Complex systems are those which exhibit one or more of the following inter-related behaviours: 1. Nonlinear behaviour: the component parts do not act in linear ways, that is the superposition of the actions of the parts is not the output of the system. 2. Emergent behaviour: the output of the system may be inexpressible in terms of the rules or equations of the component parts. 3. Self-organisation: order appears from the chaotic interactions of individuals and the rules they obey. 4. Layers of description: in which a rule may apply at some higher levels of description but not at lower layers. 5. Adaptation: in which the environment becomes encoded in the rules governing the structure and/or behaviour of the parts (in this case strictly agents) that undergo selection in which those that are by some measure better become more numerous than those that are not as “fit”. A single cell is a complex system: we cannot explain all of its behaviour as simply the sum of its parts. Similarly, DNA structures, social networks, cancers, the brain, and living beings are intricate complex systems. This thesis tackles all of these topics from a complex systems approach. I have skirted some of the philosophical issues of complex systems and mainly focussed on appropriate tools to analyse these systems, addressing important questions such as: • What is the best way to extract information from DNA? • How can we model and analyse mutations in DNA? • Can we determine the likely spread of both viruses and ideas in social networks? • How can we model the growth of cancer? • How can we model and analyse interactions between genes in such living systems as the fruit fly, cancers, and humans? • Can complex systems techniques give us some insight into the human brain? / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1290759 / Thesis (Ph.D.)-- School of Electrical and Electronic Engineering, 2007

Complex systems are those which exhibit one or more of the following inter-related behaviours: 1. Nonlinear behaviour: the component parts do not act in linear ways, that is the superposition of the actions of the parts is not the output of the system. 2. Emergent behaviour: the output of the system may be inexpressible in terms of the rules or equations of the component parts. 3. Self-organisation: order appears from the chaotic interactions of individuals and the rules they obey. 4. Layers of description: in which a rule may apply at some higher levels of description but not at lower layers. 5. Adaptation: in which the environment becomes encoded in the rules governing the structure and/or behaviour of the parts (in this case strictly agents) that undergo selection in which those that are by some measure better become more numerous than those that are not as “fit”. A single cell is a complex system: we cannot explain all of its behaviour as simply the sum of its parts. Similarly, DNA structures, social networks, cancers, the brain, and living beings are intricate complex systems. This thesis tackles all of these topics from a complex systems approach. I have skirted some of the philosophical issues of complex systems and mainly focussed on appropriate tools to analyse these systems, addressing important questions such as: • What is the best way to extract information from DNA? • How can we model and analyse mutations in DNA? • Can we determine the likely spread of both viruses and ideas in social networks? • How can we model the growth of cancer? • How can we model and analyse interactions between genes in such living systems as the fruit fly, cancers, and humans? • Can complex systems techniques give us some insight into the human brain? / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1290759 / Thesis (Ph.D.)-- School of Electrical and Electronic Engineering, 2007

