Dissertations / Theses on the topic 'Principe de Hamilton'
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Marone-Hitz, Pernelle. "Modélisation de structures spatiales déployées par des mètres ruban : vers un outil métier basé sur des modèles de poutre à section flexible et la méthode asymptotique numérique." Thesis, Ecole centrale de Marseille, 2014. http://www.theses.fr/2014ECDM0011/document.
Dimensions of spatial satellites tend to grow bigger and bigger, whereas the volume in launchers remains very limited. Deployable structures must be used to meet this contradiction. To expand the offer of possible solutions, the Research Department of Thales Alenia Space is currently studying tape springs as an innovative deployment solution. The first structure to be considered is a telescope that is deployed by the uncoiling of six tape springs that also ensure the positioning of the secondary mirror. Other deployable structures that use the properties of tape springs are under investigation : mast, solar panels,...Specific modeling tools then appear compulsory to model deployment scenarios and multiply the tested configurations. Two previous PhD thesis lead to the development of energetic rod models with flexible cross-sections that account for planar ([Guinot2011])and three dimensional behavior of tape springs ([Picault2014]). This PhD thesis presents several contributions on these rod models with flexible cross-sections. The hypotheses of the model were improved. Re-positioning the reference rod line so that it passes through the sections' centroids leads to results that are closer to experimental scenarios (creation and disappearance of folds in the spring). The hypotheses and equations of the model are now definitively formalized.We have derived the 1D local equations in the three-dimensional behavior case in the most generalist way. Then, the derivation of the equations in simplified cases (restriction to 2D behavior, shallow cross-section) enabled us to obtain several analytic solutions and the equations to implement in the specific modeling tool.We have developed on the continuation software ManLab the first elements towards a home made, efficient modeling tool dedicated to the modeling of tape springs. Two main contributions can be listed :- A generalist tool, efficient in calculus times, to study 1D differential problems (BVP, Boundary Value Problems). The local equations of the rod models with flexible cross sections were implemented in this tool, with a discretization based on polynomial interpolation and orthogonal collocation.- A specific finite element for rods with flexible cross sections and its implementation in ManLab.These elements enabled us to perform several numerical simulations and have a better understanding of the behavior of tape springs thanks to full bifurcation diagrams obtained for significant tests
Nguyen, Thi Tuyen. "Comportement en temps long des solutions de quelques équations de Hamilton-Jacobi du premier et second ordre, locales et non-locales, dans des cas non-périodiques." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S089/document.
The main aim of this thesis is to study large time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN in presence of an Ornstein-Uhlenbeck drift. We also consider the same issue for a first order Hamilton-Jacobi equation. In the first case, which is the core of the thesis, we generalize the results obtained by Fujita, Ishii and Loreti (2006) in several directions. The first one is to consider more general operators. We first replace the Laplacian by a general diffusion matrix and then consider a non-local integro-differential operator of fractional Laplacian type. The second kind of extension is to deal with more general Hamiltonians which are merely sublinear
Claisse, Julien. "Dynamique des populations : contrôle stochastique et modélisation hybride du cancer." Phd thesis, Université Nice Sophia Antipolis, 2014. http://tel.archives-ouvertes.fr/tel-01066020.
Delacroix, Bastien. "Développement d'un modèle intégral avec transport d'une fonction couleur pour la simulation d'écoulements de films minces partiellement mouillants." Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0005.
Why does a drop of water tend to form a sphere? Why does it cling to its leaf in the morning dew? On the contrary, why does it flow down towards the ground? All these seemingly simplistic questions involve highly complex microscopic phenomena whose physical nature is still the subject of debate. However, understanding them is a major challenge in many industrial applications. This is particularly true in aeronautics, where a thin film forms on the wings after the aircraft has passed through a cloud or after a defreezing operation. The evolution of the wetted surface by this film, like its transition into rivulets under the effect of air shear, as well as its eventual refreezing a little further outside the protection zones, is not taken into account in thermal defrost simulation tools; or only in a rudimentary way via empirical correlations. However, this ice accretion must be controlled for safety reasons and aerodynamic performance. This is why it is necessary to improve existing tools by developing new models capable of considering the influence of capillary forces on a macroscopic scale, specifically at the contact line level, in order to be able to predict the dynamics of a sheared film.The overall objective of this study is therefore to develop a suitable model for large-scale simulation of partially wetting thin film flow.To answer this objective, an approach based on a Shallow-water equations was adopted. However, this system in its classical form does not allow the simulation of thin films with partial wetting effects. One solution to consider these effects is to add a macroscopic force concentrated to the contact line. This singular force enables the macroscopic Young-Dupré law to be verified locally. The issue with this approach is to localize the force at the contact line only. Unlike other models in the literature, which are all based on the use of an adjustable parameter allowing the distinction between dry and wet zones, we offer here an approach involving the transport of a color function. This function, defined as equal to one in wet zones and zero in dry zones, has the advantage of having an identically zero gradient, except at the contact line, enabling the contact line force to be localized.The introduction of this color function needs a partial reformulation of the Shallow-water equations, in order to integrate this new function in the expression of the various force terms acting on the film. In order to justify the choice of this new formulation, a method based on an eulerian formulation of Hamilton's principle was used. This method helps to obtain a momentum equation compatible with the conservation of energy of the system under study, with the only starting point being an expression of the system's energy density as a function of the variables used.This new system of equations, in addition to being completely calibration parameter free, has the advantage of being entirely hyperbolic in the case where curvature effects are not taken into account. This has helped us to develop an HLLC-type Riemann solver to solve this equation system numerically. In order to test out the robustness of the physical and numerical models, a set of verification and validation cases was set up.Finally, curvature terms were considered in the final numerical scheme, considerably extending the scope of application of this new color function model. In this way, problems where capillary effects are predominant could be simulated
Kogevnikov, Ivan. "Modélisation des systèmes de dimension infinie - Application à la dynamique des pneumatiques." Phd thesis, Ecole des Ponts ParisTech, 2006. http://pastel.archives-ouvertes.fr/pastel-00001850.
Guinot, François. "Déploiement régulé de structures spatiales : vers un modèle unidimensionnel de mètre ruban composite." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10019.
