Microtubules are a part of the cell cytoskeleton that performs different functions, such as providing the mechanical support for the shape of a cell, acting as tracks along which the motor protein move organelles from one part of the cell to another, or the forming mitotic spindle during the cell division. The microtubules are dynamic structures, namely they can grow and shrink. The phase of microtubule growth alternates with the phase of shrinkage that results in the dynamic microtubule network in the cell. However, to form stable and spatially well-defined structures, such as a mitotic spindle, the cell needs to control this stochastic process. This is done by microtubule-associated proteins (MAPs). One class of MAPs is the proteins of XMAP216/Dis1 family, which are microtubule polymerases. The founding member of this family is X. laevis XMAP215. XMAP215 is a processive polymerase acting on the microtubule plus end. XMAP215 binds either directly or reaches the microtubule plus end by the diffusion along the microtubule lattice. Being at the microtubule plus-end XMAP215 stays there transiently and helps to incorporate up to 25 tubulin dimers into microtubule lattice before it dissociates and, therefore, it processively tracks the growing microtubule end during polymerization. There are two hypothesis of microtubule assembly promotion: (i) XMAP215 repeatedly releases an associated tubulin dimer into the microtubule growing plus end or (ii) structurally stabilizes a polymerized tubulin intermediate at the growing plus end and, therefore, preventing depolymerization events. The first way results into the increase of on-rate of tubulin dimers at the microtubule end, whereas the second way results into the decrease of off-rate of tubulin dimers at the microtubule end. Here, I show the study of the mechanism of microtubule growth acceleration by XMAP215 and the dependence of XMAP215 polymerization activity on the applied force. To answer these questions, I investigated the addition of tubulin dimers to the plus end of the microtubule by XMAP215 and how this addition depends on the applied force. XMAP215 remains at the microtubule end for several rounds of tubulin addition surfing both growing and shrinking microtubule ends. Therefore, if one could track the position of the XMAP215 molecules at the very tip of a microtubule with sufficient resolution, it would provide the information about the dynamics of the microtubule end. The technique, which can detect the position of the object of interest with high spatial and temporal resolution in addition to being able to exert a force, is an optical trap. A calibrated optical trap not only provides a good measure of displacement but also enables force measurements. To monitor the position of the molecules of interest, the molecules of interest are usually attached to a microsphere. Hence, I tethered XMAP215 to a microsphere held by an optical trap, and used XMAP215 as a handle to interact with the microtubule tip. When the microtubule grows, the XMAP215 coated microsphere will move in the optical trap and this movement can be detected with high temporal and spatial resolution. My work demonstrates that cooperatively working XMAP215 molecules can not only polymerize microtubule but also harness the energy of microtubule polymerization or depolymerization to transport some cargo. There is an evidence that orthologues of XMAP215 in budding yeasts, fission yeasts and Drosophila localize on the kinetochores. Therefore, the ability of the bearing some load during microtubule polymerization could be potentially important for the XMAP215 functioning during cell division. I also showed the influence of external force applied to the XMAP215 molecules. Pointing toward microtubule growth, a force of 0.5 pN applied to the microtubule tip-coupled XMAP215-coated microsphere increases XMAP215 polymerization activity. However, the force of the same magnitude but applied against microtubule growth does not affect XMAP215 polymerization activity. This result can be explained by the fact, that the force acting in the direction of microtubule growth constrains XMAP215 to be at the very microtubule tip. Hence, XMAP215 can not diffuse away from plus-end and there is higher chance to incorporate tubulin dimers into the microtubule plus-end. The on- and off-rate of tubulin dimers at the microtubule end are both decreased when the external force applied either in direction of microtubule growth or opposite to it. The external force affects the off-rate slightly stronger than on-rate of tubulin dimer. Taking together, my study gives new insights into the mechanism of microtubule polymerization by XMAP215 and shows some novel properties of this protein.