Complex systems are those which exhibit one or more of the following inter-related behaviours: 1. Nonlinear behaviour: the component parts do not act in linear ways, that is the superposition of the actions of the parts is not the output of the system. 2. Emergent behaviour: the output of the system may be inexpressible in terms of the rules or equations of the component parts. 3. Self-organisation: order appears from the chaotic interactions of individuals and the rules they obey. 4. Layers of description: in which a rule may apply at some higher levels of description but not at lower layers. 5. Adaptation: in which the environment becomes encoded in the rules governing the structure and/or behaviour of the parts (in this case strictly agents) that undergo selection in which those that are by some measure better become more numerous than those that are not as “fit”. A single cell is a complex system: we cannot explain all of its behaviour as simply the sum of its parts. Similarly, DNA structures, social networks, cancers, the brain, and living beings are intricate complex systems. This thesis tackles all of these topics from a complex systems approach. I have skirted some of the philosophical issues of complex systems and mainly focussed on appropriate tools to analyse these systems, addressing important questions such as: • What is the best way to extract information from DNA? • How can we model and analyse mutations in DNA? • Can we determine the likely spread of both viruses and ideas in social networks? • How can we model the growth of cancer? • How can we model and analyse interactions between genes in such living systems as the fruit fly, cancers, and humans? • Can complex systems techniques give us some insight into the human brain? / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1290759 / Thesis (Ph.D.)-- School of Electrical and Electronic Engineering, 2007

Prospection de pétrole utilise un équipement appelé tube de forage pour forer le sol jusqu'au le niveau du réservoir. Cet équipement est une longue colonne rotative, composée par une série de tiges de forage interconnectées et les équipements auxiliaires. La dynamique de cette colonne est très complexe parce que dans des conditions opérationnelles normales, elle est soumise à des vibrations longitudinales, latérales et de torsion, qui présentent un couplage non linéaire. En outre, cette structure est soumise à effets de frottement et à des chocs dûs aux contacts mécaniques entre les paires tête de forage/sol et tube de forage/sol. Ce travail présente un modèle mécanique-mathématique pour analyser un tube de forage en configuration horizontale. Ce modèle utilise la théorie des poutres qui utilise l'inertie de rotation, la déformation de cisaillement et le couplage non linéaire entre les trois mécanismes de vibration. Les équations du modèle sont discrétisées par la méthode des éléments finis. Les incertitudes des paramètres du modèle d'interaction tête de forage/sol sont prises en compte par l'approche probabiliste paramétrique, et les distributions de probabilité des paramètres aléatoires sont construits par le principe du maximum d'entropie. Des simulations numériques sont réalisées afin de caractériser le comportement dynamique non linéaire de la structure, et en particulier, de l'outil de forage. Des phénomènes dynamiques non linéaires par nature, comme le slick-slip et le bit-bounce, sont observés dans les simulations, ainsi que les chocs. Une analyse spectrale montre étonnamment que les phénomènes slick-slip et bit-bounce résultent du mécanisme de vibration latérale, et ce phénomène de choc vient de la vibration de torsion. Cherchant à améliorer l'efficacité de l'opération de forage, un problème d'optimisation qui cherche à maximiser la vitesse de pénétration de la colonne dans le sol, sur ses limites structurelles, est proposé et résolu / Oil prospecting uses an equipment called drillstring to drill the soil until the reservoir level. This equipment is a long column under rotation, composed by a sequence of connected drill-pipes and auxiliary equipment. The dynamics of this column is very complex because, under normal operational conditions, it is subjected to longitudinal, lateral, and torsional vibrations, which presents a nonlinear coupling. Also, this structure is subjected to friction and shocks effects due to the mechanical contacts between the pairs drill-bit/soil and drill-pipes/borehole. This work presents a mechanical-mathematical model to analyze a drillstring in horizontal configuration. This model uses a beam theory which accounts rotatory inertia, shear deformation, and the nonlinear coupling between three mechanisms of vibration. The model equations are discretized using the finite element method. The uncertainties in bit-rock interaction model parameters are taken into account through a parametric probabilistic approach, and the random parameters probability distributions are constructed by means of maximum entropy principle. Numerical simulations are conducted in order to characterize the nonlinear dynamic behavior of the structure, specially, the drill-bit. Dynamical phenomena inherently nonlinear, such as slick-slip and bit-bounce, are observed in the simulations, as well as shocks. A spectral analysis shows, surprisingly, that slick-slip and bit-bounce phenomena result from the lateral vibration mechanism, and that shock phenomena comes from the torsional vibration. Seeking to increase the efficiency of the drilling process, an optimization problem that aims to maximize the rate of penetration of the column into the soil, respecting its structural limits, is proposed and solved

