Grandes esforços vêm sendo realizados atualmente com o objetivo de diagnosticar vibrações em estruturas e equipamentos, para máquinas rotativas se requer atenção ainda maior, pois correm o risco de se auto excitarem. Este trabalho tem por objetivo expor uma metodologia em dinâmica de rotores para diminuição da amplitude da resposta no domínio da frequência. Com essa finalidade, o rotor utiliza uma discretização de elementos finitos de viga de Timoshenko com funções da classe C0. A programação é implementada no programa acadêmico Meflab desenvolvida na plataforma do software MATLAB®, e no software ANSYS® Workbench para algumas validações. Os resultados numéricos são comparados com os resultados do modelo de literatura. A implementação da otimização se dá com o uso do toolbox de algoritmos genéticos existente no software MATLAB®, onde os parâmetros do algoritmo de otimização são escolhidos como sendo os diâmetros da seção transversal de cada elemento finito. A função objetivo escolhida está associada à diminuição da resposta no domínio da frequência para excitações do tipo desbalanceamento ou a evitar o posicionamento de alguma velocidade crítica dentro de um intervalo de frequências predeterminado. As restrições do problema encontram-se associadas às dimensões máximas e mínimas das seções transversais dos elementos do eixo. Em geral, para a rotação onde se requeria a diminuição da amplitude da resposta no domínio da frequência, havia uma tendência das antirressonâncias mais próximas se deslocarem para o ponto requerido. / Great efforts are been made recently in order to diagnose vibrations in structures and equipments. Rotary machines require even greater attention, for they carry the risk of auto-excitation. This paper has as an objective the exposition a rotor dynamics methodology to minimize the response amplitude in the frequency domain. With this goal, the rotor is discretized using finite Timoshenko Beams elements, with C0 class functions. The programming is implemented in the academic software Meflab, coded in the MATLAB® platform, and in the software ANSYS® Workbench to validate some results. The numerical results are compared with the results from literature model. The optimization is made utilizing the genetic algorithms toolbox existing in the MATLAB® software, where the optimization algorithms parameters are chosen as being the transverse section diameters of each finite element. The objective function chosen is associated with the response minimization in the frequency domain for unbalanced type excitations or to avoid the existence of a critical velocity within a predetermined frequency range. The problem restrictions are associated to maximum and minimum transverse section dimensions of the axis elements, as well as its total volume variation. In general, for the rotation where the frequency domain amplitude response minimization was required, there was a tendency for the closest anti-resonances to shift themselves to the required point.

Grandes esforços vêm sendo realizados atualmente com o objetivo de diagnosticar vibrações em estruturas e equipamentos, para máquinas rotativas se requer atenção ainda maior, pois correm o risco de se auto excitarem. Este trabalho tem por objetivo expor uma metodologia em dinâmica de rotores para diminuição da amplitude da resposta no domínio da frequência. Com essa finalidade, o rotor utiliza uma discretização de elementos finitos de viga de Timoshenko com funções da classe C0. A programação é implementada no programa acadêmico Meflab desenvolvida na plataforma do software MATLAB®, e no software ANSYS® Workbench para algumas validações. Os resultados numéricos são comparados com os resultados do modelo de literatura. A implementação da otimização se dá com o uso do toolbox de algoritmos genéticos existente no software MATLAB®, onde os parâmetros do algoritmo de otimização são escolhidos como sendo os diâmetros da seção transversal de cada elemento finito. A função objetivo escolhida está associada à diminuição da resposta no domínio da frequência para excitações do tipo desbalanceamento ou a evitar o posicionamento de alguma velocidade crítica dentro de um intervalo de frequências predeterminado. As restrições do problema encontram-se associadas às dimensões máximas e mínimas das seções transversais dos elementos do eixo. Em geral, para a rotação onde se requeria a diminuição da amplitude da resposta no domínio da frequência, havia uma tendência das antirressonâncias mais próximas se deslocarem para o ponto requerido. / Great efforts are been made recently in order to diagnose vibrations in structures and equipments. Rotary machines require even greater attention, for they carry the risk of auto-excitation. This paper has as an objective the exposition a rotor dynamics methodology to minimize the response amplitude in the frequency domain. With this goal, the rotor is discretized using finite Timoshenko Beams elements, with C0 class functions. The programming is implemented in the academic software Meflab, coded in the MATLAB® platform, and in the software ANSYS® Workbench to validate some results. The numerical results are compared with the results from literature model. The optimization is made utilizing the genetic algorithms toolbox existing in the MATLAB® software, where the optimization algorithms parameters are chosen as being the transverse section diameters of each finite element. The objective function chosen is associated with the response minimization in the frequency domain for unbalanced type excitations or to avoid the existence of a critical velocity within a predetermined frequency range. The problem restrictions are associated to maximum and minimum transverse section dimensions of the axis elements, as well as its total volume variation. In general, for the rotation where the frequency domain amplitude response minimization was required, there was a tendency for the closest anti-resonances to shift themselves to the required point.