[pt] Estruturas com elementos de seção aberta e paredes delgadas são amplamente utilizados em estruturas metálicas. Estes elementos têm, em geral, baixa rigidez a torção. Para seções monosimétricas e assimétricas, quando o centro de cisalhamento não coincide com o centro de gravidade, pode ocorrer acoplamento entre flexão e torção. Devido à baixa rigidez à torção, podem ocorrer grandes rotações das seções transversais da viga. Assim, uma análise do comportamento de tais elementos estruturais, levando em consideração a não linearidade geométrica, é desejável. Com este objetivo, equações diferenciais parciais de movimento que descrevem o acoplamento flexão-flexão-torção são utilizadas, em conjunto com o método de Galerkin, para se obter um conjunto de equações discretizadas de movimentos, que é resolvido pelo método Runge-Kutta. A partir das equações linearizadas, obtêm-se as frequências naturais, cargas críticas axiais e a relação entre carga axial e frequência para vigas com diferentes condições de contorno. A seguir, estudam-se as oscilações não lineares e bifurcações de uma viga engastada-livre submetida a cargas laterais harmônicas. Uma análise paramétrica detalhada, usando várias ferramentas de dinâmica não linear, investiga o comportamento dinâmico não linear e não planar da viga nas três primeiras regiões de ressonância e a influência da não linearidade, posição do carregamento, restrições à torção e parâmetros de controle do carregamento na estabilidade dinâmica da estrutura. / [en] Structural elements with open and thin-walled section are widely used in metal structures. These elements have, in general, low torsional stiffness. For monosymmetric and asymmetric sections, when the shear center does not coincide with the center of gravity coupling between bending and torsion may occur. Due to the low torsional stiffness, large twist beam cross sections may arise. Thus, an analysis of the behavior of such structural elements, taking into account the geometric nonlinearity, is desirable. For this purpose, partial differential equations describing the flexural-flexural-torsional coupling are used in conjunction with the Galerkin method to obtain a set of discretized equations of motion, which is solved by the Runge-Kutta method. From the linearized equations, we obtain the natural frequencies, axial critical loads, and the axial load and frequency relationship for beams with different boundary conditions. Next, we study the nonlinear oscillations and bifurcations of a clamped-free beam subjected to harmonic lateral loads. A detailed parametric analysis, using various nonlinear dynamics tools, investigates the nonlinear dynamic behavior and nonplanar motions of the beam for the first three regions of resonance and the influence of the non-linearity, loading position, torsional restraints and load control parameters on the dynamic stability of the structure.

[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.

Microtubules are a part of the cell cytoskeleton that performs different functions, such as providing the mechanical support for the shape of a cell, acting as tracks along which the motor protein move organelles from one part of the cell to another, or the forming mitotic spindle during the cell division. The microtubules are dynamic structures, namely they can grow and shrink. The phase of microtubule growth alternates with the phase of shrinkage that results in the dynamic microtubule network in the cell. However, to form stable and spatially well-defined structures, such as a mitotic spindle, the cell needs to control this stochastic process. This is done by microtubule-associated proteins (MAPs). One class of MAPs is the proteins of XMAP216/Dis1 family, which are microtubule polymerases. The founding member of this family is X. laevis XMAP215. XMAP215 is a processive polymerase acting on the microtubule plus end. XMAP215 binds either directly or reaches the microtubule plus end by the diffusion along the microtubule lattice. Being at the microtubule plus-end XMAP215 stays there transiently and helps to incorporate up to 25 tubulin dimers into microtubule lattice before it dissociates and, therefore, it processively tracks the growing microtubule end during polymerization. There are two hypothesis of microtubule assembly promotion: (i) XMAP215 repeatedly releases an associated tubulin dimer into the microtubule growing plus end or (ii) structurally stabilizes a polymerized tubulin intermediate at the growing plus end and, therefore, preventing depolymerization events. The first way results into the increase of on-rate of tubulin dimers at the microtubule end, whereas the second way results into the decrease of off-rate of tubulin dimers at the microtubule end. Here, I show the study of the mechanism of microtubule growth acceleration by XMAP215 and the dependence of XMAP215 polymerization activity on the applied force. To answer these questions, I investigated the addition of tubulin dimers to the plus end of