The research department of Thales Alenia Space is studying new concepts of space telescopes whose secondary mirror is deployed thanks to the unreeling of six tape-springs. A breadboard using metallic tape-springs has been built during preliminary studies and has exhibited a deployment that is too energetic and induce too important shocks.In this thesis a new kind of tape-spring with a controlled uncoiling speed is introduced. Secondly a rod model with highly deformable thin-walled cross-sections describing the dynamic behaviour of tape-springs is derived.In order to over come the deployment speed of a tape spring, a viscoelastic layer is stuck on its sides. Thanks to its properties varying with the temperature, the viscoelastic layer is used to maintain the tape-spring in a coiled configuration at low temperature whereas a local heating leads to a controlled uncoiling. These phenomenons have been underlined experimentally and numerically.Because of the high complexity of classical shell models and the lack of details of simplified models, smart modelling methods need to be developed to describe the highly non linear behaviour of a tape-spring. A planar rod model with highly deformable thin-walled cross-sections that accounts for large displacements and large rotations in dynamics is proposed. Starting from a classical shellmodel, the main additional assumption consists in introducing an elastica kinematics to describe thelarge changes of the cross-section shape with very few parameters. The expressions of the strain andkinetic energies are derived by performing an analytical integration over the section. The Hamilton principle is directly introduced in a suitable finite element software to solve the problem. Several examples (folding, coiling and deployment of a tape spring) are studied through the FEM software COMSOL to demonstrate the ability of the 4-parameter model to account for several phenomena: creation of a single fold and associated snap-through behaviour, splitting of a fold into two, motion of a fold along the tape during a dynamic deployment, scenarios of coiling and uncoiling of a bistable tape-spring
Valcárcel, Flores Carlos Enrique [UNESP]. "Estudo clássico completo do formalismo de Hamilton-Jacobi." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/102544.
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Nesta tese, apresentamos a formulação clássica completa da teoria de Hamilton-Jacobi para sistemas vinculados. Usando o método de Lagrangianas Equivalentes de Carathéodory obtemos um conjunto de Equações Diferenciais Parciais de Hamilton-Jacobi, também chamado de Hamiltonianos. A Condição de Integrabilidade nos permite dividir os Hamiltonianos entre involutivos e não-involutivos. Construímos os Parênteses Generalizados a fim de eliminar os Hamiltonianos não-involutivos, enquanto que relacionamos os Hamiltonianos involutivos com o Gerador das transformações canônicas. Por outro lado, a Equação de Lie é resultado da realização das variações totais no funciona lde ação, e que é relacionada às simetrias da teoria. Usamos a Equação de Lie e a estrutura das Equaçõoes Características, que indicam a evolução dinâmica do sistemas, para associar o Gerador de transformações canônicas às simetrias de calibre. Aplicamos o formalismo de Hamilton-Jacobi ao modelo da Mecânica Quântica Topologica, ao modelo BF bi-dimensional equivalente à Teoria de Jackiw-Teitelboim, ao campo de Yang-Mills Topologicamente Massivo e seu equivalente Auto-dual, assim como para o campo da Gravitação linearizada
It is presented the complete classical formulation of the Hamilton-Jacobi theory for constrained systems. From fixed point variations and using the Carathéodory’s method of Equivalent Lagrangian we obtain a set of Hamilton-Jacobi Partial Differential Equations, also called Hamiltonians. The Integrability Condition allow us to divide the Hamiltonians between involutive and non-involutive ones. We build the Generalized Brackets in order to eliminate the non-involutive Hamiltonians, whereas we relate the involutive Hamiltonians to the Generator of Canonical Transformations. On the other hand, we build the Lie Equation, result of perform total variations to the action functional and which is related to the symmetries of the theory. We use the Lie equation along with the structure of the Characteristic Equations, related to the dynamical evolution of the systems, to associate the Generator of Canonical Transformation to Gaugesymmetries. We apply this formalism to the Topologically Quantum Mechanics, the two dimensional BF model equivalent to the Jackiw-Teitelboim theory, the Topologically Massive Yang-Mills field as well as its correspondent self-dual and to the Linearized Gravity field
Valcárcel, Flores Carlos Enrique. "Estudo clássico completo do formalismo de Hamilton-Jacobi /." São Paulo, 2012. http://hdl.handle.net/11449/102544.
Banca: Abraham Zimerman
Banca: Denis Dalmazi
Banca: Ion Vasile Vancea
Banca: Vladislav Kupriyanov
Resumo: Nesta tese, apresentamos a formulação clássica completa da teoria de Hamilton-Jacobi para sistemas vinculados. Usando o método de Lagrangianas Equivalentes de Carathéodory obtemos um conjunto de Equações Diferenciais Parciais de Hamilton-Jacobi, também chamado de Hamiltonianos. A Condição de Integrabilidade nos permite dividir os Hamiltonianos entre involutivos e não-involutivos. Construímos os Parênteses Generalizados a fim de eliminar os Hamiltonianos não-involutivos, enquanto que relacionamos os Hamiltonianos involutivos com o Gerador das transformações canônicas. Por outro lado, a Equação de Lie é resultado da realização das variações totais no funciona lde ação, e que é relacionada às simetrias da teoria. Usamos a Equação de Lie e a estrutura das Equaçõoes Características, que indicam a evolução dinâmica do sistemas, para associar o Gerador de transformações canônicas às simetrias de calibre. Aplicamos o formalismo de Hamilton-Jacobi ao modelo da Mecânica Quântica Topologica, ao modelo BF bi-dimensional equivalente à Teoria de Jackiw-Teitelboim, ao campo de Yang-Mills Topologicamente Massivo e seu equivalente Auto-dual, assim como para o campo da Gravitação linearizada
Abstract: It is presented the complete classical formulation of the Hamilton-Jacobi theory for constrained systems. From fixed point variations and using the Carathéodory's method of Equivalent Lagrangian we obtain a set of Hamilton-Jacobi Partial Differential Equations, also called Hamiltonians. The Integrability Condition allow us to divide the Hamiltonians between involutive and non-involutive ones. We build the Generalized Brackets in order to eliminate the non-involutive Hamiltonians, whereas we relate the involutive Hamiltonians to the Generator of Canonical Transformations. On the other hand, we build the Lie Equation, result of perform total variations to the action functional and which is related to the symmetries of the theory. We use the Lie equation along with the structure of the Characteristic Equations, related to the dynamical evolution of the systems, to associate the Generator of Canonical Transformation to Gaugesymmetries. We apply this formalism to the Topologically Quantum Mechanics, the two dimensional BF model equivalent to the Jackiw-Teitelboim theory, the Topologically Massive Yang-Mills field as well as its correspondent self-dual and to the Linearized Gravity field
Doutor
Maia, Natália Tenório [UNESP]. "Estudo sobre a teoria de vínculos de Hamilton-Jacobi." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/132007.
