journal article Nov 01, 1982

Dynamic analysis by direct superposition of Ritz vectors

View at Publisher Save 10.1002/eqe.4290100606
Abstract
AbstractThe solution of the eigenvalue problem for large structures is often the most costly phase of a dynamic response analysis. In this paper, the need for the exact solution of this large eigenvalue problem is eliminated. A new algorithm, based on error minimization, is presented for the generation of a sequence of Ritz vectors. These orthogonal vectors are used to reduce the size of the system. Only Ritz vectors with a large participation factor are used in the subsequent mode superposition analysis. In all examples studied, the superposition of Ritz vectors yields more accurate results, with fewer vectors, than if the exact eigenvectors are used. The proposed method not only reduces computer time requirements significantly but provides an error estimation for the dynamic analysis. The approach automatically includes the advantages of the proven numerical techniques of static condensation, Guyan reduction and static correction due to higher mode truncation.
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References
5
[2]
J. M.DickensandE. L.Wilson ‘Numerical method for dynamic substructure analysis’ UCB/EERC‐80/20 1980.
[4]
G. H.Powell „Missing Mass' correction in modal analysis of piping system SMIRT conf. Berlin (1979).
[5]
R. G.SchendlerandR. H.MacNeal ‘Optimum structural representation in aeroelastic analysis’ Aeronautical Systems Division W‐PAEB Ohio U.S.A. ASD‐TR‐61‐680 1962.
Cited By
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The Quadratic Eigenvalue Problem

Françoise Tisseur, Karl Meerbergen · 2001

SIAM Review
Earthquake Engineering & Struct...
Earthquake Engineering & Struct...
Earthquake Engineering & Struct...
Metrics
306
Citations
5
References
Details
Published
Nov 01, 1982
Vol/Issue
10(6)
Pages
813-821
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Cite This Article
Edward L. Wilson, Ming‐Wu Yuan, John M. Dickens (1982). Dynamic analysis by direct superposition of Ritz vectors. Earthquake Engineering & Structural Dynamics, 10(6), 813-821. https://doi.org/10.1002/eqe.4290100606
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