Les matériaux composites sont largement utilisés dans l'industrie en raison de leur bonne tenue mécanique et de leur faible densité. La diversité des domaines d’application des matériaux composites donne lieu à une grande variété de modes de sollicitation et d’endommagement. De ce fait, l’évaluation de leurs propriétés et le contrôle de leur état présentent un grand intérêt industriel. Dans ce travail, une nouvelle méthode d’évaluation et de contrôle non destructif dite par sonothermographie est explorée. Cette méthode est basée sur l'analyse du champ thermique induit par des ondes ultrasonores de puissance dans les matériaux absorbants tels que les composites. Deux applications complémentaires sont étudiées, d’une part l’évaluation des propriétés thermiques du matériau et d’autre part le contrôle non destructif de structures par thermographie infrarouge. Dans ce cadre, le problème direct de la sonothermographie est résolu numériquement à partir d’un modèle par éléments finis. Ce modèle permet de simuler le champ thermique induit par la propagation d’ondes ultrasonores dans un matériau absorbant dont les propriétés sont connues. Les simulations réalisées permettent de montrer l’applicabilité de la sonothermographie à la détection de défauts. Une nouvelle approche de caractérisation thermique est également développée. Cette approche basée sur la formulation faible de l’équation de conduction de la chaleur permet une estimation robuste de la diffusivité thermique du matériau à partir du champ thermique induit par les ondes ultrasonores de puissance. Des résultats expérimentaux sont présentés pour le cas de plaques minces. / The composite materials are widely used in industry because of their high mechanical resistance and low density. The diversity of composite materials application fields gives rise to a large variety of solicitation and damage conditions. For this reason, the evaluation of their properties and their health monitoring are of great industrial interest. In this work, a new method of evaluation and non-destructive testing named sonothermography is explored. This method is based on the analysis of thermal fields induced by ultrasonic waves in absorbent materials such as composites. Two additional applications are studied: the evaluation of the thermal properties of the material and the non-destructive testing of structures by infrared thermography. In this framework, the direct problem of sonothermography is solved numerically using a model based on the finite element method. This model allows to simulate the thermal field induced by the propagation of ultrasonic waves in absorbent material whose properties are known. The simulations carried out show the applicability of the sonothermography for the detection of defects. An innovative approach for thermal characterization is also developed. This approach based on the weak formulation of the heat conduction equation allows a robust estimate of the thermal diffusivity of the material from the thermal field induced by ultrasonic waves. Experimental results are presented for thin plates.

When modeling interest rates, using strong formulations of underlying differential equations is prone to bad numerical approximations and high computational costs, due to close to non-smoothness in the probability density function of the interest rate. To circumvent these problems, a weak formulation of the Fokker–Planck equation using Gaussian radial basis functions is suggested. This approach is used in a parameter estimation process for two interest rate models: the Vasicek model and the Cox–Ingersoll–Ross model. In this thesis, such an approach is shown to yield good numerical approximations at low computational costs.

Micro-assembly processes suffer from some breaches due to the continuing trend towards an increase in the production capabilities as well as in the size reduction of the components manipulated. Usual manipulating schemes have reached their limit and capillary forces constitute a valuable alternative strategy. The goal of this work is to describe the dynamics of liquid bridges in the application of micro-assembly processes. The description is obtained using the Kelvin-Voigt model, with a spring, a damper, and a mass connected in parallel, supported by numerical simulations, analytical approximations and experiments. The works is divided into three parts. First we present important aspects of microfluidics, as well as the constitutive equations and an overview of numerical approaches used to describe fluid flow problems with moving interfaces. The second part is devoted to the capillary rise case, intended to validate and to compare the numerical approaches to analytical laws and experimental results. The implementation of the slipping and the dynamic contact angles is discussed. The last part focuses on the dynamics of the liquid bridge. The liquid bridge is confined between two circular and parallel plates and presents an axial symmetry. The description reveals that the stiffness depends on the surface tension and on the shape of the air/liquid interface, the damping coefficient depends on the viscosity and the volume of liquid and the equivalent mass depends on the density and the volume.

