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Title: An iterative substructuring approach to the calculation of eigensolution and eigensensitivity
Authors: Weng, S
Xia, Y 
Xu, YL 
Zhu, HP
Issue Date: 4-Jul-2011
Source: Journal of sound and vibration, July 2011, v. 330, no. 14, p. 3368-3380
Abstract: The eigensolutions and associated eigensensitivities of an analytical model are usually calculated at the global structure level, which is time-consuming or even prohibitive for large-scale structures. Several substructuring approaches have been proposed that divide the global structure into some manageable substructures and assemble parts of the eigensolutions and eigensensitivities of the substructures to recover those of the global structure. However, these approaches are not usually accurate, as only the lowest eigensolutions and eigensensitivities are retained and the higher modes are excluded. In this paper, a new iterative substructuring method is proposed to accurately obtain the eigensolutions and eigensensitivities of structures. With this new approach, the contribution of the higher modes to the reduced eigenequation is retained as a residual flexibility matrix in an iterated form, which allows the eigenvalues and eigenvalue derivatives to be obtained from the previous results. The eigenvectors and their derivative matrices can be calculated from a reduced eigenequation directly without iteration. Upon convergence, the iterative scheme reproduces the eigensolutions and eigensensitivities of the original structure exactly. The computational efficiency and numerical accuracy of the proposed method are verified by the applications to a cantilever plate structure and an actual super-tall structure.
Keywords: Computational efficiency
Iterative methods
Mathematical models
Numerical methods
Publisher: Academic Press
Journal: Journal of sound and vibration 
ISSN: 0022-460X
EISSN: 1095-8568
Rights: © 2011 Elsevier Ltd. All rights reserved.
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Sound and Vibration. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Sound and Vibration, Vol 330, Issue 14, (4 July 2011) DOI 10.1016/j.jsv.2011.02.001.
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