the microtubule by XMAP215 and how this addition depends on the applied force. XMAP215 remains at the microtubule end for several rounds of tubulin addition surfing both growing and shrinking microtubule ends. Therefore, if one could track the position of the XMAP215 molecules at the very tip of a microtubule with sufficient resolution, it would provide the information about the dynamics of the microtubule end. The technique, which can detect the position of the object of interest with high spatial and temporal resolution in addition to being able to exert a force, is an optical trap. A calibrated optical trap not only provides a good measure of displacement but also enables force measurements. To monitor the position of the molecules of interest, the molecules of interest are usually attached to a microsphere. Hence, I tethered XMAP215 to a microsphere held by an optical trap, and used XMAP215 as a handle to interact with the microtubule tip. When the microtubule grows, the XMAP215 coated microsphere will move in the optical trap and this movement can be detected with high temporal and spatial resolution. My work demonstrates that cooperatively working XMAP215 molecules can not only polymerize microtubule but also harness the energy of microtubule polymerization or depolymerization to transport some cargo. There is an evidence that orthologues of XMAP215 in budding yeasts, fission yeasts and Drosophila localize on the kinetochores. Therefore, the ability of the bearing some load during microtubule polymerization could be potentially important for the XMAP215 functioning during cell division. I also showed the influence of external force applied to the XMAP215 molecules. Pointing toward microtubule growth, a force of 0.5 pN applied to the microtubule tip-coupled XMAP215-coated microsphere increases XMAP215 polymerization activity. However, the force of the same magnitude but applied against microtubule growth does not affect XMAP215 polymerization activity. This result can be explained by the fact, that the force acting in the direction of microtubule growth constrains XMAP215 to be at the very microtubule tip. Hence, XMAP215 can not diffuse away from plus-end and there is higher chance to incorporate tubulin dimers into the microtubule plus-end. The on- and off-rate of tubulin dimers at the microtubule end are both decreased when the external force applied either in direction of microtubule growth or opposite to it. The external force affects the off-rate slightly stronger than on-rate of tubulin dimer. Taking together, my study gives new insights into the mechanism of microtubule polymerization by XMAP215 and shows some novel properties of this protein.

Eukaryontische Zellen besitzen ein Zytoskelett, ein zelluläres Netzwerk aus Biopolymeren. Unter diesen Biopolymeren sind die Mikrotubuli weitgehend konserviert. Diese aus Tubulin aufgebauten Filamente sind dynamisch und wechseln zwischen Phasen des Wachstums und der Schrumpfung. Die genauen Mechanismen, die die dynamische Instabilität der Mikrotubuli bestimmen, werden noch erforscht. Die Allgegenwart von Mikrotubuli wirft die Frage auf, wie sie in verschiedenen thermischen Umgebungen konservierte Funktionen ausführen können. Um dieser Fragestellung nachzugehen, habe ich verwandte Froscharten mit unterschiedlich temperierten Lebensräumen untersucht: Xenopus laevis (16-22 °C), Xenopus borealis (19-23 °C) und Xenopus tropicalis (22-30 °C). Um zu untersuchen, ob sich die biochemischen Eigenschaften von Tubulin und die Dynamik der Mikrotubuli bei den drei Arten an die Temperatur angepasst hat, habe ich die Methoden der Tubulin-Affinitätsreinigung und die temperaturgesteuerte TIRF-Mikroskopie zur Rekonstitution der Mikrotubuli-Dynamik kombiniert. Dabei habe ich festgestellt, dass bei einer Temperatur von 25°C die Wachstumsgeschwindigkeit der Mikrotubuli im Bezug zur thermischen Nische der einzelnen Arten negativ korreliert. Die Verwendung der Arrhenius-Gleichung zum Vergleich der Aktivierungsenergie der Mikrotubuli-Polymerisation für jede Spezies ergab, dass die freie Energie des Tubulins umso höher ist, je kälter die thermische Nische der Spezies ist. Die Mikrotubuli von X. laevis und X. borealis zeigten eine längere Lebensdauer und wurden häufiger zerstört als die von X. tropicalis. Die Tubuline von X. laevis und X. borealis sind phosphoryliert, im Gegensatz zu X. tropicalis. Die Ergebnisse zeigen, dass sich Xenopus Tubulin und die Dynamik der Mikrotubuli an die Temperatur angepasst haben. Kalt lebende Arten kommen mit der niedrigeren Energie des Milieus zurecht, durch verbessertes Wachstum und Stabilität. / Eukaryotic cells hold a cytoskeleton, a cellular network of biopolymers. Among the filaments of the cytoskeleton, microtubules are widely conserved. Built from tubulin, those filaments are dynamic, alternating between phases of growth and shrinkage. The biochemical properties of tubulin shape the dynamic behavior of microtubules, which is crucial for many cellular processes. The