Analyse modale pour les coques minces en révolution

Abstract : The subject of this thesis is the study of the Koiter operator for thin shells with respect to their thickness. Here we consider only the case of axisymmetric and clamped thin shells. The Koiter operator is the sum of a membrane operator which does not depend of the thickness and a bending operator. The spectrum of the Koiter operator is discrete whereas the one of the membrane operator contains essential spectrum. Using the axial symmetry of the problem, we decompose the operators towards the angular frequency k. In a constructive way we are looking for a solution of the eigenvalue problem as a formal power series in the inverse of k. Therefore we obtain a formal reduction theorem which brings us to the study of a scalar problem. Then we focus on the case of a cylindrical shell and we construct quasimodes cor- responding to the smallest eigenvalues. When we add the bending operator, we select an angular frequency k which depends on the thickness and some boundary layers appear. We also construct quasimodes in this regime. Numerical simulations for the membrane operator and for the underlying Lamé model made with the finite element library Melina have justified our theoritical results.
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https://tel.archives-ouvertes.fr/tel-00541467
Contributor : Marie Beaudouin <>
Submitted on : Thursday, December 2, 2010 - 4:01:11 PM
Last modification on : Friday, November 16, 2018 - 1:31:40 AM
Long-term archiving on : Monday, November 5, 2012 - 11:05:50 AM

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  • HAL Id : tel-00541467, version 1

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Marie Beaudouin. Analyse modale pour les coques minces en révolution. Mathématiques [math]. Université Rennes 1, 2010. Français. ⟨tel-00541467⟩

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