Reduced order modeling of nonlinear structural systems using nonlinear normal modes and invariant manifolds

Construction de modèles réduits de systèmes non linéaires par modes non linéaires et variétés invariantes

Eric Pesheck (1)

1 Vibrations and acoustics laboratory

In many applications, it is advantageous to achieve a thorough understanding of the dynamics of a complex structure. These structures may take many forms, including rotorcraft, buildings, bridges, vehicles, and aircraft. Modern design tools, such as Finite Element Analysis, have greatly expanded the modeling detail available for such structures. However, these techniques are limited in their abilities, especially when the structure dynamics enter a nonlinear regime. This limitation is often countered by sacrificing either time | through a large, expensive computer model, or accuracy | through the elimination of possibly significant in uences. As it is of continual interest to expand the performance envelope of such structures, they are becoming lighter, more exible and, consequently, more nonlinear. This trend points out a need for effcient, analytically rigorous, widely applicable analysis techniques for nonlinear structural systems. The primary goal of this dissertation is to address this need through the further development and implementation of model reduction through nonlinear normal modes. This work extends the invariant manifold approach, with the primary goal of obtaining accurate reduced order models of nonlinear structural systems.

Dans de nombreux domaines, il est primordial de bien comprendre la dynamique de structures complexes. Les outils numériques modernes, comme la méthode des éléments finis, ont grandement amélioré le niveau de modélisation mais sont souvent limitées au cadre linéaire. Pourtant l'évolution des structures, plus légères et plus flexibles, vers un comportement non linéaire suggère la mise en œuvre de méthodes adaptées, couplant rapidité et précision. C'est dans cet esprit que ce travail de recherche développe une méthode de réduction de modèles non linéaires basée sur les variétés invariantes.

Mots clés: Nonlinear normal modes; reduced-order model; invariant manifold

Mots clés: mode non linéaire; réduction de modèle; variété invariante

Domaines: Mécanique [physics.med-ph]

Eric Pesheck. Reduced order modeling of nonlinear structural systems using nonlinear normal modes and invariant manifolds. Mechanics [physics.med-ph]. University of Michigan, 2000. English. ⟨NNT : ⟩. ⟨tel-00361026⟩