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
A teoria de Hamilton-Jacobi geralmente é apresentada como uma extensão da teoria de Hamilton através das transformações canônicas. No entanto, o matemático Constantin Carathéodory mostrou que essa teoria, sua existência e validade, independem do formalismo hamiltoniano. Neste trabalho, apresentaremos a abordagem de Carathéodory para a teoria de Hamilton-Jacobi. Partindo desse procedimento, construiremos uma teoria de vínculos para que se possa resolver problemas com vínculos involutivos e não-involutivos. Para isso, analisaremos a integrabilidade das equações e introduziremos a operação dos parênteses generalizados que, no lugar do parênteses de Poisson, passará a descrever a dinâmica de sistemas vinculados. Mostraremos uma aplicação dessa teoria de vínculos no modelo BF da teoria de campos. Para finalizar, trataremos da Termodinâmica Axiomática de Carathéodory e também da teoria de Hamilton-Jacobi na Termodinâmica, o que é válido para ilustrar a grande abrangência desse formalismo
The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the field theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism
CNPq: 133488/2011-0
Maia, N. T. (Natália Tenório). "Estudo sobre a teoria de vínculos de Hamilton-Jacobi /." São Paulo, 2013. http://hdl.handle.net/11449/132007.
Co-orientador:
Banca:Andrey Yuryevich Mikhaylov
Banca: Edmundo Capelas de Oliveira
Resumo: A teoria de Hamilton-Jacobi geralmente é apresentada como uma extensão da teoria de Hamilton através das transformações canônicas. No entanto, o matemático Constantin Carathéodory mostrou que essa teoria, sua existência e validade, independem do formalismo hamiltoniano. Neste trabalho, apresentaremos a abordagem de Carathéodory para a teoria de Hamilton-Jacobi. Partindo desse procedimento, construiremos uma teoria de vínculos para que se possa resolver problemas com vínculos involutivos e não-involutivos. Para isso, analisaremos a integrabilidade das equações e introduziremos a operação dos parênteses generalizados que, no lugar do parênteses de Poisson, passará a descrever a dinâmica de sistemas vinculados. Mostraremos uma aplicação dessa teoria de vínculos no modelo BF da teoria de campos. Para finalizar, trataremos da Termodinâmica Axiomática de Carathéodory e também da teoria de Hamilton-Jacobi na Termodinâmica, o que é válido para ilustrar a grande abrangência desse formalismo
Abstract: The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the field theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism
Mestre
Rondepierre, Aude. "Algorithmes hybrides pour le contrôle optimal des systèmes non linéaires." Phd thesis, Grenoble INPG, 2006. http://tel.archives-ouvertes.fr/tel-00112203.
Barbagallo, Mathias. "Statistical energy analysis and variational principles for the prediction of sound transmission in multilayered structures." Doctoral thesis, KTH, MWL Marcus Wallenberg Laboratoriet, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-118427.
QC 20130218
Barreto, Gilmar Wilian. "Projeto de uma perfuratriz multifuncional para execução de estacas e desenvolvimento de um ensaio de campo que utiliza o sistema de monitoração eletrônica da perfuratriz." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-18032015-152955/.
This thesis presents the design of a drilling rig that allows the execution of five types of deep foundation, and the development of a field test that allows measuring the skin friction resistance developed between the instrument involved by the excavated ground and the natural soil. The drilling rig was designed to make continuous flight auger, bored pile, continuous flight auger with segmented auger, root pile and hollow-auger pile. The continuous flight auger and bored piles are widely used in Brazil; the root pile and hollow-auger pile are used for in special conditions, and the continuous flight auger with segmented auger, is although more recent, but its application has had increased application grown in over the last ten years. For the multifunctional drilling rig, calculations and basic designs of the main sets are presented. For the new field test denominated FDT - Full Displacement Test, a theoretical development based on the universal principle of energy conservation was made carried out resulting and the result, in practical terms, was to obtain in the attainment of the skin friction defined in this thesis as equivalent unit skin friction (fse). The results obtained from the data acquired by the electronic monitoring system of drilling rigs were consistent among themselves, indicating the possibility of practically achieve the repeatability of the test. Among the various tests performed, emphasis was given to tests in the experimental field of foundations and geotechnics, of the College of Agricultural Engineering FEAGRI, Campinas University UNICAMP, and were correlated to the skin friction resistance obtained from the static load tests performed on site by Albuquerque (2001), based on the adjustments done to the instrumented level depth of 11.70 m, for which a factor (G2) was given in each type tested (bored, C.F.A and omega). From the adjustments made to the 11,70 m level, load-bearing capacity of skin friction predictions were made for other instrumented levels (5.00 m; 11.10 m and 12.00 m) presenting consistent results.
Rousseau, Grégory. "Véhicule hybride et commande optimale." Phd thesis, École Nationale Supérieure des Mines de Paris, 2008. http://pastel.archives-ouvertes.fr/pastel-00005237.
Ašković, Veljko. "Aerial vehicle guidance problem through the Pontryagin Maximum Principle and Hamilton Jacobi Bellman approach." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS553.
This thesis is mainly composed of two parts. In the first part, we investigate the large time behavior of the value function associated to an optimal control problem in the finite dimensional case. We first establish the large time asymptotic expansion in the linear quadratic (LQ) theory. We then generalize this expansion to nonlinear dynamical systems more precisely within the class of dissipative systems. In the second part, we solve numerically the guidance problem of an aerial vehicle. We first model mathematically the equations of motion. Then, we implement three methods in order to solve the problem: a direct method, an indirect method based on the continuation process and the shooting method. Finally, we implement a numerical method derived from the Hamilton Jacobi Bellman theory in order to compute optimal trajectories and at the same time the reachable sets
Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Análisis de vibración libre de vigas laminadas de materiales compuestos utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2021. http://hdl.handle.net/10757/657266.