[pt] Nesse trabalho, calcula-se a dinâmica de sistemas contínuos unidimensionais. Problemas de barras e vigas com diferentes condições de contorno e condições intermediárias são tratados no contexto da formulação fraca para que seja aplicado o Método de Elementos Finitos; e então seja possível calcular as aproximações das freqüências naturais e dos modos de vibração do sistema. Uma vez conhecidos os modos (exata ou aproximadamente), constrói-se um modelo reduzido de equações diferenciais ordinárias e, então, calcula-se a dinâmica do sistema. Essa dissertação propõe um material didático a ser utilizado no curso de Vibrações, com o intuito de auxiliar os alunos de graduação no estudo de sistemas contínuos, através do desenvolvimento da formulação fraca e aplicação do MEF. / [en] In this work, the dynamic of one-dimensional continuum systems is calculated. Problems of bars and beams with different boundary and intermediate conditions are treated in the context of weak formulation, so the Finite Element Method (FEM) can be applied; and it is possible to calculate the approximation of natural frequencies and vibration modes of the system. Once the modes are known (exactly or approximately), a reduced-model of ordinary differential equations is constructed and the dynamic of the system is calculated. This essay proposes a didactic material to be used at the Vibration course, with the purpose to help undergraduate students in the studies of continuum systems, through the development of the weak formulation and the application of the FEM.

Micro-assembly processes suffer from some breaches due to the continuing trend towards an increase in the production capabilities as well as in the size reduction of the components manipulated. Usual manipulating schemes have reached their limit and capillary forces constitute a valuable alternative strategy.<p><p>The goal of this work is to describe the dynamics of liquid bridges in the application of micro-assembly processes. The description is obtained using the Kelvin-Voigt model, with a spring, a damper, and a mass connected in parallel, supported by numerical simulations, analytical approximations and experiments.<p><p>The works is divided into three parts. First we present important aspects of microfluidics, as well as the constitutive equations and an overview of numerical approaches used to describe fluid flow problems with moving interfaces.<p><p>The second part is devoted to the capillary rise case, intended to validate and to compare the numerical approaches to analytical laws and experimental results. The implementation of the slipping and the dynamic contact angles is discussed.<p><p>The last part focuses on the dynamics of the liquid bridge. The liquid bridge is confined between two circular and parallel plates and presents an axial symmetry. The description reveals that the stiffness depends on the surface tension and on the shape of the air/liquid interface, the damping coefficient depends on the viscosity and the volume of liquid and the equivalent mass depends on the density and the volume.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

[pt] Neste trabalho a Análise de Vibrações é tratada no contexto da formulação fraca. Um sistema contínuo é formulado abstratamente em um espaço de Hilbert e uma base de projeção é escolhida para a dinâmica. Um esquema de convergência para a aproximação é garantido à medida em que se aumenta o número de funções da base usada para representar a resposta do problema. Esta é a idéia por traz de métodos como o Método dos Elementos Finitos e o Método dos Modos Supostos, que derivam do Método de Galerkin. Esta estratégia é diferente do que comumente é ensinado nos cursos de vibrações, onde um sistema massa-mola é analisado, e sistemas discretos formados por massas, molas e amortecedores são discutidos. Nestes casos não se sabe qual é o erro cometido na análise numérica. A Análise de Vibrações é muito usada na manutenção preditiva de máquinas rotativas. Alguns fenômenos observados nesses equipamentos motivaram o desenvolvimento de um modelo numérico que pudesse reproduzir tais fenômenos para melhor entendê-los. Um sistema rotor-mancal é modelado e sua resposta dinâmica comparada qualitativamente com a resposta dinâmica captada através de acelerômetros fixados nos mancais de um exaustor da Companhia Siderúrgica de Tubarão (CST). Durante o trabalho diversos programas foram desenvolvidos através da plataforma MATLAB. / [en] Vibration Analysis is treated in the context of weak formulation. A continuous system is formulated in the Hilbert space and one base is selected to project the dynamics. An approximation scheme is guaranteed by increasing the number of functions in the base used to represent the response. This is the idea behind methods like the Finite Element Method and Assumed Modes Method, which derive from Galerkin Method. This strategy is different from what is commonly taught in vibration courses, where a mass-spring system is analyzed and discrete systems composed by masses, springs and dashpots are discussed. In those cases the error of the numerical analysis is not known. Vibration Analysis is very used in predictive maintenance of rotating machines. Some phenomenons observed in those machines motivated the development of a numerical model that could reproduce such phenomenons to better understand them. A rotor-bearing system is modelled and its dynamic response is qualitative compared to the dynamic response captured by accelerometers fixed on the bearings of a blower of the steel company Companhia Siderúrgica de Tubarão (CST). During this work several programs were developed using MATLAB software.