The nonlinear static and dynamic response of circular and annular plates under electrostatic, thermal, and combined loading is investigated. The main motivation for the study of these phenomena is providing fundamental insights into the mechanics of micro-electro-mechanical-systems (MEMS). MEMS devices are usually miniaturization of the corresponding macro-scale devices. The basic mechanics of the components of many MEMS devices can be modeled using conventional structural theories. Some of the most used and actively researched MEMS devices- namely pressure sensors and micropumps- use circular or annular diaphragms as principle components. The actuation and sensing principles of these devices are usually electrostatic in nature. Most MEMS devices are required to operate under wide environmental conditions, thus, a study of thermal effects on the performance of these devices is a major design consideration. There exists a wide arsenal of analytic, semi-analytic, and numerical tools for nonlinear analysis of continuous systems. The present work uses different tools for the analysis of different types of problems. The selection of the analysis tools is guided by two principles. The first consideration is that the analysis should reveal the fundamental mechanics and dynamics of the problem rather than simply generating numerical data. The second consideration is numerical efficiency. Guided by the same principles, the basic structural model adopted in this work is the von-Karman plate model. This model captures the basic nonlinear phenomena in the plate with minimal complexity in the equations of motion, thus providing a balance between simplicity and accuracy. We address a wide array of problems for a variety of loading and boundary conditions. We start by analyzing annular plates under static electrostatic loading including the variation of the plate natural frequencies with the applied voltage. We also analyze parametric resonances in plates subjected to sinusoidally varying thermal loads. We investigate the prebuckling and postbuckling static thermal response and the corresponding variation of the natural frequencies. Finally, we close by investigating the problem of a circular plate under a combination of thermal and electrostatic loading. The results of this investigation demonstrate the importance of including nonlinear phenomena in the modeling of MEMS devices both for correct quantitative predictions and for qualitative description of operations. / Ph. D.

[pt] Este trabalho apresenta a análise numérica de vasos de pressão cilíndricos modelados por cascas e placas axissimétricas submetidas a carregamento de pressão interna uniformemente distribuída, utilizando-se a técnica de elementos finitos. São consideradas análises de junções entre superfícies com diferentes espessuras, tais como paredes finas (razão entre o raio e a espessura superior a 10) e moderadamente espessas (razão entre o raio e a espessura inferior a 5). Os campos de deslocamento considerados são os referentes aos elementos planos axissimétricos. A partir deste modelo são avaliadas as tensões na transição entre as superfícies e os resultados comparados com soluções analíticas simplificadas. Conclui-se que a solução analítica aproximada é aceitável para uma grande faixa de valores envolvendo placas e cascas de espessuras moderadamente espessas, enquanto que, para paredes finas, a análise por elementos finitos é necessária para verificação do comportamento das tensões na junção. Testes numéricos utilizando o programa ANSYS são apresentados para demonstrar o desempenho de análises lineares axissimétricas, empregando elementos quadráticos em comparação com as soluções analíticas e avaliando também as limitações do modelo analítico na região da descontinuidade geométrica do modelo proposto. / [en] This work presents the numerical analysis of cylindrical pressure vessels, modeled using axisymmetric shells and plates elements under internal pressure loads. The numerical analysis considers surface joints for various surface thickness ratios, from thin (ratio between radius and thickness greater than 10) to thick (ratio between radius and thickness less than 5) shells. Element displacement fields of axisymmetric plane elements are used to evaluate the stress state at the surfaces junctions, and the obtained results are compared to simplified analytical solutions. It is concluded that analytical approximate results present an acceptable solution for a large range of plates to shells geometries up to moderately thick shells, whereas for thin shells the finite element solution is necessary to be considered in order to accurately verify the stresses at plate to shell junction. Numerical tests applying ANSYS program are presented to demonstrate the performance of linear axisymmetric analysis applying quadratic elements in comparison to the analytical solutions also evaluating the limitations of the analytical model in the region of the geometric discontinuity of the proposed model.

Le réverbérateur à plaque est un dispositif électromécanique de réverbération artificielle utilisé dans les studios d'enregistrement pour traiter les signaux audio enregistrés dépourvus d'effet de salle. Ce dispositif simule la réverbération à partir des vibrations de flexion d'une plaque mince. L'objectif de cette thèse est la simulation par modèles physiques d'un réverbérateur à plaque générique permettant à l'utilisateur le choix des principaux paramètres : caractéristiques géométriques et physiques du matériau de la plaque, conditions aux limites, positions de l'excitateur et des accéléromètres, et l'influence d'une plaque poreuse à proximité. Outre la compréhension des phénomènes entrant en jeu dans de tels dispositifs, cette approche permet la simulation de réverbérateurs à plaque existants comme l'EMT-140 ou l'EMT-240, mais aussi de réverbérateurs avec d'autres jeux de paramètres réels ou fictifs. La démarche entreprise s'articule en trois points : la modélisation du dispositif, les mesures sur un réverbérateur EMT-140 et la définition des outils numériques pour la synthèse sonore dans le domaine audible. La modélisation développée relève de la dynamique et de la vibroacoustique, et porte une attention particulière sur les mécanismes d'amortissement en raison de leur grande influence dans la perception de l'effet de réverbération. La démarche expérimentale, effectuée sur un réverbérateur EMT-140, permet l'identification des paramètres d'un dispositif réel et l'identification des limites de validité de la modélisation. L'outil de simulation dans le domaine temporel repose sur la méthode des différences finies.