Dans cette Thèse, la conception robuste avec un modèle incertain d'un système électromécanique avec vibro-impact est fait. Le système électromécanique est constitué d'un chariot, dont le mouvement est excité par un moteur à courant continu et un marteau embarqué dans ce chariot. Le marteau est relié au chariot par un ressort non linéaire et par un amortisseur linéaire, de façon qu'un mouvement relatif existe entre eux. Une barrière flexible linéaire, placé à l'extérieur du chariot limite les mouvements de marteau. En raison du mouvement relatif entre le marteau et la barrière, impacts peuvent se produire entre ces deux éléments. Le modèle du système développé prend en compte l'influence du courant continu moteur dans le comportement dynamique du système. Certains paramètres du système sont incertains, tels comme les coefficients de rigidité et d'amortissement de la barrière flexible. L'objectif de la Thèse est de réaliser une optimisation de ce système électromécanique par rapport aux paramètres de conception afin de maximiser l'impact puissance sous la contrainte que la puissance électrique consommée par le moteur à courant continu est inférieure à une valeur maximale. Pour choisir les paramètres de conception dans le problème d'optimisation, une analyse de sensibilité a été réalisée afin de définir les paramètres du système les plus sensibles. L'optimisation est formulée dans le cadre de la conception robuste en raison de la présence d'incertitudes dans le modèle. Les lois de probabilités liées aux variables aléatoires du problème sont construites en utilisant le Principe du Maximum l'Entropie et les statistiques de la réponse stochastique du système sont calculées en utilisant la méthode de Monte Carlo. L'ensemble d'équations non linéaires sont présentés, et un solveur temporel adapté est développé. Le problème d'optimisation non linéaire stochastique est résolu pour différents niveaux d'incertitudes, et aussi pour le cas déterministe. Les résultats sont différents, ce qui montre l'importance de la modélisation stochastique / In this Thesis, the robust design with an uncertain model of a vibro-impact electromechanical system is done. The electromechanical system is composed of a cart, whose motion is excited by a DC motor (motor with continuous current), and an embarked hammer into this cart. The hammer is connected to the cart by a nonlinear spring component and by a linear damper, so that a relative motion exists between them. A linear flexible barrier, placed outside of the cart, constrains the hammer movements. Due to the relative movement between the hammer and the barrier, impacts can occur between these two elements. The developed model of the system takes into account the influence of the DC motor in the dynamic behavior of the system. Some system parameters are uncertain, such as the stiffness and the damping coefficients of the flexible barrier. The objective of the Thesis is to perform an optimization of this electromechanical system with respect to design parameters in order to maximize the impact power under the constraint that the electric power consumed by the DC motor is lower than a maximum value. To chose the design parameters in the optimization problem, an sensitivity analysis was performed in order to define the most sensitive system parameters. The optimization is formulated in the framework of robust design due to the presence of uncertainties in the model. The probability distributions of random variables are constructed using the Maximum Entropy Principle and statistics of the stochastic response of the system are computed using the Monte Carlo method. The set of nonlinear equations are presented, and an adapted time domain solver is developed. The stochastic nonlinear constrained design optimization problem is solved for different levels of uncertainties, and also for the deterministic case. The results are different and this show the importance of the stochastic modeling

