Most of the methodologies dealing with viscoelastic damping focused exclusively on the frequency dependence behavior of the material. Only a few looked into the temperature dependence of the model, although none of them has taken a more serious investigation on the control design subjected to temperature disturbances. The general purpose of this work is to develop and investigate structures with damping modeled by means of internal variables. Thermodynamic principles are used to develop models, which are based on a generalized Maxwell element. Initially, studies are conducted to verify how the method of reduced variables can be applied to account for temperature dependence, as well as to evaluate the number of internal variables necessary for good accuracy of material properties representation. Lumped and finite element models are characterized and validated against other methods. A constrained layer damping model is experimentally validated for many temperatures. A control analysis is carried out on the models with the purpose to identify the role played by the internal variables on the control design. The results show that moving the internal poles is very expensive in terms of control energy. It is also shown that it is not always possible to eliminate the internal coordinates in the reduced order model if the system is highly damped. The problem of having the internal pole moved is solved by applying partial pole placement. This technique shows similar performance as compared to the linear quadratic Gaussian regulator. The control designs are implemented and it is shown that good regulation can be achieved for a fixed temperature. It is further shown that the controller will lose its performance when the model is subjected to temperature changes. To investigate the behavior of the model under different temperatures, a linear temperature-dependent model is developed, which clearly shows how the temperature affects the time response of the model. This model is used as a baseline to develop an adaptive and a time-varying controllers. With the aid of the shift factor, the eigenvalue variation with temperature is used as a time-varying function in the design. The results show that good track performance and regulation can be achieved with a control law that is capable of compensating for temperature variations. / Ph. D.

Ce mémoire présente des travaux de thèse consacrés à la caractérisation et la modélisation des hétérogénéités spatio-temporelles dans les écoulements granulaires cisaillés entre deux parois rigides. De nombreuses simulations ont permis de révéler le rôle crucial des dimensions de l’écoulement et l’influence des interactions des grains avec les parois (avec leur rugosité) sur le comportement global. Pour des systèmes allant jusqu'à une épaisseur de cent diamètres, des profils de vitesse non homogènes ont été mis en évidence, alors que la contrainte cisaillante est constante dans le volume, mettant en défaut le modèle viscoplastique au sein de l’écoulement. Pour réconcilier ces deux observations, nous avons enrichi le modèle viscoplastique en reliant la viscosité à une variable interne qui porte la perturbation due à la présence des parois. Cette nouvelle formulation de la viscosité permet de rétablir la validité d'une loi de comportement locale prenant en compte simultanément l’épaisseur de l’écoulement, la rugosité des parois et le nombre inertiel.Cette dépendance de la viscosité à une variable interne liée à la connectivité des grains ou à leur agitation à compacité fixée, suggère que, d’une manière générale,les écoulements granulaires doivent être décrits en termes d’au moins trois paramètres en fonction du nombre inertiel : le coefficient de frottement, la compacité et la connectivité. / This PhD work is devoted to the description and modeling of spatiotemporal inhomogeneities in granular flows sheared between two rigid walls. Our extensive simulations reveal the crucial role played by flow dimensions and the interactions of the grains with the walls and their roughness. For granular systems with increasingly larger thickness, non uniform strain profiles are evidenced while the shear stress remains uniform. This observation contradicts the common viscoelastic approach based on inertial number in the bulk of the flow. In order to reconcile these observations, we propose a viscoplastic model by a introducing an internal variable carrying the wall-induced perturbations of the flow. This re-formulation of granular viscosity reaffirms the local rheology by accounting for flow thickness, wall routines and inertialeffects. The well-defined dependence of the viscosity on an internal variable pertaining to grain connectivity or kinematic randomness at constant packing fraction, suggests that granular flows should be described by at least three parameters as a function of the inertial number:friction coefficient, packing fraction and connectivity.