Le travail de cette thèse a été réalisé dans le cadre d'une collaboration entre EDF R&D et le LMA de Marseille (CNRS). Le but était de développer des outils théoriques et numériques pour le calcul de modes non-linéaires de structures industrielles possédant des non-linéarités localisées à jeu. La méthode de calcul utilisée est une combinaison de la méthode d'équilibrage harmonique (EH) et de la méthode asymptotique numérique (MAN), appelée EHMAN. Elle est réputée pour sa robustesse sur les problèmes réguliers. L'enjeu de ce travail de thèse est de l'appliquer sur des problèmes non-réguliers régularisés de type butée à jeu pour lequel un grand nombre d'harmonique est nécessaire. Des améliorations ont été apportées à la méthode de base pour rendre effectif le traitement de modèles à "grand" nombre de degrés de liberté (DDL). Les développements réalisés pendant la thèse ont été capitalisés par la création de nouveaux opérateurs dans Code_Aster.Une étude approfondie d'un système à 2 degrés de liberté a permis de faire émerger quelques caractéristiques des systèmes non-linéaires à jeu. Celles-ci ont servi entre autre à établir une méthodologie pour l'étude de systèmes à grand nombre de DDL. Pour finir, la potentialité des modes non-linéaires comme outil de diagnostic vibratoire est démontrée avec l'étude d'un tube cintré de générateur de vapeur. Le calcul des modes non-linéaires a monté l'existence d'une interaction entre un mode hors-plan (basse fréquence) et un mode plan (haute fréquence) expliquant des régimes vibratoires non-standards. Ce résultat, impossible à obtenir avec les outils de l'analyse modale linéaire, est confirmé expérimentalement. / This work is a collaboration between EDF R&D and the Laboratory of Mechanics and Acoustics. The objective is to develop theoretical and numerical tools to compute nonlinear normal modes (NNMs) of structures with localized nonlinearities.We use an approach combining the harmonic balance and the asymptotic numerical methods, known for its robustness principally for smooth systems. Regularization techniques are used to apply this approach for the study of nonsmooth problems. Moreover, several aspects of the method are improved to allow the computation of NNMs for systems with a high number of degrees of freedom (DOF). Finally, the method is implemented in Code_Aster, an open-source finite element solver developed by EDF R&D.The nonlinear normal modes of a two degrees-of-freedom system are studied and some original characteristics are observed. These observations are then used to develop a methodology for the study of systems with a high number of DOFs. The developed method is finally used to compute the NNMs for a model U-tube of a nuclear plant steam generator. The analysis of the NNMs reveals the presence of an interaction between an out-of-plane (low frequency) and an in-plane (high frequency) modes, a result also confirmed by the experiment. This modal interaction is not possible using linear modal analysis and confirms the interest of NNMs as a diagnostic tool in structural dynamics.

The normal-mode spectrum of rotating Earth models is made up of the seismic modes, the rotational modes and the spectrum of the liquid core. The local equations for the infinitesimal elastic-gravitational deformation, based on a Lagrangian perturbation of a spherically-averaged Earth model using the theory of hydrostatic equilibrium, are first established. A comparison is made between this approach and the classical global angular momentum approach to Earth rotation variations. The splitting of the seismic modes by rotation and ellipticity is then computed. Numerical investigation also shows that, by changing the structure of the liquid core, the rotational modes and core spectrum interact to give rise to avoided crossings, which provide a physically plausible mechanism to explain the observed double frequency of the Chandler wobble. The analogy with other oscillatory physical systems allows for a better understanding of the avoided crossing phenomenon.

L'augmentation de l'interaction lumière-matière aux échelles micro et nanométriques est un des fers de lance de la nanophotonique. En effet, le contrôle de la répartition spatiale de la lumière grâce à l'interaction résonante entre nanostructures et ondes électromagnétiques a conduit aux développements de nombreuses applications dans des domaines variés tels que les télécommunications,la spectroscopie et la détection d'objets. Le ralentissement de la lumière, sujet de la thèse, obtenue grâces à l'interférence d'ondes contre-propageantes dans des milieux périodiques ou le confinement sub-longueur d'onde dans des guides d'ondes plasmoniques, est associé à une compression des pulses lumineux et une forte augmentation du champ électrique, deux phénomènes clés pour la miniaturisation de composées optiques et l'augmentation de l'interaction lumière matière. / Enhancing light-matter interactions at micro and nanoscales is one of the spearheads of nanophotonics. Indeed, the control of the field distribution due to the resonant interaction of nanostructures with electromagnetic waves has prompted the development of numerous optical components for many applications in telecommunication, spectroscopy or sensing. A promising approach lies in the control of light speed in nanostructures. Light slowdown, obtained by wave interferences in periodic structures or subwavelength confinement in plasmonic waveguides, is associated to pulse compressions and large field enhancements,which are envisioned as key processes for the miniaturization of optical devices and the enhancement of light-matter interactions.The thesis studies both fundamental aspects and possible applications related to slow light in photonic and plasmonic nanostructures. In particular, we study the impact of periodic system sizes on the group velocity reduction and propose a novelfamily of resonators that implement slow light on very small spatial scales. We then investigate the role of fabrication disorder in slow periodic waveguides on light localization and demonstrate how modal properties influence the confinement of localized modes. Also we propose a new hollow-core photonic crystal waveguide that provides efficient and remote couplings between the waveguide and atoms thatare trapped away from it. Finally we demonstrate the important role played by slow plasmons on the emission of quantum emitters placed in nanogap plasmonic antennas and explain how large radiation efficiency can be achieved by overcoming quenching in the metal. Additionally, one part of the thesis is devoted to thederivation of a novel modal method to accurately describe the dynamics of plasmonic resonators under short pulse illumination.

Microelectromechanical systems (MEMS) depend on mechanical deformation to sense their environment, enhance electrical circuitry, or store data. Nonlinear forces arising from multiphysics phenomena at the micro- and nanoscale -- van der Waals forces, electrostatic fields, dielectric charging, capillary forces, surface roughness, asperity interactions -- lead to challenging problems for analysis, simulation, and measurement of the deforming device elements. Herein, a foundation for the study of mechanical deformation is provided through computational and experimental studies of MEMS microcantilever capacitive switches. Numerical techniques are built to capture deformation equilibria expediently. A compact analytical model is developed from principle multiphysics governing operation. Experimental measurements support the phenomena predicted by the analytical model, and finite element method (FEM) simulations confirm device-specific performance. Altogether, the static multistability and quasistatic performance of the electrostatically-actuated switches are confirmed across analysis, simulation, and experimentation. <p><br></p> <p>The nonlinear multiphysics forces present in the devices are critical to the switching behavior exploited for novel applications, but are also a culprit in a common failure mode when the attractive forces overcome the restorative and repulsive forces to result in two elements sticking together. Quasistatic operation is functional for switching between multistable states during normal conditions, but is insufficient under such stiction-failure. Exploration of dynamic methods for stiction release is often the only option for many system configurations. But how and when is release achieved? To investigate the fundamental mechanism of dynamic release, an atomic force microscopy (AFM) system -- a microcantilever with a motion-controlled base and a single-asperity probe tip, measured and actuated via lasers -- is configured to replicate elements of a stiction-failed MEMS device. Through this surrogate, observable dynamic signatures of microcantilever deflection indicate the onset of detachment between the probe and a sample.</p>