The objective of this work is to study the local and global nonlinear vibrations of isotropic single-layered and multi-layered cross-ply doubly curved shallow shells with simply supported boundary conditions. The study is based-on the full nonlinear partial-differential equations of motion for shells. These equations of motion are based-on the von K\'rm\'{a}n-type geometric nonlinear theory and the first-order shear-deformation theory, they are developed by using a variational approach. Many approximate shell theories are presented. We used two approaches to study the responses of shells to a primary resonance: a $direct$ approach and a $discretization$ approach. In the discretization approach, the nonlinear partial-differential equations are discretized using the Galerkin procedure to reduce them to an infinite system of nonlinearly coupled second-order ordinary-differential equations. An approximate solution of this set is then obtained by using the method of multiple scales for the case of primary resonance. The resulting equations describing the modulations of the amplitude and phase of the excited mode are used to generate frequency- and force-response curves. The effect of the number of modes retained in the approximation on the predicted responses is discussed and the shortcomings of using low-order discretization models are demonstrated. In the direct approach, the method of multiple scales is applied directly to the nonlinear partial-differential equations of motion and associated boundary conditions for the same cases treated using the discretization approach. The results obtained from these two approaches are compared. For the global analysis, a finite number of equations are integrated numerically to calculate the limit cycles and their stability, and hence their bifurcations, using Floquet theory. The use of this theory requires integrating $2n+(2n)^2$ nonlinear first-order ordinary-differential equations simultaneously, where $n$ is the number of modes retained in the discretization. A convergence study is conducted to determine the number of modes needed to obtain robust results. The discretized system of equation are used to study the nonlinear vibrations of shells to subharmonic resonances of order one-half. The effect of the number of modes retained in the approximation is presented. Also, the effect of the number of layers on the shell parameters is shown. Modal interaction between the first and second modes in the case of a two-to-one internal resonance is investigated. We use the method of multiple scales to determine the modulation equations that govern the slow dynamics of the response. A pseudo-arclength scheme is used to determine the fixed points of the modulation equations and the stability of these fixed points is investigated. In some cases, the fixed points undergo Hopf bifurcations, which result in dynamic solutions. A combination of a long-time integration and Floquet theory is used to determine the detailed solution branches and chaotic solutions and their stability. The limit cycles may undergo symmetry-breaking, saddle node, and period-doubling bifurcations. / Ph. D.

[pt] O objetivo desta tese de doutorado é estudar a influência do acoplamento de modos de flambagem no comportamento estático e particularmente no comportamento dinâmico não-linear de elementos estruturais suscetíveis a flambagem. Para isto, usam-se dois modelos discretos conhecidos por seu complexo comportamento não-linear: o modelo de Augusti e um modelo de torre estaiada com dois graus de liberdade. Inicialmente estuda-se a estabilidade dos dois modelos perfeitos, incluindo a obtenção de todos os caminhos de equilíbrio pré- e pós-críticos e o efeito das imperfeições na capacidade de carga da estrutura e na estabilidade dos diversos caminhos de equilíbrio. O objetivo desta análise é entender como as diversas soluções pós-críticas instáveis e as imperfeições influenciam a geometria da superfície de energia potencial, o contorno do vale potencial pré-crítico e a integridade da estrutura frente a inevitáveis perturbações externas. A seguir estuda-se o comportamento dos modelos em vibração livre. Após a identificação das freqüências naturais, dos modos lineares de vibração e das ressonâncias internas, estuda-se, com o objetivo de entender a dinâmica dos modelos, usando as ferramentas da mecânica Hamiltoniana, a geometria da região segura que circunda a posição de equilíbrio pré-crítica, cuja estabilidade se deseja preservar, e as variedades invariantes dos pontos de sela que definem esta região. Ainda, no contexto da análise das vibrações