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Une méthode de calcul des modes de vibrations non linéaires de structures

Abstract : The aim of this thesis is to evaluate new theoric and numeric tools for non linear modes computation of structures with geometric non linearity discretused by the finite element method. The invariant surface which caracterises the non linear mode is defined with a family of periodic orbits solution of the equation of motion. Each orbit is time discretised (Newmark or Simo scheme) and formulated with a global system containing all unknows for every time steps, this is the simultaneous method, by opposition with the classic shooting method. The orbit family solution of the global system is obtained with the continuation method ANM (Asymptotic Numerical Method). Some variations around the ANM are also adressed. We introduced new approach to control continuation around a bifurcation point by adding a perturbation to the non linear system. We also present a software, MANLAB, allowing interactive continuation of complex bifurcation diagrams, which is applied to the family of periodic orbits.
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https://tel.archives-ouvertes.fr/tel-00487857
Contributor : Rémi Arquier <>
Submitted on : Monday, May 31, 2010 - 12:00:08 PM
Last modification on : Thursday, January 23, 2020 - 6:22:03 PM
Long-term archiving on: : Thursday, September 16, 2010 - 4:08:04 PM

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  • HAL Id : tel-00487857, version 1

Citation

Remi Arquier. Une méthode de calcul des modes de vibrations non linéaires de structures. Mécanique [physics.med-ph]. Université de la Méditerranée - Aix-Marseille II, 2007. Français. ⟨tel-00487857⟩

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