Sur le calcul numérique des modes non linéaires

François Blanc (1) , Kerem Ege (2) , Cyril Touzé (1) , Jean-François Mercier (3) , Anne-Sophie Bonnet-Ben Dhia (4)

1 UME - Unité de Mécanique
2 LVA - Laboratoire Vibrations Acoustique
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
4 UMA - Unité de Mathématiques Appliquées

This paper deals with non linear normal modes (NNM) computation. The partial differential equations (PDE) governing the geometry of the NNM in phase space is solved via a finite difference scheme. The PDE is integrated as a transport equation, the initial conditions of which are searched so as to result in periodic solutions. The solving and optimisation algorithms are tested on a 2 dof system with cubic non-linearities. This example let us discuss the algorithms' convergence and implementation. The results are also compared to computations with more standard continuation methods.

Mots clés: Modes non linéaires; calcul numérique; équation de transport; réduction de modèle

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

François Blanc, Kerem Ege, Cyril Touzé, Jean-François Mercier, Anne-Sophie Bonnet-Ben Dhia. Sur le calcul numérique des modes non linéaires. CFM 20111 - 20ième Congrès Français de Mécanique, Aug 2011, Besançon, France. pp.1-6. ⟨hal-00627519⟩