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Enroulement, contact et vibrations de tiges élastiques

Abstract : This dissertation deals with equilibrium, stability and vibrations of twisted rods. First the model used (i.e. the Kirchhoff equations) is presented from two perspectives : (i) as a direct theory, the special Cosserat theory of rods, and (ii) as a 3D -> 1D asymptotic theory. The core of the text is dedicated to a relatively comprehensive study of equilibrium solutions of a clamped twisted rods with or without self-contact. Results are applied to DNA supercoiling and single-molecule experiments. Then the case of a rod with intrinsic curvature and twist coiled around a rigid cylinder is examined. The equilibrium equations obtained are applied to analyze biology related problems as the growth of a climbing plant around a pole and the secondary structure of the protein keratin. Finally the dynamics of a planar elastica is considered in two different configurations. First the dynamics of a bent and released cantilever is analyzed and shown to give rise to curvature overshoots. Second the in-plane vibrations of a planar clamped elastica after buckling are numerically computed and the role of extensibility is examined.
Mots-clés : élasticité poutres adn
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Contributor : Sébastien Neukirch <>
Submitted on : Tuesday, February 7, 2012 - 10:41:09 PM
Last modification on : Wednesday, December 9, 2020 - 3:17:02 PM
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  • HAL Id : tel-00667562, version 1


Sebastien Neukirch. Enroulement, contact et vibrations de tiges élastiques. Mécanique des structures [physics.class-ph]. Université Pierre et Marie Curie - Paris VI, 2009. ⟨tel-00667562⟩



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