precise mechanisms determining microtubule dynamic instability are still under investigation. The ubiquity of microtubules raises the question of how they can perform conserved functions within various thermal environments. To address this, I turned to closely related frog species living at different temperatures, Xenopus laevis (niche: 16-22°C), Xenopus borealis (19-23°C) and Xenopus tropicalis (22-30°C). To probe whether the biochemical properties of tubulin and microtubule dynamics adapted to temperature across those three species, I combined tubulin affinity purification and temperature-controlled TIRF microscopy of in vitro reconstitution of microtubule dynamics. I found that at 25°C, the microtubule growth velocity inversely correlates with the thermal niche of each species. Adjusting temperature to each species’ endogenous condition modulates the growth rate differences across species. Using the Arrhenius equation to compare the activation energy of microtubule polymerization for each species suggested that the colder the thermal niche of the species, the higher the free energy of its tubulin. Microtubules from the cold-adapted species X. laevis and X. borealis have longer lifetimes and rescue more often than those of X. tropicalis, both at 25°C and at each species’ endogenous condition. X. laevis and X. borealis tubulins are phosphorylated, contrary to X. tropicalis. My results show that Xenopus tubulin and microtubule dynamics have adapted to temperature. Cold-living species cope with the lower energy of the milieu by facilitating growth and stability.

[pt] Há um interesse crescente na aplicação de vigas e colunas de paredes finas de materiais compostos em vários campos da engenharia. No entanto, pouco se sabe sobre seu comportamento não linear local e global sob cargas estáticas e dinâmicas. Aqui se apresenta a análise local e global de um perfil com seção canal de polímero reforçado com fibras. Na análise global, as equações não lineares de movimento da coluna de parede fina são derivadas em termos dos dois deslocamentos de flexão e do ângulo de torção, levando em consideração grandes deslocamentos, efeitos de empenamento e encurtamento. As equações de movimento não lineares governantes são discretizadas no espaço usando o método de Galerkin. Para a análise local, a seção do canal é discretizada em três placas, que são modeladas usando duas teorias não lineares de placas: a teoria clássica e a teoria de deformação por cisalhamento de primeira ordem. O sistema contínuo é discretizado usando o método de Ritz. Inicialmente são determinados analiticamente, através da resolução dos respectivos problemas de autovalor, a carga e modo crítico, as frequências naturais de vibração, bem como a relação carga-frequência do perfil em função da sua geometria e das propriedades do material. A seguir são obtidos, usando o método de Newton-Raphson e técnicas de continuação, os caminhos pós-críticos da estrutura perfeita e os caminhos não lineares de equilíbrio da estrutura imperfeita e investiga-se a sensibilidade a imperfeições, considerando diversos tipos de imperfeições geométricas. Finalmente, investigam-se as oscilações não lineares e a instabilidade paramétrica da coluna sob cargas axiais harmônicas. As equações de movimento não lineares são resolvidas numericamente pelo método de Runge-Kutta de quarta ordem. As regiões de instabilidade paramétrica são determinadas como uma função dos parâmetros do material ortotrópico, amortecimento e geometria da seção transversal. Os diagramas de bifurcação são obtidos empregando técnicas de continuação e o método da força bruta, e a estabilidade das soluções é posteriormente investigada usando a teoria de Floquet. A análise de bifurcação permite a identificação das bifurcações associadas às fronteiras de instabilidade paramétrica, bem como a existência de soluções coexistentes. Em seguida, a evolução das bacias de atração das soluções coexistentes em função da magnitude da excitação é investigada, a fim de avaliar a integridade dinâmica das soluções. Os resultados demonstram que a coluna pode perder estabilidade em níveis de carga bem abaixo da carga de flambagem estática e, portanto, o projetista deve ter cuidado ao lidar com essas estruturas sujeitas a cargas axiais variáveis no tempo. / [en] The continuous system is discretized using the Ritz method. Initially, the load and critical mode of the profile, its natural frequencies, as well as the load-frequency relation are determined analytically as a function of the column geometry and material properties by solving the respective eigenvalue problems. Next, using the Newton-Raphson method and continuation techniques, the post-critical paths of the perfect structure and the non-linear equilibrium paths of the imperfect structure are obtained and the imperfection sensitivity is investigated, considering several types of geometric imperfections. Finally, the nonlinear oscillations and parametric instability of the column under harmonic