Submitted by Helmut Patrocinio (hell.kenn@gmail.com) on 2017-12-01T23:43:39Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Heloisa_Onias_Dissertacao_2012.pdf: 9805428 bytes, checksum: 00e0f3bac6584320107351966c70da69 (MD5) / Approved for entry into archive by Ismael Pereira (ismael@neuro.ufrn.br) on 2017-12-04T12:33:01Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Heloisa_Onias_Dissertacao_2012.pdf: 9805428 bytes, checksum: 00e0f3bac6584320107351966c70da69 (MD5) / Made available in DSpace on 2017-12-04T12:33:37Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Heloisa_Onias_Dissertacao_2012.pdf: 9805428 bytes, checksum: 00e0f3bac6584320107351966c70da69 (MD5) Previous issue date: 2012-08 / O circuito RLD, formado por um resistor, um indutor e um diodo em s?rie, apresenta uma din?mica muito rica quando for?ado por uma tens?o externa harm?nica e vem sendo estudado h? d?cadas. Contudo, ainda existem t?picos em din?mica n?o-linear sendo estudados com variantes deste circuito. Varreduras nos par?metros de controle podem fazer com que esse sistema oscile eletronicamente entre regi?es peri?dicas e regi?es ca?ticas. O diodo ? o elemento n?o linear respons?vel pelo surgimento do caos. Utilizando um modelo de capacit?ncia n?o linear para descrever o comportamento do diodo, podemos escrever as equa??es para esse sistema e estudar a sua din?mica numericamente. Nosso principal objetivo foi o estudo de expoentes cr?ticos complexos em bifurca??es din?micas. Para isso, realizamos um estudo num?rico do circuito RLD for?ado senoidalmente utilizando como par?metros de controle a frequ?ncia e a amplitude da tens?o de entrada. Constru?mos, a partir das s?ries temporais da corrente total e da tens?o no diodo, diagramas de bifurca??o com diferentes cortes estrobosc?picos, que apresentam cascata de dobramento de per?odo, janelas peri?dicas e transi??o intermitente. Tamb?m realizamos estudos num?ricos do comportamento da m?dia na regi?o de transi??o caos-peri?dico na busca de encontrar um expoente cr?tico caracter?stico e oscilas??es na m?dia, elementos que j? foram observados no mapa log?stico. N?o foram poss?veis observar numericamente as oscila??es, mas observamos um decaimento exponencial com expoente cr?tico de aproximadamente 0,5. Montamos um sistema de controle, aquisi??o e tratamento de dados experimentais no qual ? poss?vel a realiza??o remota de experimentos simult?neos com dois circuitos diferentes. Obtivemos diagramas de bifurca??es experimentais nos quais observamos que o sistema apresentahisterese e alta sensibilidade ?s condi??es do experimento como, por exemplo, o passo de varredura do par?metro de controle. / The RLD circuit, formed by a resistor, an inductor and a diode in series, displays a very rich dynamics when forced by an external harmonic voltage, and it has being studied for decades. However, there are some topics in nonlinear dynamics that are still studied with variants of this circuit nowadays. Changes in the control parameters may cause electronic oscillations between regular and chaotic regions.The diode is the nonlinear element responsible for the appearance of chaos. Using a nonlinear capacitance model to describe the behavior of the diode, we can write the equations for this system and study its dynamics numerically. Our main objective was the study of critical exponents in complex dynamic bifurcations. For that, we did a numerical study of the RLD circuit forced sinusoidally using as control parameters the amplitude of the input voltage and the frequency. We made, from the time series obtained, bifurcation diagrams with different stroboscopic cuts, which have cascade of period-doubling, periodic windows and intermittent transition. We also did numerical studies of the average behavior in the periodic-chaos transition region searching for characteristic critical exponent and oscilas??es on average, elements that have been observed in the logistic map. It was not possible to observe the oscillations numerically, but we observed an exponential decay with critical exponent of approximately 0.5. We set up a system able to control, acquire and process experimental data making it possible to perform remote simultaneous experiments with two different circuits. We have obtained experimental diagrams bifurcations in which we observe that the system has hysteresis and high sensitivity to the conditions of the experiment such as the step of scanning the control parameter.