livres, determinam-se todos os modos não-lineares de vibração, sua estabilidade e sua relação freqüência-amplitude. Estes modos não-lineares estáveis e instáveis, que surgem em virtude do acoplamento modal e das simetrias dos modelos, controlam e explicam a sua dinâmica sob vibração forçada. Com base nesses resultados, estuda-se o comportamento dos modelos sob uma excitação de base, através de um estudo sistemático de bifurcações globais e locais, e a integridade das soluções estáveis através da evolução e estratificação das bacias de atração e das medidas de integridade dinâmica. Finalmente estuda-se como aumentar a segurança da estrutura através do controle das bifurcações globais homoclínicas e heteroclínicas. A presente tese revela um conjunto de comportamentos que são típicos dos dois modelos e que podem ser entendidos como fenômenos característicos de estruturas que exibem acoplamento modal. Assim, a principal contribuição deste trabalho reside na identificação de algumas características e aspectos particulares dessa classe de estruturas, assunto inédito na literatura. / [en] The aim of this thesis is to study the influence of coupled buckling modes on the static and particularly on the nonlinear dynamic behavior of structural components liable to buckling. For this, two discrete two degrees of freedom models known for their complex nonlinear behavior are selected: the well-known Augusti’s model and a simplified model of cable-stayed tower. Initially, the stability analysis of the perfect models is conducted, including the identification of all pre- and post-critical equilibrium paths, and the effect of imperfections on the load capacity of the structure and stability of the various equilibrium paths. The purpose of this analysis is to understand how the various unstable post-critical solutions and imperfections influence the geometry of the potential energy surface, the contour of the pre-buckling potential well and the integrity of the structure under the inevitable external disturbances. Then the behavior of the models in free vibration is investigated, including the identification of the natural frequencies, linear vibration modes and possible internal resonance. To understand the dynamics of the models, the geometry of the safe region surrounding the pre-buckling equilibrium position and the invariant manifolds of saddle points that define this region are obtained using the tools of Hamiltonian mechanics. Also, as part of the free vibrations analysis, all stable and unstable nonlinear vibration modes and their frequency-amplitude relations are obtained. These nonlinear stable and unstable modes, which arise due to modal coupling and the symmetries of the models, control and explain the dynamics of the model under forced vibration. Based on these results, we study the behavior of the models subjected to a base excitation through a systematic study of the global and local bifurcations, and the integrity of stable solutions through the evolution and stratification of the basins of attraction and dynamic integrity measures. Finally, we study how to increase the safety of the structure through the control of global homoclinic and heteroclinic bifurcations. This thesis identifies a number of behaviors that are typical of the two models and can be understood as characteristic phenomena of structures exhibiting modal coupling. Thus the main contribution of this work is to identify certain characteristics and particular aspects of this class of structures, a first contribution to this research area.

Pervasive computing sa zameriava odstránenie zložitostí pri interakcii s výpočtovou technikou a zvýšenie efektivity pri jej každodennom používaní. Ale i po viac ako 15 rokoch od sformulovania hlavných cieľov Pervasive computingu existujú aspekty interakcie ktoré stále nie sú súčasťou užívateľskej skúsenosti s dnešnou technológiou. Bezproblémová integrácia s prostredím vedúca k technologickej neviditeľnosti, alebo interakcia naprieč rôznymi zariadeniami predstavujú stále veľkú výzvu. Hlavným cieľom tejto práce je prispieť k tomu, aby sa ciele Pervasive computingu priblížili k realizovaniu tým, že predstavíme spôsob intuitívneho zdieľania informácií medzi osobným a verejne umiestneným zariadením. Predstavili sme tri interakčné techniky, ktoré podporujú intuitívnu výmenu obsahu medzi osobným zariadením a zdieľaným displejom. Tieto techniky sú založené na prenose videa, rozšírenej realite a analýze pohľadových dát. Okrem interakčných techník sme tiež predstavili mechanizmus pre získavanie, prenos a rekonštrukciu aplikačného stavu na cieľovom zariadení.

