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, ROM non linéaire est paramétré par rapport à la vitesse de rotation de la structure et il est construit de manière à être valide pour une plage donnée de vitesses de rotation. iv) La non-linéarité géométrique est combinée avec la non-linéarité de contact frottant en utilisant une base réduite de type Craig-Bampton qui est capable de conserver certains des degrés de liberté

. Dans-le and . Code_aster, et les langages de programmation Python [van Rossum, 1995] et Fortran ont été utilisés. Code _Aster est capable d'exécuter du code Python fournissant un environnement intégré pour le FOM et la ROM. Le modèle d'ordre réduit est entièrement implémenté en Python/Fortran, ce qui conduit à une programmation très flexible, Le code_Aster est capable de fournir les informations nécessaires pour effectuer la construction OFFline des ROMs et pour effectuer les solutions FOM utilisées comme référence, 1989.

, avec non linéarités de grand déplacement et contact frottant qui est le problème physique pour lequel les modèles d'ordre réduit (ROM) sont développés et étudiés dans les chapitres suivants. Premièrement, la forme "l'intégrale" ou "faible" du problème physique, proprice à la discrétisation, est obtenue à partir de sa "forme différentielle" ou "forte". Ensuite, avec la méthode des éléments finis (FEM) la formulation continue est discrétisée et le modèle d'haute fidelité (FOM) de la structure est défini. Le mouvement de la structure est représenté comme la somme d'un déplacement statique induit par la rotation, Chapitre 1: Équations du mouvement de structures nonlinéaires en rotation Ce premier chapitre fournit les bases théoriques pour résoudre la dynamique de structures tournantes

F. Le and . Défini, dans ce chapitre fournira la solution de référence des modèles d'ordre réduit (ROM) développés plus tard

, avec non linéarités de type géométrique et de contact frottant s'écrit, Mü p +, en fonction de la vitesse de rotation, ?. Les vecteurs u p ,u p etü p représentent les déplacements, vitesses et accélérations physiques des noeuds de la structure, 2009.

. Stepc,

, Phase hors ligne: construction de la base des forces non linéaires La base non linéaire utilisée pour approximer les forces non linéaires FOM, ? f , est calculée par une procédure POD dont la base est calculée par une SVD

. Comme-indiqué-dans-l'eqn, 75), les forces non linéaires sont collectées pour un nombre donné de snapshots qui représentent un ensemble de déplacements caractéristiques dans la réponse, Ensuite, pour chaque instant, les forces non linéaires associées sont évaluées