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Application de la géométrie différentielle des groupes de Lie à la dynamique non linéaire des milieux curvilignes

Abstract : The aim of this work is the study of the dynamic behavior of cables, in the assumption of large displacements, which introduces a geometrical non linearity appearing in the inertial term and in the rigidity term. The cable is modelled by a succession of rigid sections linked to each other by an elastic medium without mass. No assumption is made for the sake of simplicity in the description of internal forces. In the proposed model, a non linear elastic behavior law may be introduced, that would involve a new non linear term. Differential geometry of Lie groups allows us to obtain a simple and compact writing of dynamic equations and makes the numerical processing easier. The equations are solved by a numerical algorithm written in the same manner as the equations, and this avoids large computations and the requirements for high storage. Finally, the proposed model is applied to two concrete examples ; the first, taken from industrial world treats the problem of the dynamics of robotic cables, the second, from civil engineering, deals with vibrations of tall buildings.
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Submitted on : Wednesday, February 23, 2011 - 1:43:24 PM
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Ibrahim Alame. Application de la géométrie différentielle des groupes de Lie à la dynamique non linéaire des milieux curvilignes. Géométrie différentielle [math.DG]. Ecole Nationale des Ponts et Chaussées, 1992. Français. ⟨pastel-00568707⟩

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