In this work, is presented a finite element model that describes the free vibration behavior of laminated composite beams. The model is developed by the Hamilton principle and the Timoshenko theory that includes shear deformations. Composite laminates are assumed to be orthotropic with fibers oriented in different directions, such as Angle Ply and Cross Ply cases. This investigation works out on a MAPLE program for laminated composites materials that will be completed all in MATLAB program. In order to validate the model, the results are compared with different literatures, also verify the formulation that is quite accurate and obtain quite satisfactory results in the investigation. High order interpolations are assumed to approximate fundamental variables. A convergence study and parametric study will be carried out with the same number of laminas in different directions.
Tesis
Oussaily, Aya. "Étude théorique et numérique des systèmes modélisant la dynamique des densités des dislocations." Thesis, Compiègne, 2021. https://bibliotheque.utc.fr/Default/doc/SYRACUSE/2021COMP2634.
In this thesis, we are interested in the theoretical and numerical studies of dislocations densities. Dislocations are linear defects that move in crystals when those are subjected to exterior stress. More generally, the dynamics of dislocations densities are described by a system of transport equations where the velocity field depends non locally on the dislocations densities. First, we are interested in the study of a one dimensional submodel of a (2 × 2) Hamilton-Jacobi system introduced by Groma and Balogh in 1999, proposed in the two dimensional case. For this system, we prove global existence and uniqueness results. Adding to that, considering nondecreasing initial data, we study this problem numerically by proposing a finite difference implicit scheme for which we show the convergence. Then, inspired by the first work, we show a more general theory which allows us to get similar results of existence and uniqueness of solution in the case of one dimensional eikonal systems. By considering nondecreasing initial data, we study this problem numerically. Under certain conditions on the velocity, we propose a finite difference implicit scheme allowing us to calculate the discrete solution and simulate then the dislocations dynamics via this model
Neves, Luis Fernando de Seixas. "Metodologia para a determinação da eficiência do ensaio SPT através de prova de carga estática sobre o amostrador padrão." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-02032016-142441/.
The standard penetration test (SPT) is the most used soil investigation tool in the world. Due to the great number of variables that influences its results, the measurement of the efficiency becomes imperative to the transposition of experiences between developed practices in different places. Unfortunately, the measurement of the efficiency through the instrumentation of the hammer impact is economically inpracticable to most of the soil investigation firms in Brazil. This work presents a methodology to determinate the SPT efficiency based on the Hamilton\'s principle and on the execution of static load test over the sampler, what seems to be a good alternative to end this situation.
Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Análisis de vibración libre de vigas laminadas de materiales compuestos utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2001. http://hdl.handle.net/10757/654828.
This research focuses on the free vibration analysis of Timoshkenko beams using the finite element method. The model is developed using the Hamilton principle and the Timoshenko beam theory that includes shear deformations. high order interpolations are assumed for the approximation of the fundamental variables. The materials to be used are isotropic. A program for these materials is implemented in MATLAB. Results are compared with others obtained in the literature to validate the model. A parametric study is carried out with the same length and different slenderness. It is verified that the formulation is quite precise with satisfactory results to the investigation.
Trabajo de investigación
Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Vibración libre de vigas de material isotrópico utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2021. http://hdl.handle.net/10757/654828.
This research focuses on the free vibration analysis of Timoshkenko beams using the finite element method. The model is developed using the Hamilton principle and the Timoshenko beam theory that includes shear deformations. high order interpolations are assumed for the approximation of the fundamental variables. The materials to be used are isotropic. A program for these materials is implemented in MATLAB. Results are compared with others obtained in the literature to validate the model. A parametric study is carried out with the same length and different slenderness. It is verified that the formulation is quite precise with satisfactory results to the investigation.
Trabajo de investigación
Morais, Thaise da Silva Oliveira. "Interpretação racional de resultados de ensaios SPT com base em conceitos de energia." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-29022016-111249/.
The Standard Penetration Test (SPT) with measurement of the index of resistance to dynamic penetration of the sampler (NSPT) is one of the most widespread in situ tests in Brazil. The popularity of this test is due to its practicality, low cost, acquired experience by practitioners and simple applicability of its results. However, this test has been widely criticized because of variation in equipment and procedures, which causes significant dispersion in the results. The NSPT index is usually used to estimate the bearing capacity and settlement of foundations, using empirical or semi-empirical correlations. This fact also receives criticism, as these correlations are based on practical observations without any scientific basis. The NSPT index depends on the amount of energy delivered to the sampler, during the blow in the SPT test. Thus, knowing the equipment efficiency allows normalizing the NSPT values to a standard reference value. The international reference value corresponds to an efficiency of 60%. In this way, the rational analysis of the results of SPT tests essentially depends on the estimation of the quantities of energy involved in the test. This research presents the rational interpretation of the SPT test results based on monitoring the amounts of energy involved in the test. The energies were indirectly obtained through force and acceleration signals during the stress wave propagation along the string of rods. For this, rod subassemblies instrumented with load cells and accelerometers were used. A suitable data acquisition system for monitoring dynamic events was also used. The SPT tests were performed with instrumented subassemblies placed at two positions along the string of rods (top and bottom simultaneously). Thus, from this arrangement, the amounts of energy accountable for the sampler penetration and the energy losses occurred were determined. Likewise, the dynamic resistances mobilized in the soil-sampler system during the penetration were determined from the force and acceleration signals at the top of the sampler. These experimental results were compared with those theoretical results, based on the Principle of Hamilton. With the efficiency results, the length of recovered samples and the external skin friction in the soil-sampler system, the balance of the reactions mobilized in the sampler was verified, as proposed by Aoki (2013). Thus, the tip and skin friction (internal and external) resistances in the soil-sampler system were obtained.
Gourma, Mustapha. "Towards better understanding of the Smoothed Particle Hydrodynamic Method." Thesis, Cranfield University, 2003. http://hdl.handle.net/1826/133.
Buechler, Miles A. "Variational Modeling of Ionic Polymer-Based Structures." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/34309.
Master of Science
Machů, Zdeněk. "Výpočtové modelování piezoelektrických vrstevnatých kompozitů a analýza jejich elektro-mechanické odezvy při harmonickém kmitání." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-400492.
Noreña, Pablo Cesar Trejo. "Estimativa da eficiência do ensaio SPT através da execução da prova de carga estática sobre o amostrador." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-08112012-113424/.
