A sparse preconditioned iterative method for vibration analysis of geometrically mistuned bladed disks

Abstract : In this paper, the Static Mode Compensation method to predict geometrical mistuning effects on the response of bladed disks is reviewed and its limitations are analyzed. This method proved to be effective only for narrow clusters of modes under localized low rank perturbation. A new algorithm is introduced to address its deficiencies that draws on optimal preconditioned methods for generalized eigenvalue problem featuring sparse matrix vector multiplications, being more attractive under limited memory constraints of multi-millon DOF FEM models. The central idea of the SMC is to correct nominal eigenspace using modal acceleration method. It has been extended here by replacing the quasi-static set of modes with inexact solutions of the linear Jacobi-Davidson correction equations. Some heuristic strategies are discussed to lower the computational effort given the block-circulant structure of the nominal system. Numerical experiments on an industrial scale bladed disk model show that this leads to a very competitive tool. Computational performance and accuracy of both methods is compared in two areas of spectrum. The study demonstrates low accuracy of SMC method in the modal interaction zone, while validating efficiency and accuracy of the new algorithmin both areas.
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Soumis le : samedi 21 février 2009 - 20:40:47
Dernière modification le : lundi 6 avril 2009 - 20:53:18
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Vladislav Ganine, Mathias Legrand, Hannah Michalska, Christophe Pierre. A sparse preconditioned iterative method for vibration analysis of geometrically mistuned bladed disks. Computers & Structures, Elsevier, 2009, 87 (5-6), pp.342-354. <10.1016/j.compstruc.2008.12.011>. <hal-00363296>

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