Grandes esforços vêm sendo realizados atualmente com o objetivo de diagnosticar vibrações em estruturas e equipamentos, para máquinas rotativas se requer atenção ainda maior, pois correm o risco de se auto excitarem. Este trabalho tem por objetivo expor uma metodologia em dinâmica de rotores para diminuição da amplitude da resposta no domínio da frequência. Com essa finalidade, o rotor utiliza uma discretização de elementos finitos de viga de Timoshenko com funções da classe C0. A programação é implementada no programa acadêmico Meflab desenvolvida na plataforma do software MATLAB®, e no software ANSYS® Workbench para algumas validações. Os resultados numéricos são comparados com os resultados do modelo de literatura. A implementação da otimização se dá com o uso do toolbox de algoritmos genéticos existente no software MATLAB®, onde os parâmetros do algoritmo de otimização são escolhidos como sendo os diâmetros da seção transversal de cada elemento finito. A função objetivo escolhida está associada à diminuição da resposta no domínio da frequência para excitações do tipo desbalanceamento ou a evitar o posicionamento de alguma velocidade crítica dentro de um intervalo de frequências predeterminado. As restrições do problema encontram-se associadas às dimensões máximas e mínimas das seções transversais dos elementos do eixo. Em geral, para a rotação onde se requeria a diminuição da amplitude da resposta no domínio da frequência, havia uma tendência das antirressonâncias mais próximas se deslocarem para o ponto requerido. / Great efforts are been made recently in order to diagnose vibrations in structures and equipments. Rotary machines require even greater attention, for they carry the risk of auto-excitation. This paper has as an objective the exposition a rotor dynamics methodology to minimize the response amplitude in the frequency domain. With this goal, the rotor is discretized using finite Timoshenko Beams elements, with C0 class functions. The programming is implemented in the academic software Meflab, coded in the MATLAB® platform, and in the software ANSYS® Workbench to validate some results. The numerical results are compared with the results from literature model. The optimization is made utilizing the genetic algorithms toolbox existing in the MATLAB® software, where the optimization algorithms parameters are chosen as being the transverse section diameters of each finite element. The objective function chosen is associated with the response minimization in the frequency domain for unbalanced type excitations or to avoid the existence of a critical velocity within a predetermined frequency range. The problem restrictions are associated to maximum and minimum transverse section dimensions of the axis elements, as well as its total volume variation. In general, for the rotation where the frequency domain amplitude response minimization was required, there was a tendency for the closest anti-resonances to shift themselves to the required point.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2017-09-04T18:41:46Z No. of bitstreams: 2 Dissertação - Igor Cézar Silva Braga - 2017.pdf: 70087425 bytes, checksum: ae19e7f77dfd72abcaac00b9fa6bfbe1 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-15T14:10:20Z (GMT) No. of bitstreams: 2 Dissertação - Igor Cézar Silva Braga - 2017.pdf: 70087425 bytes, checksum: ae19e7f77dfd72abcaac00b9fa6bfbe1 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-09-15T14:10:20Z (GMT). No. of bitstreams: 2 Dissertação - Igor Cézar Silva Braga - 2017.pdf: 70087425 bytes, checksum: ae19e7f77dfd72abcaac00b9fa6bfbe1 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-06-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Arches are structural elements of curvilinear form transmitting normal efforts of simple compression and with wide applicability in civil engineering, being used in bridges, domes, soccer stadiums and so on. Therefore, studies that involve physical and geometric parameters to analyze the behavior of arches are necessary. This work aims to study the static and dynamic instability of tri-articulated discrete arcs, with axial and rotational rigidities the supports and under the action of a time dependent load. The arche is evaluated is a discrete and continuous system. The discrete system consists of three degrees of freedom that describe the vertical displacement and two horizontal displacements; the continuous system composed of two degrees of freedom, with an axial displacement and another in the direction radial. For the discrete system a parametric analysis was performed by varying the axial stiffness and rotational rigidities in the supports, besides the height of the arch, considering first the post-critical path study, with the influence of the parametric variation in the obtained results and the effect of the symmetry