The Standard Penetration Test, SPT, is one of the most used one for subsoil information in the USA and Brazil. The data obtained in this dynamic test, such as the penetration resistance index, NSPT, the soil classification and phreatic level are used by different methods to estimate the shallow and deep foundations load capacity. For the same soil, the index NSPT can be different if different equipments are used, because different SPT equipments show different efficiency levels. Having this in mind, an alternative to estimate the essay efficiency of the SPT test is using the static load test (SLT) to the sampler. This test was implemented in order to evaluate the efficiency of SPT. To do so, 13 dynamic tests and 13 static tests were performed in the experimental campus of the State University of São Paulo at Bauru (Unesp- Bauru-Brazil). To estimate the efficiency of the SPT test through the dynamic test, a data acquisition system was used to register accelerations and forces at the located section close to the sampler SPT. The dynamic test was modified so that it would be possible to use many nominal potential energy of the hammer and elevation systems. The estimation of the efficiency made through the SLT tests was based on Hamilton\'s principle. Furthermore, by comparing the dynamic and static behavior, we can get the soil-sampler interface static resistance. This resistance is calculated by using the field data through various estimation methods such as Aoki\'s (2007), De Souza\'s (2009) and Odebrecht\'s (2003). The estimates of the efficiency obtained through SLT test were found to be consistent with those obtained through the SPT modified tests. We conclude that SLT is a simple and non-expensive alternative to obtain the efficiency of SPT equipment.
Getgood, Thomas. "On the necessity of the maximum principle for systems in the proof of Hamilton's matrix Harnack inequality." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66799.
L'équation de la chaleur, bien comprise dans les espaces plats, présete un certain degré de difficulté sur les variétés Riemannienne. Parmi les outils importants pour comprendre ses solutions, on trouve l'inégalité matricielle d'Hamilton [7]. Ensuite, nous présenterons un nouvel outil qui est le théorèm de rang invariable et nous l'utiliserons afin de créer une nouvelle prueve de l'inégalité matricielle d'Hamilton. Cette nouvelle prueve nous fournie le meme hypotèses mais sans avoir recours au principe du maximum pour les systèmes d'équations d'Hamilton [6]. Finalement, nous discuterons les implications potentielles de cette nouvelle technique de preuve.
Wahbi, Wassim. "Contrôle stochastique sur les réseaux." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED072.
This thesis consists of three parts which deal with quasi linear parabolic PDE on a junction, stochastic diffusion on a junction and stochastic control on a junction with control at the junction point. We begin in the first Chapter by introducing and studying a new class of non degenerate quasi linear parabolic PDE on a junction, satisfying a Neumann (or Kirchoff) non linear and non dynamical condition at the junction point. We prove the existence and the uniqueness of a classical solution. The main motivation of studying this new mathematical object is the analysis of stochastic control problems with control at the junction point, and the characterization of the value function of the problem in terms of Hamilton Jacobi Bellman equations. For this end, in the second Chapter we give a proof of the existence of a diffusion on a junction. The process is characterized by its local time at the junction point, whose quadratic approximation is centrally related to the ellipticty assumption of the second order terms around the junction point.We then provide an It's formula for this process. Thanks to the previous results, in the last Chapter we study a problem of stochastic control on a junction, with control at the junction point. The set of controls is the set of the probability measures (admissible rules) satisfying a martingale problem. We prove the compactness of the admissible rules and the dynamic programming principle
Tabet, Tchamba Thierry Wilfried. "Comportement asymptotique des solutions du problème de Cauchy-Dirichlet généralisé pour des équations de Hamilton-Jacobi visqueuses." Thesis, Tours, 2010. http://www.theses.fr/2010TOUR4007/document.
The main goal of this thesis is the general study of the large time behavior of theunique solution of the Cauchy-Dirichlet problem for viscous Hamilton-Jacobi equations of subandsuperquadratic types. This work splits into three parts. After a brief review of basic conceptsof the theory on the viscosity solutions which is the framework of this work, the first part mainlyprovides results on the global in time existence and the uniqueness of the viscosity solution of theabove mentioned Cauchy-Dirichlet problem. The second part studies the large time behavior ofthat solution for superquadratic Hamiltonians. Under rather general assumtions, we prove thatthe behavior of the solution depends on the the sign of the unique ergodic constant c∗ of theergodic problem associated with boundary condition of state constraint-type. When c∗ < 0; weobtain (i) a convergence to the unique solution of the associated stationary problem whereaswhen c∗ ≥ 0; we obtain (ii) a behavior of Hamilton-Jacobi–type (or ergodic-type) happen.In thethird part, devoted to the study for subquadratic Hamiltonians, we prove that a behavior of(i)-type happens when the unique ergodic constant c∗; of the ergodic problem associated withblow-up boundary condition, is non-positve and when c∗ > 0 and 3/2 < m ≤ 2; we obtain abehavior of (ii)-type. But when c∗ = 0 ou c∗ > 0 et 1 < m ≤ 3/2; we prove that for some domains,the function u(x; t)+c∗t is unbounded from below where u is the solution of the studied viscousHamilton-Jacobi, thus providing us with a result of non-convergence
Lukiantchuki, Juliana Azoia. "Interpretação de resultados do ensaio SPT com base em instrumentação dinâmica." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-24052013-103725/.
The standard penetration test (SPT) is usually used to estimate the soil strength through the NSPT index which represents the dynamic reaction force of the sampler penetration into the soil. This index is directly used in empirical or semi-empirical correlations for the determination of the bearing capacity and foundation settlements. However, this test has been criticized due to the use of these empirical correlations, often based on practical observation without any scientific basis. Criticism is also related to result dispersion due to the use of different types of equipment and execution procedures. The NSPT index depends on the amount of energy that is effectively transmitted to the sampler during the hammer fall. Thus, rational analyses of the SPT test results essentially depend on the estimation of this amount of energy. For this reason, several studies related to the energy involved in SPT test have been developed. This research presents interpretations of the SPT test results from the amounts of energy involved during the hammer fall. These amounts of energy are indirectly assessed by means of normal force and acceleration signals during the stress wave propagation along the string of rods. For this reason, a device that includes instrumentation capable of registering these signals of normal force and acceleration was developed. A series of tests was performed with the instrumentation installed at the top and the bottom of the string of rods. This arrangement allowed estimating the amount of energy available at the top and bottom of the string of rods. Thus, it was possible to estimate the efficiency of the SPT equipment basing on the amount of energy that actually reaches the sampler. From the recorded signals, it was also possible to assess the dynamic reaction force mobilized in the soil-sample system. The results were compared with other results obtained by theoretical methods, based on the Hamilton´s Principle, for evaluating the static and dynamic reaction force of the soil. These analyzes have shown that theoretical equations may be suitable for the determination of the soil strength, provided that the amount of energy that actually reaches the sampler be considered. Thus, these theoretical equations can be easily incorporated into the practice of foundation designs contributing to the development of methods based on the amount of energy required for the penetration of the sampler into the soil.