Inviscid fluid inside thin pipe system is first analytically solved for eigenfrequencies and eigenmodes using Modal Interaction Model method with fluid-structure interaction condition at boundary. Shear-diaphragm boundary condition is used for comparing and validating Analytic results with Simulation using COMSOL Multiphysics. Effect of viscosity is also compared using Newtonian fluid model. Experiment is performed using simple pipe geometry and fluid to measure transfer accelerance which is post-processed to extract cirumferential modes up to order 4; this is used to compare and validate Experiemental results with Simulation. Good correlation is obtained between Analytic, Experiment and Simulation results with n=0 breathing modes requiring modification of governing equations to incorporate compressibility effects due to changing pipe cross-section area. / En analytisk lösning för egenfrekvenser och egenmoder för en icke-viskös fluid inuti ett tunt rörsystem är först framtagen med användning av en modbaserad modell för interaktion mellan fluid och struktur som randvillkor. Idealiserad randvillkor används för att jämföra och validera analytiska resultat med simulationer i COMSOL Multiphysics. Effekten av viskositet jämförs också med hjälp av en Newtonsk fluidmodell. Experiment genomförs med simpel rörgeometri samt fluid för att mäta acceleransen som är analyserad för till att få ut mo-der i omkretsled upp till fjärde ordningen; detta i sin tur används för att jämföra och validera de experimentella resultaten med simulering-ar. Det erhålls bra korrelation mellan de analytiska-, simulerade- samt experimentella resultaten. Undantaget för n=0 grundmoder då krävs modifikation av differentialekvationerna till att inkorporera kompressibilitetseffekter

In this work, the random vibration of higher-order nonlinear beams and composite plates subjected to stochastic loading is studied. The fourth-order nonlinear beam equation is examined to study the effect of rotary inertia and shear deformation on the root mean square values of displacement response. A new linearly coupled equivalent linearization method is proposed and compared with the widely used traditional equivalent linearization method. The new method is proven to yield closer predictions to the numerical simulation results of the nonlinear beam vibration. A systematical investigation of the nonlinear random vibration of composite plates is conducted in which effects of nonlinearity, choices of different plate theories (the first order shear deformation plate theory and the classical plate theory), and temperature gradient on the plate statistical transverse response are addressed. Attention is paid to calculate the R.M.S. values of stress components since they directly affect the fatigue life of the structure. A statistical data reconstruction technique named ARMA modeling and its applications in random vibration data analysis are discussed. The model is applied to the simulation data of nonlinear beams. It is shown that good estimations of both the nonlinear frequencies and the power spectral densities are given by the technique. / Ph. D.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-09-22T20:32:01Z No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-23T15:24:03Z (GMT) No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-23T15:24:03Z (GMT). No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-02-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The aim of this work is to investigate the interaction and modal coupling phenomena on the nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and lateral loads. The equations of motion of the cylindrical shell are deduced from their energy functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally, the problem is reduced to a system of nonlinear ordinary differential equations by the application of the standard Galerkin method. The modal expansion that describes the transverse displacement of the shell is obtained by applying perturbation techniques, which identifies the importance of each term in the modal expansion by the power of the perturbation parameter. The Karhunen-Loève method is applied in order to verify the importance of each term in the modal expansion, quantifying the contribution of each of these terms in the total energy of the system. The starting solution used in the perturbation procedure contains two modes of vibration with the same natural frequency and their respective companion modes, yielding a modal expansion able to describe the modal interaction between these two modes. Then, the influence of modal interaction on the nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is studied. From the analysis of the resonance curves, the parametric instability and escape boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the cylindrical shell is possible to identify situations in which the consideration of modal interaction is necessary. / Neste trabalho estudam-se as vibrações não lineares de cascas cilíndricas simplesmente apoiadas sujeitas a um carregamento lateral e a um carregamento axial, ambos harmônicos, com o objetivo de se analisar fenômenos como o acoplamento e a interação modal. As equações de movimento da casca cilíndrica são deduzidas a partir de seus funcionais de energia. O campo de deformações da casca cilíndrica é descrito com base na teoria não linear de Donnell para cascas esbeltas e o problema é reduzido a um sistema de equações diferenciais ordinárias não lineares a partir da aplicação do método de Galerkin. As expansões modais que descrevem o campo de deslocamento transversal da casca são obtidas através da aplicação do método da perturbação, que identifica a importância de cada termo da expansão modal a partir da potência do parâmetro de perturbação. O método de Karhunen-Loève é aplicado a fim de se verificar a importância de cada termo da expansão modal, quantificando a participação de cada um desses termos na energia total do sistema. Utilizam-se, como solução inicial do método da perturbação, dois modos de vibração com frequência natural igual e com seus respectivos companion modes, obtendo-se uma expansão modal capaz de descrever a interação modal entre esses dois modos. Em seguida, analisa-se a influência da interação modal no comportamento não linear da casca cilíndrica submetidas a cargas laterais e axiais harmônicas. A partir da análise das curvas de ressonância, das fronteiras de instabilidade paramétrica, dos diagramas de bifurcação, das bacias de atração e dos planosfase da casca cilíndrica é possível identificar em quais situações de carregamento a consideração da interação modal se faz necessária.