[pt] A estabilidade das colunas de um pórtico plano depende da importância relativa da rigidez à flexão e rigidez lateral de cada coluna e elementos adjacentes. Um exemplo típico é a maior capacidade de carga de pórticos planos com restrição lateral em comparação com pórticos semelhantes, sem restrição lateral. Também esta restrição tem uma influência importante na resposta pós-crítica e na sensibilidade à imperfeição da estrutura. A carga de flambagem pode ser dominada pela rigidez à flexão da coluna ou pela rigidez das restrições laterais. Dependendo dos valores relativos desses parâmetros, pode ocorrer interação modal. Nesse caso, podem surgir vários caminhos pós-críticos, acoplados e desacoplados, levando a uma topologia complexa da energia potencial total com vários pontos críticos (máximos, mínimos e selas). Os caminhos pós-críticos instáveis influenciam na sua capacidade de carga e na sensibilidade da estrutura a imperfeições. Isso leva a um complexo comportamento dinâmico não linear da estrutura carregada axialmente. No presente trabalho, um modelo conceitual de dois graus de liberdade de um elemento de pórtico plano sob compressão é estudado. Uma análise detalhada é realizada a fim de estudar como a rigidez lateral influencia: os comportamentos pré- e pós-crítico, a instabilidade paramétrica do modelo sob uma excitação harmônica axial e o comportamento ressonante do sistema estrutural carregado axialmente sob uma excitação de base; contribuindo para uma melhor compreensão da resposta não linear desta classe de estruturas. A análise das bifurcações mostra que a estrutura pode exibir várias soluções estáveis e instáveis coexistentes, levando a bacias de atração entrelaçadas, cuja topologia controla a integridade dinâmica da estrutura em um ambiente dinâmico. Para estudar o comportamento não linear do modelo, foram utilizadas várias estratégias numéricas para obter os caminhos de equilíbrio não lineares, pontos fixos estáveis e instáveis, diagramas de bifurcação e bacias de atração. / [en] The stability of columns in a portal frame depends on the relative importance of the flexural and lateral stiffness of the column and connected elements. A typical example is the higher load capacity of non-sway frames as compared with that of similar frames with no lateral restrain. Also this restrain has an important influence on the post-critical response and imperfection sensitivity of the structure. The buckling load may be either dominated by the flexural stiffness of the columns or by the stiffness of the lateral restrains. Depending on the relative values of these parameters, interactive buckling may occur. In such case, several coupled and uncoupled post-buckling paths may arise, leading to a complex topology of the energy landscape with several critical points (maxima, minima and saddles). The resulting unstable post-buckling paths influence the structure s imperfection sensitivity and load carrying capacity of the structure. This leads to an involved nonlinear dynamic behaviour of the axially loaded structure. In the present work, a conceptual two-degree-of-freedom model of a plane-frame column is studied. A detailed analysis is conducted to study how the lateral stiffness influences the static buckling and post-buckling behavior, the parametric instability of the model under under axial harmonic excitation and the resonant behavior of the axially loaded structural system under base excitation, contributing to a better understanding of the nonlinear response of this class of structures. The bifurcation analysis shows that the structure may display several coexisting stable and unstable solutions, leading to intertwining basins of attraction, whose topology controls the dynamic integrity of the structure in a dynamic environment. To study the non-linear behavior of the model, several numerical strategies were used to obtain the nonlinear equilibrium paths, stable and unstable fixed points, bifurcation diagrams and basins of attraction.

[pt] Uma prospecção bem sucedida de petróleo e gás requer muitos esforços para se sobrepor os desafios encontrados, tais como vibrações axiais, laterais e torcionais. Estes fenômenos podem causar a falha prematura de componentes do sistema de perfuração, disfunção nos equipamentos de medição e aumento no tempo e custo no processo de perfuração. Em particular, vibrações torcionais estão presentes em grande parte dos processos de perfuração e podem alcançar um estado crítico: stick-slip. Um melhor entendimento sobre este fenômeno proporciona ferramentas para evitar o aumento do tempo e do custo da prospecção, assegurando o investimento e sucesso do processo de perfuração. Neste trabalho, é descrito um procedimento experimental com um atrito não linear objetivando induzir stick-slip e é feito uma modelagem analítica simples do problema. O modelo de atrito é baseado em um atrito seco imposto por um dispositivo de freio desenvolvido. O comportamento não linear da bancada experimental é analisada e o modelo numérico é validado comparando diagramas de bifurcações numérica e experimentais. / [en] A successful oil and gas prospecting requires many efforts to overcome the encountered challenges, some of these challenges include drill string axial, lateral and torsional vibrations. These phenomena may cause premature component failures of the drilling system, dysfunction of measurement equipments, and increase time and costs of the prospecting process. Torsional vibrations are present in most drilling processes and may reach a severe state: stick-slip. An improved understanding about the stick-slip phenomenon provides tools to avoid the increase of prospecting time and costs, assuring the investment and success of the drilling process. Firstly, a numerical analysis of the drill string is performed with different friction models. These models are proposed in order to get familiar with the drill string dynamics. Also, it is described the experimental procedure with a nonlinear friction aiming to induce stick-slip and is performed a simple analytical modeling of the problem. The friction model is based on dry friction imposed by a break device. The nonlinear behavior of the experimental apparatus is analyzed and the numerical model is validated comparing experimental and numerical bifurcation diagrams.