Adams, Ross Montague. "A study of a class of invariant optimal control problems on the Euclidean group SE(2)." Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1006060.
Flygare, Mattias. "Holonomic versus nonholonomic constraints." Thesis, Karlstads universitet, Avdelningen för fysik och elektroteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-13378.
GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.
Veronese, Andrea. "Portfolio optimization in presence of a self-exciting jump process: from theory to practice." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/339574.
Widehammar, Svante. "A Method for Dispersive Split Hopkinson Pressure Bar Analysis Applied to High Strain Rate Testing of Spruce Wood." Doctoral thesis, Uppsala University, Department of Materials Science, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2872.
En metod för dispersiv analys av försök med delad hopkinsonstång tillämpad på provning av granved vid hög töjningshastighet
Syftet var att etablera en metod för att studera sambandet mellan spänning och töjning för granved vid hög töjningshastighet. Detta åstadkoms genom att anpassa och något vidareutveckla tekniken med delad hopkinsonstång ("Split Hopkinson Pressure Bar", SHPB).
Vanligtvis har hopkinsonstavar cirkulärt tvärsnitt och en diameter som är mycket mindre än de verksamma våglängderna. Under sådana förhållanden är vågutbredningen i stängerna approximativt ickedispersiv, och en endimensionell (1D) vågutbredningsmodell kan användas. När det, som är fallet i denna studie, däremot inte kan säkerställas att stängernas tvärdimensioner är små i förhållande till våglängderna, är en helt igenom 1D vågutbredningsmodell otillräcklig, och tvärsnittets geometri, vilken var kvadratisk i denna studie, måste beaktas. Därför utvecklades med hjälp av Hamiltons princip en approximativ 3D vågutbredningsmodell för stänger med godtyckligt tvärsnitt. Modellen ger ett dispersionssamband (vågtal som funktion av vinkelfrekvens) samt medelvärden för förskjutningar och spänningar över gränsytorna mellan stänger och provstav. En kalibreringsprocedur utvecklades också.
Provning av granved genomfördes vid hög töjningshastighet (omkring 103 s-1) med den anpassade SHPB-tekniken, samt för jämförelse vid låg (8×10-3 s-1) och måttlig (17 s-1) töjningshastighet med en servohydraulisk provningsmaskin. Fukthalterna i veden motsvarade ugnstorr, fibermättnad och fullständig mättnad, och proven utfördes i radiell, tangentiell och axiell riktning i förhållande till trädets stam. För vart fall utfördes fem försök vid rumstemperatur. Resultaten visar töjningshastighetsberoendet för sambandet mellan spänning och töjning för granved under alla studerade förhållanden.
The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique.
Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed.
Tests on spruce wood specimens were carried out at a high strain rate (about 103 s-1) using the adapted SHPB technique, and for comparison at low (8×10-3 s-1) and medium (17 s-1) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.
Schwalbe, Karsten. "Stochastic Fluctuations in Endoreversible Systems." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-219268.
In this thesis, the influence of stochastic fluctuations on the performance of endoreversible engines is investigated for the first time. For this, a Novikov-engine with three different heat transport laws (Newtonian, Fourier, asymmetric) is considered. While the maximum work output and corresponding efficiency can be deduced easily in the case of constant heat bath temperatures, this changes, if these temperatures are allowed to fluctuate stochastically. In the latter case, stochastic optimal control theory has to be used to find the maximum of the expected work output and the corresponding control policy. In general, solving such problems leads to a non-linear, partial differential equation coupled to an optimization, called the stochastic Hamilton-Jacobi-Bellman equation. However, as presented in this thesis, calculations can be simplified, if one assumes that the fluctuations are independent of the considered control variable. In this case, analytic considerations show that the equations for performance measures like work output and efficiency keep their original form, but terms have to be replaced by appropriate time averages and expectation values, depending on the considered control type. Based on an analysis of the performance measures in the case of a uniform distribution of the hot temperature of the Novikov engine, conclusions on their monotonicity behavior are drawn. The comparison of several, time independent, symmetric distributions reveals a to date unknown extension to the Curzon-Ahlborn efficiency in the case of small fluctuations. Furthermore, an analysis of a Novikov engine with asymmetric heat transport, where the behavior of the hot temperature is described by an Ornstein-Uhlenbeck process, is performed. Finally, a Novikov engine with Fourier heat transport is considered, where the dynamics of the hot temperature depends on the control variable. By solving the corresponding Hamilton-Jacobi-Bellman equation, new conclusions how to optimally control such systems are drawn
Tocci, Monaco Giovanni. "Analisi di nano piastre composite con effetti piezo-elettro-magneto-igrotermici e teoria non locale: teoria e applicazioni." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
MAININI, ALESSANDRA. "Saggi in economia dell'informazione." Doctoral thesis, Università Cattolica del Sacro Cuore, 2009. http://hdl.handle.net/10280/504.
This thesis is a collection of three essays about information economics. The first essay studies the possible negative effects of elections on voters’ welfare. In fact, the optimal control of politicians depends on the interplay of disciplining, selection and rent-shrinking effects in a non-trivial way. We show that too much control on the politician may reduce social welfare. The second essay studies an agency model of electoral competition where the incumbent’s ability is unknown to the voters as well as to the politician herself. The analysis is developed in a continuous-time stochastic framework using dynamic programming techniques. Competence is unobservable to everyone and learned over time in a Bayesian fashion through the observation of the value of the public sector. Politicians can divert resources being in office thus reducing the economy wealth but this rent is lower (all other things the same) with an electoral constraint. The third essay describes a continuous-time principal-agent model in which the output is a diffusion process whose drift is determined by the agent’s unobserved effort and by manager’s competence (it is assumed symmetric information about it). We study separately both explicit incentives arising from the contract and implicit incentives arising from career concerns.. All the analysis is developed in a continuous-time stochastic framework; we apply dynamic programming and filtering techniques.