[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.

Pour les compresseurs axiaux et centrifuges, la minimisation du jeu, entre l’extrémité des aubes et le carter qui les entoure, augmente l’efficacité aérodynamique des turbomachines mais favorise également l’apparition de contacts structuraux. En présence du contact, les deux structures échangent de l’énergie et le système peut devenir instable lorsque ses fréquences propres, exprimées dans le même repère, sont égales. Nous verrons qu’il existe également la possibilité de créer des réponses forcées lorsque les harmoniques de la vitesse de rotation coïncident avec les fréquences propres de la structure fixe ou tournante. Dans les deux cas, les structures peuvent subir des endommagements assez importants. La maitrise de l’interaction aube-carter est donc logiquement un phénomène que les constructeurs de turbomachines doivent intégrer lors de la définition d’un moteur. Ainsi, dans l’étape de conception des compresseurs, il faut prévoir le comportement vibratoire du système en prenant en compte les phénomènes physiques les plus influents. Dans ce contexte, ce travail de recherche est focalise sur l’étude du comportement mécanique et thermomécanique résultant de l’interaction aube-carter entre un compresseur centrifuge (ou rouet) expérimental du premier étage de compression d’un moteur d’hélicoptère et son couvercle qui est recouvert d’un matériau abradable afin de réduire la sévérité du contact. L’objectif majeur des travaux présentes dans ce manuscrit est d’établir un scénario plausible pour expliquer les divers phénomènes présents lors du contact et de créer une base de données expérimentales, dans un environnement de laboratoire au travers d’un essai réaliste et maitrisé. Puis, il s’agit de confronter et valider les interprétations expérimentales sur un modèle numérique. Pour atteindre nos objectifs, nous avons utilisé un dispositif d’essai adapté afin de fournir des données fiables sur le comportement dynamique et thermomécanique en situation de contact aube-carter. L’analyse des résultats expérimentaux et numériques montre des évènements transitoires concomitants entre la structure fixe et tournante. Le contenu spectral des réponses est caractérise par la présence d’harmoniques de la vitesse de rotation et de sidebands, qui influencent le comportement dynamique du système lorsqu’ils coïncident avec les fréquences propres des structures. / In axial and centrifugal compressors, minimizing the clearance between the blade tips of the impeller and its surrounding casing increases the aerodynamic efficiency, but also the probability of contacts. An energy exchange is then produced between the two structures, leading to forced excitation of the natural modes and potentially to dynamical instabilities, such as interaction phenomena. In both cases, the structures suffer subsequent structural damages. Mastering blade-to-casing interactions is thus a phenomenon that turbomachinery manufacturers must incorporate into the design process of an engine. Compressor designers must predict the vibration behavior of the system, taking into account the predominant physical phenomena. In this context, this work focuses on the study of the dynamic and thermomecanichal behavior resulting from blade-to-casing interactions between a low-pressure centrifugal compressor (or impeller) and a casing lined with abradable coating. The main purpose of this work is to build a likely scenario to explain the various phenomena present when contact occurs, and the creation of a database for subsequent comparisons with numerical simulations. To achieve this, a test rig heavily instrumented has been used in order to better understand the influence of various physical phenomena (dynamic, wearing, heating). Analysis of experimental and numerical results shows transient events, characterized by a simultaneous increase in amplitude on both the rotating and stationary structures. The spectral content of the response highlights the presence of harmonics of the rotating speed and some sidebands aside from the main excited frequencies, which may cause the system to become unstable when they coincide with the natural frequencies of structures.