[pt] Prospecção de petróleo usa um equipamento chamado coluna de perfuração para escavar o solo até o nível do reservatório. Este equipamento é uma longa coluna, sob rotação, composto por uma sequência de tubos de perfura ção e equipamentos auxiliares conectados. A dinâmica desta coluna é muito complexa, porque sob condições normais de operação, ela está sujeita à vibrações longitudinais, laterais e torcionais, que apresentam um acoplamento não-linear. Além disso, a estrutura está submetida a efeitos de atrito e choque devido a contatos mecânicos entre os pares broca/rocha e tubos de perfuração/parede do poço. Este trabalho apresenta um modelo mecânico-matemático para analisar uma coluna de perfuração em configuração horizontal. Este modelo usa uma teoria de viga com inércia de rotação, deformação cisalhante e acoplamento não-linear entre os três mecanismos de vibração. As equações do modelo são discretizadas utilizando o método dos elementos finitos. As incertezas dos parâmetros do modelo de interação broca-rocha são levandas em conta através de uma abordagem probabilística paramétrica, e as distribuições de probabilidades dos parâmetros aleatórios são construídas por meio do princípio da entropia máxima. Simulações numéricas são conduzidas de forma a caracterizar o comportamento dinâmico não-linear da estrutura, especialmente, da broca. Fenômenos dinâmicos inerentemente não-lineares, como stick-slip e bit-bounce, são observados nas simulações, bem como choques. Uma análise espectral mostra que, surpreendentemente, os fenômenos de stick-slip e bit-bounce são resultado do mecanismo de vibração lateral, e que os fenômenos de choque decorrem da vibração torcional. Visando aumentar a eficiência do processo de perfuração, um problema de otimização que tem como objetivo maximizar a taxa de penetração da coluna no solo, respeitando os seus limites estruturais, é proposto e resolvido. / [en] Oil prospecting uses an equipment called drillstring to drill the soil until the reservoir level. This equipment is a long column under rotation, composed by a sequence of connected drill-pipes and auxiliary equipment. The dynamics of this column is very complex because, under normal operational conditions, it is subjected to longitudinal, lateral, and torsional vibrations, which presents a nonlinear coupling. Also, this structure is subjected to friction and shocks effects due to the mechanical contacts between the pairs drill-bit/soil and drill-pipes/borehole. This work presents a mechanical-mathematical model to analyze a drillstring in horizontal configuration. This model uses a beam theory which accounts rotatory inertia, shear deformation, and the nonlinear coupling between three mechanisms of vibration. The model equations are discretized using the finite element method. The uncertainties in bit-rock interaction model parameters are taken into account through a parametric probabilistic approach, and the random parameters probability distributions are constructed by means of maximum entropy principle. Numerical simulations are conducted in order to characterize the nonlinear dynamic behavior of the structure, specially, the drill-bit. Dynamical phenomena inherently nonlinear, such as slick-slip and bit-bounce, are observed in the simulations, as well as shocks. A spectral analysis shows, surprisingly, that slick-slip and bit-bounce phenomena result from the lateral vibration mechanism, and that shock phenomena comes from the torsional vibration. Seeking to increase the efficiency of the drilling process, an optimization problem that aims to maximize the rate of penetration of the column into the soil, respecting its structural limits, is proposed and solved. / [fr] La prospection de pétrole utilise un équipement appelé tube de forage pour forer le sol jusqu au niveau du réservoir. Cet équipement est une longue colonne rotative, composée d une série de tiges de forage interconnectées et d équipements auxiliaires. La dynamique de cette colonne est très complexe car dans des conditions opérationnelles normales, elle est soumise à des vibrations longitudinales, latérales et de torsion, qui présentent un couplage non linéaire. En outre, cette structure est soumise à des effets de frottement et à des chocs dûs aux contacts mécaniques entre les paires tête de forage/sol et tube