MAININI, ALESSANDRA. "Saggi in economia dell'informazione." Doctoral thesis, Università Cattolica del Sacro Cuore, 2009. http://hdl.handle.net/10280/504.
This thesis is a collection of three essays about information economics. The first essay studies the possible negative effects of elections on voters’ welfare. In fact, the optimal control of politicians depends on the interplay of disciplining, selection and rent-shrinking effects in a non-trivial way. We show that too much control on the politician may reduce social welfare. The second essay studies an agency model of electoral competition where the incumbent’s ability is unknown to the voters as well as to the politician herself. The analysis is developed in a continuous-time stochastic framework using dynamic programming techniques. Competence is unobservable to everyone and learned over time in a Bayesian fashion through the observation of the value of the public sector. Politicians can divert resources being in office thus reducing the economy wealth but this rent is lower (all other things the same) with an electoral constraint. The third essay describes a continuous-time principal-agent model in which the output is a diffusion process whose drift is determined by the agent’s unobserved effort and by manager’s competence (it is assumed symmetric information about it). We study separately both explicit incentives arising from the contract and implicit incentives arising from career concerns.. All the analysis is developed in a continuous-time stochastic framework; we apply dynamic programming and filtering techniques.
Lo, Hung-Chieh. "Vibration Characteristics of Thin-Walled Noncircular Composite Cylinders." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/77207.
Ph. D.
Lorenz, Michael. "Berechnungsmodelle zur Beschreibung der Interaktion von bewegtem Sägedraht und Ingot." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-130678.
The aim of the present thesis is to generate macroscopic models to describe the wire sawing process. The principal purpose is to illustrate basic effects and to investigate the influence of important process parameters relating to the dynamics of the system. A fundamental point is the modeling of the moving wire. Because of the axially movement of the continuum the boundary conditions and spatial acting loads are non-material. The precise kinematical description of this issue is the pre-condition for the correct evaluation of HAMILTON’s principle to characterize the dynamics of the system. The resultant complex system behavior is a consequence of the movement of the wire, of the formulation of the contact forces as follower loads and of explicitly time-dependent model parameters. The results of research contain studies of steady state equilibrium solutions and the proof of their LJAPUNOW stability, the calculation of eigenfrequencies, steady state time solutions under harmonically oscillating contact forces and the simulation of the material removal during the cutting process
Hermosilla, Cristopher. "Problèmes de commande optimale sur des domaines structurés et lois de commandes en boucles fermées stratifiées." Palaiseau, École nationale supérieure de techniques avancées, 2015. http://www.theses.fr/2015ESTA0011.
The aim of this dissertation is to study some issues in Control Theory of ordinary differential equations. Optimal control problems with tame state-constraints and feedback controls with stratified discontinuities are of special interest. The techniques employed along the manuscript have been chiefly taken from control theory, nonsmooth analysis, variational analysis, tame geometry, convex analysis and differential inclusions theory. The first part of the thesis is devoted to provide general results and definitions required for a good understanding of the entire manuscript. In particular, a strong invariance criterion adapted to manifolds is presented. Moreover, a short insight into manifolds and stratifications is done. The notions of relatively wedged sets is introduced and in addition, some of its properties are stated. The second part is concerned with the characterization of the Value Function of an optimal control problem with state-constraints. Three cases have been taken into account. The first one treats stratifiable state-constraints, that is, sets that can be decomposed into manifolds of different dimensions. The second case is focused on linear systems with convex state-constraints, and the last one considers convex state-constraints as well, but from a penalization point of view. In the latter situation, the dynamics are nonlinear and verify an absorbing property at the boundary. The third part is about discontinuous feedbacks laws whose singularities form a stratified set on the state-space. This type of controls yields to consider stratified discontinuous ordinary differential equations, which motivates an analysis of existence of solutions and robustness with respect to external perturbation for these equations. The construction of a suboptimal continuous feedback from an optimal one is also addressed in this part. The fourth part is dedicated to investigate optimal control problems on networks. The main feature of this contribution is that no controllability assumption around the junctions is imposed. The results can also be extended to generalized notions of networks, where the junction is not a single point but a manifold
Prieto, Martínez Pere Daniel. "Geometrical structures of higher-order dynamical systems and field theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/284215.
La física geomètrica és una branca relativament jove de la matemàtica aplicada que es va iniciar als anys 60 i 70 qua A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, entre molts altres, van començar a estudiar diversos problemes en física usant mètodes de geometria diferencial. Aquesta "geometrització" proporciona una manera d'analitzar les característiques dels sistemes físics des d'una perspectiva global, obtenint així propietats qualitatives que faciliten la integració de les equacions que els descriuen. D'ençà s'ha produït un fort desenvolupamewnt en el tractament intrínsic d'una gran varietat de problemes en física teòrica, matemàtica aplicada i teoria de control usant mètodes de geometria diferencial. Gran part del treball realitzat en la física geomètrica des dels seus primers dies s'ha dedicat a l'estudi de teories de primer ordre, és a dir, teories tals que la informació física depèn en, com a molt, derivades de primer ordre de les coordenades de posició generalitzades (velocitats). Tanmateix, hi ha teories en física en les que la informació física depèn de manera explícita en acceleracions o derivades d'ordre superior de les coordenades de posició generalitzades, requerint, per tant, d'eines geomètriques més sofisticades per a modelar-les de manera acurada. En aquesta Tesi Doctoral ens proposem donar una descripció geomètrica d'algunes d'aquestes teories. En particular, estudiarem sistemes dinàmics i teories de camps tals que la seva informació dinàmica ve donada en termes d'una funció lagrangiana, o d'un hamiltonià que prové d'un sitema lagrangià. Per a ser més precisos emprarem la formulació unificada Lagrangiana-Hamiltoniana per tal de desenvolupar marcs geomètrics per a sistemes dinàmics d'ordre superior autònoms i no autònoms, i per a teories de camps de segon ordre. Amb aquest marc geomètric estudiarem alguns exemples físics rellevants i algunes aplicacions, com la teoria de Hamilton-Jacobi per a sistemes mecànics d'ordre superior, partícules relativístiques amb spin i problemes de deformació en mecànica, i l'equació de Korteweg-de Vries i altres sistemes en teories de camps.
