Réduction d'ordre de modèle d'un phénomène d'amortissement non-linéaire dans le cadre des microsystèmes.

Abstract : This thesis deals with reduced-order modelling of squeeze-film damping, a fluidic phenomenon that is commonly encountered in MEMS. In the first chapter, reduced-order modelling methods are presented. For linear systems, well-established theories exist. They can be adapted to nonlinear systems. However, the resulting reduced-order models are valid in a certain region of the state-space only, depending on the training trajectory. The method of nonlinear normal modes, which does not depend on a training trajectory is also introduced. Chapter two is focused on the squeeze-film damping phenomenon governed by the Reynolds equation. We first establish the equation from appropriate hypotheses, and then present the different resolutions of its linear and nonlinear form found in literature. The results from a model based on the Reynolds equation are then compared to results from a finite element Navier-Stokes model, in order to validate the various hypotheses made. An original method of resolution based on a change of variable is then proposed. Several other method of resolution are studied as well as different projection bases amongst those presented in chapter one.Chapter three is dedicated to the modelling a micro-switch, a candidate to the replacement of switches based on transistors in RF communications. Its modelling implies the coupling of three domains: mechanics, electrostatics, and fluidics with Reynolds equation. Following a description of the models from literature, a coupled model is proposed, the fluidic model being the one presented in chapter two. This model is validated compared to finite difference models as well as experimental data from the literature.Finally, the fourth chapter aims at reducing the evaluation cost of the coupled micro-switch model established in chapter three. The first method consists in finding an approximation function of the projection of the fluidic force on the first linear mechanical mode as a function of the mechanical modal coordinates, position and speed. This method is applicable in the incompressible case only. In the compressible case, the Reynolds equation has to be solved. The method of Rewienski and al., which consists in piecewise-linearizing the functions governing the dynamics, is used. Another method based on a piecewise-linear approach, taking advantage of the particular structure of the model presented in chapter two, thus not depending on a training trajectory, is proposed.
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Autre. Ecole Centrale Paris, 2010. Français. 〈NNT : 2010ECAP0039〉
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Alexia Missoffe. Réduction d'ordre de modèle d'un phénomène d'amortissement non-linéaire dans le cadre des microsystèmes.. Autre. Ecole Centrale Paris, 2010. Français. 〈NNT : 2010ECAP0039〉. 〈tel-00552076v2〉



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