Nonlinear dynamical analysis for coupled fluid-structure systems

International audienceThe present research concerns the numerical dynamical analysis in elasto-acoustics, taking into account the geometrical non-linearities induced by the large displacements/deformations of the structure and assuming the internal acoustic fluid occupying an internal cavity coupled to the structure to remain in a linear range of vibration. More particularly, the modeling includes sloshing and capillarity effects on the free surface. A numerical application is presented

Analyse d'une expérimentation exhibant une instabilité dans un liquide avec un modèle réduit non linéaire fluide-structure

National audienceCet article propose de revisiter et d’expliquer, au travers d’un modèle réduit numérique fluide-structure, une observation expérimentale d’un phénomène de résonance de la surface libre d’un liquide dans un réservoir cylindrique. Le système expérimental a été simulé par un modèle numérique du cylindre élastique en présence de non-linéarités géométriques, partiellement rempli d’un liquide acoustique prenant en compte les effets de ballottement. Les résultats obtenus montrent qu’une excitation inattendue de grande amplitude des modes de ballottement a lieu lorsque la structure est excitée sur certaines de ses résonances

Application au désaccordage des roues aubagées.Dynamique des structures tournantes à symétrie cyclique en présence d'incertitudes aléatoires

The objective of this research is to propose new probabilistic methodologies for the dynamic analysis of themistuning of rotating structures with cyclic symmetry in the low frequency range. The structure under consideration is a bladeddisk. Firstly, a recent nonparametric probabilistic model is used for constructing a direct probabilistic approach, allowingthe dynamic amplification of the forced response on blades induced by mistuning to be analyzed. Particularly, such aprobabilistic approach allows the blade-eigenfrequencies mistuning and the blade-modal-shape mistuning to be modeled withcoherence. Secondly, an inverse probabilistic approach, based on an identification method of the dispersion parameterscontrolling the nonparametric probability model, is constructed in order to define the blade tolerances yielding a givenprobability level of the dynamic amplification of the forced response. Finally, both methodologies are numerically applied on asimple case and on a complex structure. The mistuned forced response obtained with the nonparametric probabilistic model andwith the parametric probabilistic approach traditionally used in the mistuning context are compared. In addition, the inverseprobabilistic approach allows the blade tolerances to be optimized in order to reduce the amplifications of the forcedresponse. The analysis of these results validate the relevance of the proposed methodologies.L'objet de ce travail de recherche est de proposer de nouvelles méthodologies probabilistes pour l'analysedynamique basses fréquences du désaccordage des structures tournantes à symétrie cyclique. La classe de structure étudiée estla roue aubagée. Tout d'abord, un modèle probabiliste non paramétrique récent est utilisé pour construire une approcheprobabiliste directe, permettant d'analyser l'amplification dynamique de la réponse forcée des aubes, induite par ledésaccordage. En particulier, une telle approche permet de modéliser de manière cohérente le désaccordage en fréquences desaubes et le désaccordage en modes des aubes. Ensuite, une approche probabiliste inverse, reposant sur une méthoded'identification des paramètres de dispersion du modèle probabiliste non paramétrique, est construite afin de déterminer lestolérances des aubes, conduisant à une probabilité donnée du facteur d'amplification dynamique de la réponse forcée. Enfin, cesméthodologies sont mises en oeuvre numériquement sur un exemple numérique simple et sur un modèle complexe de roue aubagée.Les réponses forcées désaccordées obtenues par le modèle probabiliste non paramétrique et par le modèle probabilisteparamétrique classiquement utilisé pour la problématique du désaccordage sont comparées. Par ailleurs, la méthodologie duproblème inverse permet d'optimiser les tolérances de l'aube pour réduire l'amplification de la réponse forcée. L'analyse desrésultats valide la pertinence des méthodologies proposées

Désaccordage des roues aubagées - concepts technologiques et modélisation.

Université d'été de l'inspection générale de mathématiques, Internat d'excellence de Sourdan, 24 août 2011

Optimisation robuste en dynamique et vibro-acoustique avec modèles numériques incertains.

Journée d'étude " Dynamique ", Fédération Francilienne de Mécanique, ENSTA, 21 janvier 201

Uncertainty Quantification for Nonlinear Structural Dynamical Systems

International audienc

Robust design optimization with respect to model and data uncertainties in computational mechanics

International audienceIn this paper, a probabilistic approach is proposed to solve the robust design optimization problem of complex dynamical systems not only with respect to system parameters uncertainties but also to model uncertainties. The possible designs are represented by a numerical finite element model whose parameters belong to an admissible set of design parameters. A recent nonparametric probabilistic model of uncertainties is used for taking into account model uncertainties and data uncertainties. The robust design optimization problem is formulated as a multi-objective optimization problem which consist to minimize a cost function including a target with respect to an admissible set of design parameters. The theory is presented followed by a numerical application

Specifying manufacturing tolerances for a given amplification factor: a nonparametric probabilistic methodology

International audienceIt is known that the forced response ofmistuned bladed disks can strongly be amplified in comparison with the forced response of the tuned system. The random character of mistuning thus requires the construction of probabilisticsmodels of randomuncertainties. This paper presents a nonparametric probabilisticmodel of random uncertainties which is adapted to the problematics of the blade mistuning. This nonparametric approach allows all the uncertainties yielding mistuning (manufacturing tolerances, dispersion of materials) to be taken into account and includes also the uncertainties due to the modeling errors. This new probabilistic model takes into account both the mistuning of the blade eigenfrequencies and the blade modal shapes. The first point concerns the construction of this nonparametric approach in order to perform a mistuning analysis. The second part is devoted to the inverse problem associated with the manufacturing tolerances. A relationship between the manufacturing tolerances and the level of mistuning is also constructed

Uncertainty modeling for robust design optimization in computational mechanics

In computational mechanics of complex dynamical systems, robust design consists in finding designs of mechanical systems by solving nonlinear constrained optimization problems using numerical models which are little sensitive to uncertainties in the vicinity of the design point. All the published works in robust design concern data uncertainties and not model uncertainties. In the present work, a probabilistic methodology is proposed to solve the robust design optimization problem not only with respect to data uncertainties but also with respect to model uncertainties in the context of dynamical systems. The possible designs are represented by a numerical finite element model whose parameters belong to an admissible set of design variables. The nonparametric model of random uncertainties is used for taking into account model uncertainties and data uncertainties

Uncertainty modeling for robust design optimization in computational mechanics

In computational mechanics of complex dynamical systems, robust design consists in finding designs of mechanical systems by solving nonlinear constrained optimization problems using numerical models which are little sensitive to uncertainties in the vicinity of the design point. All the published works in robust design concern data uncertainties and not model uncertainties. In the present work, a probabilistic methodology is proposed to solve the robust design optimization problem not only with respect to data uncertainties but also with respect to model uncertainties in the context of dynamical systems. The possible designs are represented by a numerical finite element model whose parameters belong to an admissible set of design variables. The nonparametric model of random uncertainties is used for taking into account model uncertainties and data uncertainties