Comptes Rendus
Eigenmode sensitivity of damped sandwich structures
Comptes Rendus. Mécanique, Volume 342 (2014) no. 12, pp. 700-705.

The modeling of the linear free vibration of a sandwich structure including viscoelastic layers yields a complex nonlinear eigenvalue problem. In this paper, the sensitivity of eigensolutions is computed using a homotopy-based asymptotic numerical method, then a first-order automatic differentiation. The generality of the proposed method enables us to consider any analytical frequency-dependent viscoelastic law in the modeling and the sensitivity computation. Its application potential is demonstrated by computing the sensitivity of eigenmodes, eigenfrequencies and modal loss factors of sandwich beams and plates to various perturbations.

La modélisation des vibrations linéaires libres d'une structure sandwich comportant des couches visco-élastiques conduit à un problème aux valeurs propres non linéaires complexes. Dans cet article, la sensibilité des solutions propres est calculée en utilisant une méthode asymptotique numérique, puis une différentiation automatique d'ordre un. La généralité de la méthode proposée permet de considérer toute loi visco-élastique analytique avec dépendance en fréquence dans la modélisation et le calcul de sensibilité. Son potentiel applicatif est démontré en calculant la sensibilité des valeurs et vecteurs propres, et des facteurs de perte modaux de poutres et plaques sandwich à différentes perturbations.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2014.08.001
Keywords: Vibration, Sensitivity, Sandwich structures, Viscoelastic model, Complex nonlinear eigenvalue solver, Automatic differentiation
Mot clés : Vibration, Sensibilité, Structures sandwich, Modèle viscoélastique, Solveur de problèmes aux valeurs propres complexes, Différentiation automatique

Komlanvi Lampoh 1; Isabelle Charpentier 2; Daya El Mostafa 3

1 Centre des matériaux, Mines ParisTech, 10, rue Henri-Desbruères, BP 87, 91003 Évry cedex, France
2 ICube – Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie, Université de Strasbourg et CNRS, 300, bd Sébastien-Brant, CS 10413, 67412 Illkirch, France
3 Laboratoire d'étude des microstructures et de mécanique des matériaux, UMR 7239, île du Saulcy, 57045 Metz cedex 01, France
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Komlanvi Lampoh; Isabelle Charpentier; Daya El Mostafa. Eigenmode sensitivity of damped sandwich structures. Comptes Rendus. Mécanique, Volume 342 (2014) no. 12, pp. 700-705. doi : 10.1016/j.crme.2014.08.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.08.001/

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