The first objective of this Dissertation is to present a methodology to calculate analytically the mode shapes and corresponding natural frequencies and determine critical buckling loads of mechanically coupled microbeam resonators with a focus on micromechanical filters. The second objective is to adopt a nonlinear approach to build a reduced-order model and obtain closed-form expressions for the response of the filter to a primary resonance. The third objective is to investigate the feasibility of employing subharmonic excitation to build bandpass filters consisting of either two sets of two beams coupled mechanically or two sets of clamped-clamped beams. Throughout this Dissertation, we treat filters as distributed-parameter systems. In the first part of the Dissertation, we demonstrate the methodology by considering a mechanical filter composed of two beams coupled by a weak beam. We solve a boundary-value problem (BVP) composed of five equations and twenty boundary conditions for the natural frequencies and mode shapes. We reduce the problem to a set of three linear homogeneous algebraic equations for three constants and the frequencies in order to obtain a deeper insight into the relation between the design parameters and the performance metrics. In an approach similar to the vibration problem, we solve the buckling problem to study the effect of the residual stress on the static stability of the structure. To achieve the second objective, we develop a reduced-order model for the filter by writing the Lagrangian and applying the Galerkin procedure using its analytically calculated linear global mode shapes as basis functions. The resulting model accounts for the geometric and electric nonlinearities and the coupling between them. Using the method of multiple scales, we obtain closed-form expressions for the deflection and the electric current in the case of one-to-one internal and primary resonances. The closed-form solution shows that there are three possible operating ranges, depending on the DC voltage. For low DC voltages, the effective nonlinearity is positive and the filter behavior is hardening, whereas for large DC voltages, the effective nonlinearity is negative and the filter behavior is softening. We found that, when mismatched DC voltages are applied to the primary resonators, the first mode is localized in the softer resonator and the second mode is localized in the stiffer resonator. We note that the excitation amplitude can be increased without worrying about the appearance of multivaluedness when operating the filter in the near-linear range. The upper bound in this case is the occurrence of the dynamic pull-in instability. In the softening and hardening operating ranges, the adverse effects of the multi-valued response, such as hysteresis and jumps, limit the range of the input signal. To achieve the third objective, we propose a filtration technique based on subharmonic resonance excitation to attain bandpass filters with ideal stopband rejection and sharp rolloff. The filtration mechanism depends on tuning two oscillators such that one operates in the softening range and the other operates in the hardening range. Hardware and logic schemes are necessary to realize the proposed filter. We derive a reduced-order model using a methodology similar to that used in the primary excitation case, but with all necessary changes to account for the subharmonic resonance of order one-half. We observe that some manipulations are essential for a structure of two beams coupled by a weak spring to be suitable for filtration. To avoid these complications, we use a pair of single clamped-clamped beams to achieve our goal. Using a model derived by attacking directly the distributed-parameters problem, we suggest design guidelines to select beams that are potential candidates for building a bandpass filter. We demonstrate the proposed mechanism using an example. / Ph. D.

