death rate depending on erythrocytes maturity level. A linear stability analysis allows to detect simple and double Hopf bifurcations emerging from variations of the gain in the feedback loop and from parameters associated to the survival function. Numerical simulations also suggest a loss of stability caused by interactions between two linear modes and the existence of a two dimensional torus in the phase space close to the stationary solution.