breaking in the instability by point limit or snap through, with the appearance of dynamic jumps. The natural frequency analysis is a function of the height/span ratio and the rigidities in the boundary conditions of the structures. The dynamic analysis was initiated through the instability boundaries, where it is observed how the displacements were established according to the parameters adopted, the obtained answers were proved by time responses, bifurcation diagrams and attraction basins, noting the influence of these factors in the dynamic behavior of the discrete arch. The analysis of the continuous system was established in the variation of the modified slenderness of the flexibility in the supports, observing the interference of the parameters in the post-critical path in general and in the load of the axial compression. With the asymmetry in the flexibility of the supports, the loops coming from the dynamic jumps arise. / Arcos são elementos estruturais de forma curvilínea com função de transmitir esforços normais de compressão simples e com ampla aplicabilidade na engenharia civil, pois têm o artificio estrutural de vencer grandes vãos, sendo usados em pontes, cúpulas, estádios de futebol e etc. Portanto, estudos que envolvam parâmetros físicos e geométricos para análise do comportamento de arcos se fazem necessários. Este trabalho tem como objetivo o estudo da instabilidade estática e dinâmica de arcos discretos tri-articulados, com rigidezes axiais e rigidezes rotacionais nos apoios e sob a ação de uma carga dependente do tempo. O arco é avaliado nos sistemas discreto e contínuo, sendo que o sistema discreto é composto por três graus de liberdade que descrevem um deslocamento vertical e dois deslocamentos horizontais e o sistema contínuo composto por dois graus de liberdade, sendo um deslocamento axial e outro na direção radial. Para o sistema discreto foi feita uma análise paramétrica variando a rigidez axial e as rigidezes rotacionais nos apoios, além da altura do arco, considerando primeiramente o estudo do caminho pós-críticos, com a influência da variação paramétrica nos resultados obtidos e do efeito da quebra de simetria na instabilidade por ponto limite ou snap through, com o aparecimento de saltos dinâmicos. A análise da frequência natural é em função da razão altura/vão e das rigidezes nas condições de contorno das estruturas. A análise dinâmica foi iniciada através das fronteiras de instabilidade, onde se observa como os deslocamentos se estabeleciam de acordo com os parâmetros adotados, as respostas obtidas foram comprovadas por respostas no tempo, diagramas de bifurcação e bacias de atração, constatando a influencia desses fatores no comportamento dinâmico do arco discreto. A análise do sistema contínuo se estabeleceu na variação das esbeltezes modificadas. da flexibilidade nos apoiosobservando a interferência dos parâmetros no caminho pós-crítico de forma geral e na carga de compressão axial. Com a assimetria na flexibilidade dos apoios ocasiona-se o surgimento dos loops vindos dos saltos dinâmicos.

Boundary layer rolls are a rather frequent phenomena, where regions of alternating up- and downdraft motion causes clouds to form in elongated, parallel rows oriented with the mean wind direction. The clouds can be seen during certain atmospheric conditions and are often called ”cloud streets” because of their characteristic appearance. By performing a linear instability analysis, the underlying mechanisms causing the onset of boundary layer rolls has been analysed in this study. There are two governing mech- anisms that cause the boundary layer rolls to form, the thermal instability and the dynamic instability. The thermal instability is caused by convection in an unstable airmass, while the dynamic instability usually is associated with neutral or stable conditions. The dynamic instability arise due to an inflection point in the wind profile, around which eddies develop. In a previous study by Svensson et al. (2017), rolls were observed over the Swedish east-coast, stretching out over sea during four days; 2 of May 1997, 3 of May 1997, 17 of May 2011 and 25 of May 2011. The aim of this study is to simulate the rolls on these four dates, analyse the underlying mechanisms and establish what type of instability that primarily causes the rolls to form. The linear stability analysis performed in this study indicate that the dynamic instability is the main mechanism giving rise to the rolls on all four studied dates. The rolls are found to arise over the Swedish mainland and are advected out over the sea. Both the orientation of the rolls and the modeled wind direction are in accordance with the observations. A qualitative agreement is found for the wavelength, the amplitude and the altitude of the rolls, when comparing the results of this study with the observations.

