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Thermographie infrarouge de champs ultrasonores en vue de l’évaluation et du contrôle non destructifs de matériaux composites / Infrared thermography of ultrasonic fields for the evaluation and non-destructive testing of composite materialsKouadio, Thierry 08 July 2013 (has links)
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.
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Parameter estimation in interest rate models using Gaussian radial basis functionsvon Sydow, Gustaf January 2024 (has links)
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.
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A Study of Liquid Bridge Dynamics: an Application to Micro-Assembly/Une Etude de la Dynamique du Pont Liquide: une Application au Micro-AssemblageValsamis, Jean-Baptiste 31 May 2010 (has links)
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.
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[en] DYNAMIC OF ONE-DIMENSIONAL FLEXIBLE STRUCTURES / [pt] DINÂMICA DE ESTRUTURAS FLEXÍVEIS UNIDIMENSIONAISPRISCILLA OLIVEIRA DE ALMEIDA 01 November 2006 (has links)
[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.
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A study of liquid bridge dynamics: an application to micro-assembly / Une étude de la dynamique du pont liquide: une application au micro-assemblageValsamis, Jean-Baptiste 31 May 2010 (has links)
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
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[pt] ANÁLISE DE VIBRAÇÕES DE SISTEMAS LINEARES E NÃO-LINEARES NO CONTEXTO DA FORMULAÇÃO FRACA, ANÁLISE MODAL E DECOMPOSIÇÃO DE KARHUNEN-LOÈVE / [en] VIBRATION ANALYSIS OF LINEAR AND NON-LINEAR SYSTEMS IN THE CONTEXT OF WEAK-FORMULATION, MODAL ANALYSIS AND KARHUNEN-LOÈVEN BASISTHIAGO GAMBOA RITTO 06 January 2006 (has links)
[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.
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