axial loads are investigated. Non-linear equations of motion are solved numerically by the fourth-order Runge-Kutta method. The regions of parametric instability are determined as a function of the parameters of the orthotropic material, damping ratio and cross-sectional geometry. The bifurcation diagrams are obtained using continuation techniques and the brute force method, and the stability of the solutions is further investigated using Floquet s theory. The bifurcation analysis allows the identification of the bifurcations associated with the boundaries of parametric instability, as well as the existence of coexisting solutions. Then, the evolution of the basins of attraction of the coexisting solutions as a function of the forcing magnitude is investigated, in order to evaluate the dynamic integrity of the solutions. The results demonstrate that the column can lose stability at load levels well below the static buckling load and, therefore, the designer must be careful when dealing with these structures subject to time-varying axial loads.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-03-27T12:06:51Z No. of bitstreams: 2 Dissertação - Vitor Escher Martins - 2014.pdf: 13588446 bytes, checksum: 9cceb42b5d24095bc392dc37f17c9386 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-03-27T15:28:00Z (GMT) No. of bitstreams: 2 Dissertação - Vitor Escher Martins - 2014.pdf: 13588446 bytes, checksum: 9cceb42b5d24095bc392dc37f17c9386 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-03-27T15:28:00Z (GMT). No. of bitstreams: 2 Dissertação - Vitor Escher Martins - 2014.pdf: 13588446 bytes, checksum: 9cceb42b5d24095bc392dc37f17c9386 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-06-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Over the years, fiber-reinforced composite laminated shells have been widely used as structural components in several engineering areas and industrial applications. These structures can been subjected to extreme working conditions, either by a fluid structure interaction or even by both dynamic external load and thermal load that provides additional compressive stresses acting along the shell. In the present work, the nonlinear dynamic behavior and stability of fluid-filled laminated cylindrical shells under both thermal and lateral loads is investigated. To model the shell the nonlinear Amabili-Reddy Higher-Order Shear Deformation Theory is applied, the hydrodynamic pressure of the fluid is model by the potential flow theory and a linear temperature distribution is proposed along the thickness of the shells. Classical shells theories, which neglect shear deformation and rotary inertia, give inaccurate analysis results for moderately thick laminated shells. Due to this limitation, higher-order shear deformation theories can represent better the kinematics behavior and can yield more accurate interlaminar stress.To discretize the shell a 23 d.o.f. displacement field is used containing the axial, circumferential, lateral displacements, rotations as well as the coefficients to consider the shear effect. The Ritz method is applied in order to obtain a set of nonlinear ordinary differential equations of motions, which are in turn solved by the Runge-Kutta method. The obtained resonance curves and bifurcation diagrams show the great influence of both laminated material and the temperature on the nonlinear behavior of the shells. / Ao longo dos anos cascas cilíndricas laminadas reforçadas com fibras têm sido amplamente utilizadas como componentes estruturais em diversas áreas da engenharia e aplicações industriais. Durante sua vida operacional, essas estruturas são constantemente submetidas às extremas condições de trabalho, seja em função da interação fluido- estrutura, cargas externas dinâmicas ou mesmo por cargas térmicas que produzem tensões adicionais de compressão sobre a superfície da casca. Neste trabalho será investigado o comportamento dinâmico não linear de cascas cilíndricas laminadas com a presença de um meio fluido em repouso no interior da casca, além de se estudar a influência de esforços laterais dinâmicos solicitantes, juntamente com a variações de temperatura. A teoria de Amabili-Reddy de deformação por cisalhamento de ordem superior é utilizada para modelar o comportamento mecânico dos esforços e deformações da casca, garantindo assim, uma melhor distribuição das tensões interlaminares, ou seja, ao longo de sua direção radial. A análise é realizada para cascas simplesmente apoiadas, em que são consideradas três expansões de deslocamento, respectivamente nas direções longitudinal, circunferencial e radial, além de duas expansões para as rotações da linha neutra nos planos xz z, discretizando o problema em 23 graus de liberdade. O método de Ritz é aplicado para a obtenção do sistema de equações de movimento não linear (EDO), além do método de Runge-Kutta de 4º Ordem e o método de Força Bruta que são utilizados para se investigar o comportamento dinâmico das análises em questão.

