TY - JOUR
T1 - A sparse preconditioned iterative method for vibration analysis of geometrically mistuned bladed disks
AU - Ganine, Vladislav
AU - Legrand, Mathias
AU - Michalska, Hannah
AU - Pierre, Christophe
PY - 2009/3
Y1 - 2009/3
N2 - 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 algorithm in both areas.
AB - 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 algorithm in both areas.
KW - Indirect methods
KW - Mistuning
KW - Model reduction
KW - Turbomachinery
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U2 - 10.1016/j.compstruc.2008.12.011
DO - 10.1016/j.compstruc.2008.12.011
M3 - Article
AN - SCOPUS:59849092850
SN - 0045-7949
VL - 87
SP - 342
EP - 354
JO - Computers and Structures
JF - Computers and Structures
IS - 5-6
ER -