de forage/sol. Ce travail présente un modèle mécaniquemathématique pour analyser un tube de forage en configuration horizontale. Ce modèle utilise la théorie des poutres qui utilise l inertie de rotation, la déformation de cisaillement et le couplage non linéaire entre les trois mécanismes de vibration. Les équations du modèle sont discrétisées par la méthode des éléments finis. Les incertitudes des paramètres du modèle d interaction tête de forage/sol sont prises en compte par l approche probabiliste paramétrique, et les distributions de probabilité des paramètres aléatoires sont construites par le principe du maximum d entropie. Des simulations numériques sont réalisées afin de caractériser le comportement dynamique non lináaire de la structure, et en particulier, de l outil de forage. Des phénom ènes dynamiques non linéaires par nature, comme le slick-slip et le bit- bounce, sont observés dans les simulations, ainsi que les chocs. Une analyse spectrale montre étonnamment que les phénomènes slick-slip et bit-bounce résultent du mécanisme de vibration latérale, et ce phénomène de choc vient de la vibration de torsion. Cherchant à améliorer l efficacité de l opération de forage, un problème d optimisation, qui cherche à maximiser la vitesse de pénétration de la colonne dans le sol, sur ses limites structurelles, est proposé et résolu.

[pt] Em virtude de sua eficiência, elementos estruturais de paredes finas com seções abertas são comuns em estruturas de aço, sendo secção em I, L, C e T usuais na prática de engenharia. A maior parte das vigas de parede fina tem uma boa resistência à flexão em relação ao eixo principal de inércia, mas uma baixa rigidez à flexão em relação ao eixo de menor inércia e uma baixa rigidez em torção. É por isso que estes elementos apresentam em geral uma instabilidade que leva a um acoplamento de flexo-torção. Muitas destas estruturas trabalham em um regime não linear e uma formulação não linear que leve em conta grandes deslocamentos e os acoplamentos inerentes é necessária. Neste trabalho um modelo não linear para vigas de seção aberta e paredes finas, considerando grandes deslocamentos, os efeitos de encurtamento e acoplamentos em flexão e torção é adotado. Inicialmente um estudo das frequências naturais, das cargas críticas e da relação frequência-carga axial é apresentado para diversos perfis. Com base nestes resultados, faz-se um estudo detalhado do comportamento dinâmico não linear destes perfis destacando o efeito do acoplamento não linear na região de ressonância e sua influência na estabilidade dinâmica da estrutura. Para isto são usadas diversas ferramentas de dinâmica não linear, tais como diagramas de bifurcação, respostas no tempo e plano de fase e bacias de atração. Os resultados mostram que a consideração dos acoplamentos não lineares é essencial para se avaliar o nível de segurança destas estruturas. / [en] Due to its efficiency, thin-walled structural elements with open sections, such as I, L, C and Z profiles, are common in steel structures, being usual in engineering applications. Most thin-walled beams have a good flexural strength around of the principal axis of inertia, but a low one around the axis of lower inertia as well as low torsional stiffness. That is why these elements, generally, show instabilities that lead to flexural torsional coupling. Many of these structures do not work in a linear range and a non-linear formulation that takes into account large displacements and associated couplings is required. This dissertation presents a nonlinear model for extensional beams with thin-walled open section, considering large displacements, and flexural-torsional couplings. Initially a study of the natural frequencies, critical load and axial load vs. frequency relation is presented for different profile kinds. Based on these results, a detailed study of the dynamic behavior of non-linear profiles is made, highlighting the effect of non-linear coupling in the resonance region and its influence on the dynamic stability of the structure. For this, various tools of nonlinear dynamics are used, such as bifurcation diagrams, time histories and phase-space portraits and basins of attraction. The results show that the consideration of non-linear couplings is essential to availed the safety level of these structures.