[pt] A resposta dinâmica de sistemas estruturais não lineares tem sido um item de grande interesse nas pesquisas em engenharia civil. Problemas onde há interação base flexível-estrutura são de grande importância na análise estrutural, já que a maioria das estruturas civis é apoiada sobre sistemas flexíveis (solo ou sistemas de apoio com dissipação de energia). Nesta área, o estudo de sistemas submetidos a ações sísmicas é um tópico relevante, já que estas solicitações têm um grande conteúdo de frequências, o que pode influenciar consideravelmente as respostas da estrutura. Neste contexto, o conhecimento da resposta em frequência de estruturas não lineares sob uma excitação de base é uma ferramenta útil para avaliar os potenciais efeitos de ações sísmicas sobre estes sistemas. Na presente tese é desenvolvida uma metodologia de análise não linear dinâmica de sistemas estruturais reticulados sob excitações de base, considerando não linearidade geométrica e apoios flexíveis, representados por molas unidimensionais, com comportamento elasto-plástico. Através de uma análise paramétrica é avaliada a variabilidade das respostas de sistemas esbeltos submetidos a ações sísmicas reais, sismos artificiais, assim como ações sísmicas sucessivas. O problema no espaço é resolvido pelo método dos elementos finitos. Para a análise em frequência, é apresentada uma metodologia baseada no método do balanço harmônico e no método de Galerkin, juntamente com técnicas de continuação para a obtenção das curvas de ressonância não lineares. O problema no tempo é abordado através da integração das equações de movimento pelos métodos de Runge-Kutta e Newmark, associado ao método de Newton-Raphson. / [en] The dynamic response of nonlinear structures has been a topic of interest in civil engineering research. Problems in which base-structure interaction is present have a great importance in structural analysis, since most structures rests on flexibel systems (soil or supports with dissipation). In this research area, the study of structures under the action of seismic loads represent a relevant topic, since this kind of excitations may excite several vibration modes and thus influence strongly the dynamic response. In this context, the prediction of the nonlinear structural behavior in frequency domain of structures under base excitation is a useful resource to assess the potential effects of sismic loads on these systems. In this thesis, a methodology for nonlinear dynamic analysis of plane frame structures under base excitation is presented considering geometric nonlinearity and elastic supports represented by elasto-plastic unidimensional springs. Trough a parametric analysis, the variability of the dynamic responses of slender structural systems under the actions of real earthquakes, synthetics earthquakes, as well as the action of multiple earthquakes is assessed. The structural systems here analyzed are discretized in space using a nonlinear finite element formulation. For the response in frequency domain, a scheme based on the Balance Harmonic Method and the Galerkin method, in conjunction with continuation methods, is formulated to obtain the nonlinear resonance curves. The nonlinear dynamic response in the time domain is calculated by direct integration of the equations of motion. For this, the Runge-Kutta method and the Newmark method in association with the iterative Newton-Raphson scheme are employed.