Ourodová, Ludmila. "Johann Georg de Hamilton. Život a dílo." Doctoral thesis, 2015. http://www.nusl.cz/ntk/nusl-334590.
POZZA, MARCO. "Stochastic representation formulas for viscosity solutions to nonlinear partial differential equations." Doctoral thesis, 2020. http://hdl.handle.net/11573/1386359.
Schwalbe, Karsten. "Stochastic Fluctuations in Endoreversible Systems." Doctoral thesis, 2016. https://monarch.qucosa.de/id/qucosa%3A20641.
In this thesis, the influence of stochastic fluctuations on the performance of endoreversible engines is investigated for the first time. For this, a Novikov-engine with three different heat transport laws (Newtonian, Fourier, asymmetric) is considered. While the maximum work output and corresponding efficiency can be deduced easily in the case of constant heat bath temperatures, this changes, if these temperatures are allowed to fluctuate stochastically. In the latter case, stochastic optimal control theory has to be used to find the maximum of the expected work output and the corresponding control policy. In general, solving such problems leads to a non-linear, partial differential equation coupled to an optimization, called the stochastic Hamilton-Jacobi-Bellman equation. However, as presented in this thesis, calculations can be simplified, if one assumes that the fluctuations are independent of the considered control variable. In this case, analytic considerations show that the equations for performance measures like work output and efficiency keep their original form, but terms have to be replaced by appropriate time averages and expectation values, depending on the considered control type. Based on an analysis of the performance measures in the case of a uniform distribution of the hot temperature of the Novikov engine, conclusions on their monotonicity behavior are drawn. The comparison of several, time independent, symmetric distributions reveals a to date unknown extension to the Curzon-Ahlborn efficiency in the case of small fluctuations. Furthermore, an analysis of a Novikov engine with asymmetric heat transport, where the behavior of the hot temperature is described by an Ornstein-Uhlenbeck process, is performed. Finally, a Novikov engine with Fourier heat transport is considered, where the dynamics of the hot temperature depends on the control variable. By solving the corresponding Hamilton-Jacobi-Bellman equation, new conclusions how to optimally control such systems are drawn.
Lorenz, Michael. "Berechnungsmodelle zur Beschreibung der Interaktion von bewegtem Sägedraht und Ingot." Doctoral thesis, 2013. https://tubaf.qucosa.de/id/qucosa%3A22896.
The aim of the present thesis is to generate macroscopic models to describe the wire sawing process. The principal purpose is to illustrate basic effects and to investigate the influence of important process parameters relating to the dynamics of the system. A fundamental point is the modeling of the moving wire. Because of the axially movement of the continuum the boundary conditions and spatial acting loads are non-material. The precise kinematical description of this issue is the pre-condition for the correct evaluation of HAMILTON’s principle to characterize the dynamics of the system. The resultant complex system behavior is a consequence of the movement of the wire, of the formulation of the contact forces as follower loads and of explicitly time-dependent model parameters. The results of research contain studies of steady state equilibrium solutions and the proof of their LJAPUNOW stability, the calculation of eigenfrequencies, steady state time solutions under harmonically oscillating contact forces and the simulation of the material removal during the cutting process.:1 Einleitung 1.1 Technische Problemstellung und Motivation der Arbeit 1.2 Literaturübersicht 1.3 Thema und Gliederung der Arbeit 2 Theoretische Grundlagen 2.1 Notation und mathematische Grundlagen 2.2 Kinematische Grundlagen der Kontinuumsmechanik 2.2.1 Konfiguration und Betrachtungsweisen 2.2.2 Verformungskinematik 2.2.3 Zeitableitungen 2.3 Variationsrechnung 2.3.1 Grundlagen 2.3.2 Verallgemeinerte Variationen 2.4 Kinetik / Prinzip von HAMILTON 2.5 Diskretisierung von Feldproblemen 2.6 Stabilität stationärer Lösungen 2.6.1 Grundlagen der kinetischen Stabilitätstheorie 2.6.2 Erste Methode von LJAPUNOW 2.6.3 Stabilitätsbetrachtung für bewegte Kontinua 2.7 Zeitlösung 2.7.1 Homogene Lösung der Störungsdifferentialgleichungen 2.7.2 Partikuläre Lösung der Störungsdifferentialgleichungen 3 Mechanisches Modell und Modellvarianten 3.1 Kinematik des Drahtes in LAGRANGE-Koordinaten 3.2 Kinematik des Drahtes in EULER-Koordinaten 3.3 Modell I 3.3.1 Variationsformulierung und Feldgleichungen 3.3.2 Ortsdiskretisierung der Variationsformulierung 3.3.3 Stationäre Lage, Stabilitätsuntersuchung und Zeitlösung 3.4 Modell II 3.4.1 Variationsformulierung und Feldgleichungen 3.4.2 Ortsdiskretisierung der Variationsformulierung 3.4.3 Stationäre Lage, Stabilitätsuntersuchung und Zeitlösung 3.5 Numerische Umsetzung 3.6 Berechnungsergebnisse 3.6.1 Stationäre Lagen 3.6.2 Eigenfrequenzen 3.6.3 Stabilitätsuntersuchungen 3.6.4 Zeitlösungen 4 Ankopplung des Ingot und Modellierung des Materialabtrages 4.1 FE- Modell des Gesamtblocks 4.1.1 Bestimmung der mechanischen Eigenschaften des Ingot 4.1.2 Berechnungsergebnisse 4.2 Strukturmechanisches Modell des Gesamtblocks und Ankopplung an den Sägedraht 4.3 Variationsformulierungen der gekoppelten Gesamtsysteme unter Berücksichtigung des Materialabtrages 4.3.1 Gesamtmodell I 4.3.2 Gesamtmodell II 4.4 Simulation des Schnittvorganges 5 Zusammenfassung / Ausblick 6 Verzeichnisse 6.1 Literaturverzeichnis 6.1.1 Allgemeine Literatur 6.1.2 Literatur zum Thema Drahtsägen 6.1.3 Literatur zum Thema bewegte Kontinua Anhang