Méthode Asymptotique Numérique Et Techniques de Réduction de Modèles
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Les travaux présentés dans ce Livre concernent l'étude de vibration des plaques minces amorties ayant des non linéarités de type géométrique. Nous avons considéré la théorie de von Kármán et un amortissement de type Rayleigh. La méthode de la balance harmonique est utilisée pour transformer le problème dynamique initial en un problème non linéaire algébrique équivalent. Ce dernier problème est transformé en un ensemble de problèmes linéaires en utilisant la Méthode Asymptotique Numérique. Cette dernière méthode nous a permis de trouver une grande partie de la courbe solution avec seulement quelques inversions de matrices. Cependant, l'augmentation du nombre d'harmoniques accroît la dimension du problème, ce qui conduit à une augmentation du temps de calcul. Pour remédier à cette difficulté, nous avons proposé des techniques de réduction de modèle. Ces méthodes consistent à projeter le système à résoudre sur une base de dimension réduite et obtenir ainsi des problèmes de petite dimension. Les procédures de réduction utilisées donnent des résultats dont la qualité est comparable à celle trouvée par un calcul complet sans réduction.
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