[pt] Nessa dissertação, são avaliados os comportamentos crítico e pós-crítico de uma placa retangular fina, simplesmente apoiada, sob compressão. Um modelo não-linear para placas perfeitas e com imperfeições é desenvolvido com base na teoria não-linear de placas proposta por Marguerre. O modelo discretizado possui dois graus de liberdade que são caracterizados pela flambagem em m e (m+1) meia-ondas senoidais na direção do carregamento. Obtém-se analiticamente soluções desacopladas e acopladas através de programas de álgebra simbólica (Maple V Realese 4). Realiza- se um detalhado estudo paramétrico visando identificar todas as possíveis configurações de equilíbrio e, para cada configuração determinada, analisa-se sua estabilidade. É também estudada a influência de imperfeições geométricas iniciais, tanto na superfície de energia quanto no número e estabilidade das soluções. Os resultados mostram que o acoplamento modal tem uma grande influência sobre o comportamento pós-crítico destas placas, podendo provocar mudanças bruscas dos modos de flambagem. Finalmente, é analisada a influência das imperfeições e tensões de compressão inicias nas freqüências naturais da placa, mostrando como estas freqüências podem ser utilizadas para determinar cargas críticas sem a necessidade de execução de ensaios destrutivos. / [en] The buckling and post buckling behavior of simply supported thin rectangular plates in axial compression is considered in this dissertation. A non- linear model for perfect and imperfect plates is developed based on Marguerre non-linear plate theory. The discretized model is considered as having two degrees of freedom characterized by buckling in m and (m+1) halfsinewaves axially and uncoupled and coupled solutions are obtained analytically by the use of symbolic algebra software. A detailed parametric study is conducted to identify all possible equilibrium solutions and establish their stability. The influence of initial geometric imperfections on the energy surface, number and stability of solutions is taken into account as an indispensable part of the analysis. The results shown that modal coupling has a strong influence on the post-buckling behavior of these plates and may explain abrupt changes of waveform of plates in the post-buckling range. Also, the influence of imperfections and initial compressive stress on the natural frequencies of the plate is analyzed and it is shown how these frequencies can be used to estimate safe buckling loads of rectangular plates non-destructively. / [es] Este trabajo presenta un análisis experimental de cinco vigas de concreto, simplemente apoyadas, protendidas con cables sintéticos externos, con el objetivo de estudiar la influencia de la resistencia del concreto en la variación de la fuerza de los cables de protensión y en la resistencia a la flexión de las vigas. La protensión de las vigas fue hecha con cables sintéticos conocidos como Parafil, con resistenciaa la tracción de 1950MPa y módulo de elasticidad de 126000MPa. La única variable considerada fue la resistencia del concreto, cuyos valores fueron 36, 57, 73, 74 y 104MPa. El concreto de las vigas con resistencia de 57, 73, 74 y 104MPa fueron construidos con el uso de la microsílica y aditivo superplastificante, con excepción de la viga con resistencia de 36MPa que fue construida con concreto común. Los resultados mostraron que la influencia de la resistencia del concreto sobre la resistencia a la flexión de las vigas no es grande. Para el aumento de 189% en la resistencia del concreto, se produjo un aumento en la variación de la fuerza en el cable de apenas 13.6% y un aumento de 33% en el momento de ruptura. Comparando los resultados experimentales con los resultados de las principales normas y modelos propuestos se verificó que todos ofrecen buenos resultados y subestiman los valores experimentales. Comparando los resultados experimentales con el modelo de Campos (1993) se observó que los valores de la variación en la fuerza en el cable superestiman los valores experimentales. 1267 En esta disertación, se evalúan los comportamientos crítico y poscrítico de una placa rectangular fina, simplemente apoyada, bajo compresión. Se desarrolla un modelo no lineal para placas perfectas y con imperfecciones teniendo como base la teoría no lineal de placas propuesta por Marguerre. El modelo discretizado posee dos grados de libertad que son caracterizados al flamear en m y (m+1) medias-ondas senoidales en la dirección de sobrepeso. Se obtienen analíticamente soluciones desacopladas y acopladas a través de programas de álgebra simbólica (Maple V Realese 4). Se realiza un detallado estudio paronétrico tratando de identificar todas las posibles configuraciones de equilibrio y, para cada configuración determinada se analisa la estabilidad. También se estudia la influencia de imperfecciones geométricas iniciales, tanto en la superfície de energía como en el número y estabilidad de las soluciones. Los resultados muestran que el acoplamiento modal tiene una gran influencia sobre el comportamiento poscrítico de estas placas, lo que puede provocar cambios bruscos de los modos de flamear. Finalmente, se analiza la influencia de las imperfecciones y tensiones de compresión iniciales en las frecuencias naturales de la placa, mostrando como estas frecuencias pueden ser utilizadas para determinar cargas críticas sin necesidad de ejecución de ensayos destructivos.