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This Thesis comprises of two parts containing similar studies of Nonlinear Localization induced Base Isolation of structural systems. The present method of base isolation,like other nonlinear vibration isolation methods, enjoys certain merits like capability of absorbing broad band vibrations, attenuating heavy shocks etc. The research in this thesis is an extension of this base isolation strategy first proposed by Vakakis and co-author. The strategy involves augmenting an appendage referred to as the secondary system with the main structural unit or the primary system, which we want to isolate from disturbances at the base. The primary system is coupled to the secondary system through a stiffness element. Both the primary and secondary systems have nonlinear dynamic behavior. It is seen that for certain choice of values of the coupling element, steady state vibration of very small magnitude is induced in the primary system. This result was established by considering a general discrete nonlinear system with viscous damping. Now it is a well known fact that viscous damping, though being widely used in literature as well as in practice doesn't turn out to be accurate enough to capture structural damping behaviors. Moreover, the actual damping mechanism if governed by some nonlinear function of the system variables, may influence the physics governing the nonlinear localization phenomenon in a manner rendering the present method not suitable for structural systems at the very outset. So in the present study we focus our attention in establishing the robustness and hence utility of the method by considering technically more defensible models of structural damping. These models efficiently capture certain complex phenomena which structures are known to exhibit. The occurrence of localization induced vibration isolation in structural systems in the presence of these damping models is taken as a proof of the efficacy of the method and its applicability to a wide range of situations. The present study establishes existence of localization through relevant analytical and numerical exercises. In the first part of the thesis we take up the study of nonlinear localization induced base isolation of a three degrees of freedom system having cubic nonlinearities under sinusoidal base excitation. The damping forces in the system are hysteretic in nature. In the present setting this is captured by Bouc-Wen model of hysteresis. Bouc-Wen model is one of the most widely used phenomenological model of hysteresis to have a ready-to-use mathematical description of hysteretic patterns appearing in structural engineering systems. The nature of responses of the different degrees of freedom as excitation frequency varies is a better way of analyzing the performance of the vibration isolation system. We adopt this line of approach for the present study. Normally Harmonic Balance Method (HBM) serves this purpose very well but in the present case as the hysteretic variable is not explicitly related to the system variables, HBM cannot be straightway implemented. Moreover, the hysteretic variable is related to other state variables through a relation which contains non-smooth terms. As a result, Incremental Harmonic Balance (IHB) method is used to obtain amplitude frequency relationship of the system response. The stability analysis of the solution branches is done by using Floquet Theory. Direct numerical simulation is then made use of to support our results that are obtained from this approximate numeric-analytic estimate of the amplitudefrequency relationships of the system, which helps us to analyze the efficacy of this method of base isolation for a broad class of systems. In the next part we consider a similar system where the damping forces in the system are described by functions of fractional derivative of the instantaneous displacements. Fractional Derivative based damping model has been found to be very effective in describing structural damping. We adopt half-order fractional derivative for our study, which can capture damping behavior of polymeric material very well. Typically linear and quadratic damping is considered separately as these are the two most relevant representations of structural damping. Under the assumption of smallness of certain system parameters and nonlinear terms an approximate estimate of the response at each degree of freedom of the system is obtained using Method of Multiple Scales. We then consider a situation where the nonlinear terms and certain other system parameters are no longer small. For the case where asymptotic methods are no longer valid, the assessment of performance of the vibration isolation system is made from amplitude-frequency relations. As a result, we take recourse to the Harmonic Balance Method in conjunction with arc length based continuation technique for obtaining the frequency amplitude plot for linear damping and Incremental Harmonic Balance method for quadratic damping, each of which is validated against results obtained from direct numerical simulation of the system. It needs to be appreciated that base isolation obtained this way has no counterpart in the linear theory.

Les récentes recherches sur les rotors d'hélicoptère conduisent au développement de pales de nouvelle génération présentant des géométries courbes. La double flèche de la pale BlueEdgeTM proposée par Eurocopter impose de reconsidérer les outils de calcul des charges rotors pour déterminer le torseur des efforts appliqués aux pales et aux éléments constitutifs du moyeu rotor afin de satisfaire aux exigences de conception et de certification. Les charges rotors se décomposent en contributions aéro- et élasto-dynamiques prises en compte par des modélisations distinctes. La thèse vise à définir une méthodologie de calcul de charges applicable aux pales à double flèche. Ainsi sont présentés les modèles aérodynamiques bi-dimensionnels pour calculer les vitesses induites du rotor et déterminer la répartition des efforts aérodynamiques sur le rotor. Le calcul des charges rotor nécessite de recourir à des modèles élasto-dynamiques. En résolvant les équations de la dynamique des solides pour un système mécanique, le code de mécanique du vol HOST considère une modélisation élastique de pale pour déterminer le torseur des efforts, les efforts de commande étant fournis par l'ensemble bielle de pas et plateaux cycliques. Le comportement non linéaire des adaptateurs de traînée interpales est décrit par des modèles de force de restitution. Ces travaux ont utilisé des caractérisations expérimentales sur des machines de traction de laboratoire ainsi que des essais en vol afin d'évaluer le niveau de représentativité des outils et méthodes proposés. La mise en oeuvre de l'ensemble de ces modèles détermine avec satisfaction les charges dynamiques du rotor pour des vols stabilisés. / New generation blades have led to new load computation problems due to the evolution of the general shape, with forward and backward sweep. The BlueEdgeTM blade pattented by Eurocopter imposes to reconsider the development methodology and thus it is no longer possible to speak of straight blades and the models used for load computation have to be evaluated. The objective of this thesis is to determine what has to be modified and improved in current load computation methodology in order to reach an acceptable predictive level. This work considers both aerodynamic and dynamic models implemented in the HOST multi-body computer code. The aerodynamics models are based on the hypothesis of a two dimensional flow. The use of the CFD software \emph{elsA} is evaluated. Attention is given to rotor dynamics models that have an impact on loads, such as lead-lag damper models, blade element models and hub models. This thesis presents the different models and gives orientations relating to efficient load computation methodology. The aerodynamics models are compared to windtunnels experiments from the literature. This study leads also to perform flight tests and to investigate the dampers behavior on test benches in order to confront the computed loads to the reality of the helicopter operation. The proposed methodology is able to compute with a good accuracy rotor loads for stabilized flight cases.