Microtubules are cytoskeletal protein polymers relevant to a wide range of cell functions. In order to polymerize, the constituent tubulin subunits need to bind the nucleotide GTP, but its subsequent hydrolysis to GDP in the microtubule lattice induces depolymerization. The resulting behaviour of stochastic switching between growth and shrinkage is called dynamic instability. Both dynamic instability and microtubule mechanical properties are integral to many cell functions, yet are poorly understood. The present study uses thermal fluctuation measurements of grafted microtubules with different nucleotide contents to extract stiffnesses, relaxation times, and drag coefficients with an unprecedented precision. Both the stiffness and the relaxation time data indicate that stiffness is a function of length for GDP microtubules stabilized with the chemotherapy drug taxol. By contrast, measurements on microtubules polymerized with the non-hydrolizable GTP-analogue GMPCPP show a significantly higher, but constant, stiffness. The addition of taxol is shown to not significantly affect the properties of these microtubules, but a lowering of the GMPCPP content restores the length-dependent stiffness seen for taxol microtubules. The data are interpreted on the basis of a recent biopolymer model that takes into account the anisotropic architecture of microtubules which consist of loosely coupled protofilaments arranged in a tube. Using taxol microtubules and GMPCPP microtubules as the respective analogues of the GDP and GTP state of microtubules, evidence is presented that shear coupling between neighbouring protofilaments is at least two orders of magnitude stiffer in the GTP state than in the GDP state. Previous studies of nucleotide effects on tubulin have focussed on protofilament bending, and the present study is the first to be able to show a dramatic effect on interprotofilament bonds. The finding’s profound implications for dynamic instability are discussed. In addition, internal friction is found to dominate over hydrodynamic drag for microtubules shorter than ∼ 4 μm and, like stiffness, to be affected by the bound nucleotide, but not by taxol. Furthermore, the thermal shape fluctuations of free microtubules are imaged, and the intrinsic curvatures of microtubules are shown for the first time to follow a spectrum reminiscent of thermal bending. Regarding the extraction of mechanical data, this assay, though previously described in the literature, is shown to suffer from systematic flaws.

Cette thèse étudie les instabilités dynamiques des milieux granulaires modèles saturés à l’aide d’un appareil triaxial classique. Les instabilités englobent la liquéfaction et les effondrements en compression isotrope drainée, les frottements saccadés en compression triaxiale drainée. Ces instabilités apparaissent spontanément à des contraintes effectives de confinement imprévisibles. Elles sont accompagnées de très rapides et très fortes surpressions interstitielles, malgré un drainage approprié; ce que ne présentent pas les milieux granulaires naturels. En compression isotrope drainée (consolidation), des effondrements locaux naissent instantanément. En compression triaxiale drainée, on observe de larges frottements saccadés quasi-périodiques caractérisés par des déformations volumiques et axiales contractantes. De temps en temps, ces effondrements et frottements saccadés locaux peuvent se développer en liquéfaction menant à une destruction complète de la structure granulaire. Les données à haute résolution temporelle issues de ce travail ont permis la découverte d’une nouvelle famille de liquéfaction dynamique et statique. L’étude des émissions acoustiques passives a permis l’identification de signature spectrale caractéristique. Pour les frottements saccadés, la phase de glissement peut être interprétée comme une consolidation dynamique, limitée par l’unique surface en dessous de la ligne critique de rupture dans le plan des contraintes effectives. La séquence temporelle précise des événements exclut que la pression interstitielle soit la cause principale des instabilités. Cependant, le rôle important de la surpression interstitielle est démontré dans des relations quantitatives entre les incréments de contraintes, et de déformations et l’éphémère surpression interstitielle stabilisée développée pendant la phase de glissement. Cela montre finalement la nature quasi-déterministique de ces instabilités dynamiques. Ces relations empiriques sont basées uniquement sur l’amplitude maximale de l’accélération verticale de très courte durée et sont gouvernées indépendamment par la pression de confinement et par l’indice des vides. La similarité de la surpression interstitielle entre différentes instabilités suggère fortement quelques mécanismes similaires de déclenchement, probablement à partir de ré-arrangements de la micro-structure granulaire. / This thesis reports a laboratory study on the dynamic instabilities of model saturated granular material using a triaxial apparatus. The term instability consists of isotropic collapse and liquefaction under isotropic compression and of stick-slip under triaxial compression in drained condition. The instabilities spontaneously occur at unpredictable effective stress with unexpected buildup of excess pore pressure irrespective of fully drained condition, contrasting with the instability-free behaviour of natural granular materials. In isotropic compression, instantaneous local collapse happens and in triaxial compression, very large and quasi-periodic stick-slip occurs with sudden volumetric compaction and axial contraction. Sometimes, these local failures (collapse and stick-slip) can develop into total liquefaction failure, destroying completely the granular structure. High time-resolved data permit the discovery of a new family of dynamic and static liquefaction. Passive acoustic measurements allow the identification of typical spectral signature. For stick-slip phenomenon, the slip phase with constant duration of stress drop can be interpreted as dynamic consolidation at constant deviatoric stress, limited by a unique boundary inside the critical state line in the effective stress plane. The precise temporal sequence of mechanical measurements excludes the generated pore pressure as the main cause of the instabilities. However, the role of pore pressure is emphasised by consistent quantitative relations between the amplitude of incremental stresses, incremental strains and the ephemeral stabilised excess pore pressure developed during the dynamic event, leading to the quasi-deterministic nature of granular instabilities. These empirical relations are based only on the short-lived maximum vertical acceleration and governed separately by the confining pressure and the initial void ratio. The similarity of pore pressure evolution for different kinds of instability strongly suggests some common speculative triggering mechanisms, probably originated from different rearrangements of the granular micro-structure.

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.