Stochastic reduced-order model in low frequency dynamics in presence of numerous local elastic modes

Anas Batou (1) , Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

This paper concerns the non usual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the low-frequency range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. The "global elastic modes" and the "local elastic modes" are calculated separately using a new formulation solving two generalized eigenvalue problems. The union of these two families constitutes a basis of the admissible space. Then, the reduced-order model is constructed by projection of the dynamical equation on the global elastic modes. The apparent damping generated in this reduced-order model by the power flow of the mechanical energy from the global modes to the local modes is constructed by a statistical approach. The theory is presented and is validated through an application.

Mots clés: uncertainty quantification; local modes; spatial filtering; reduced order model; ROM; nonparametric probabilistic method; structural dynamics

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]; Vibrations [physics.class-ph]

Anas Batou, Christian Soize. Stochastic reduced-order model in low frequency dynamics in presence of numerous local elastic modes. RASD 2010 - 10th International Conference on Recent Advances in Structural Dynamics, Southampton, 12 - 14 July, 2010, University of Southampton, Jul 2010, Southampton, United Kingdom. pp.1-10. ⟨hal-00692835⟩