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Structural Research Series 462PDF


Title:Solution Techniques for Large Eigenvalue Problems in Structural Dynamics
Author(s):Lee, I.W.; Robinson, A.R.
Numerical analysis
Abstract:This study treats the determination of eigenvalues and eigenvectors of large algebraic systems. The methods developed are applicable to finding the natural frequencies and modes of vibration of large structural systems. For distinct eigenvalues the method is an application of the modified Newton-Raphson method that turns out to be more efficient than the standard competing schemes. For close or multiple eigenvalues, the modified Newton-Raphson method is generalizec to form a new process. The entire set of close eigenvalues and their eigenvectors are found at the same time in a two-step procedure. The subspace of the approximate eigenvectors is first projected onto the subspace of the true eigenvectors. If the eigenvalues are multiple, the results of the first stage indicate this fact and the process terminates. If they are merely close, a single rotation in the newly found space solves a small eigenvalue problem and provides the final results for the close set. The procedure for subspace projection can be expressed as a simple extremum problem that generalizes the known extremum property of eigenvectors. Computational effort and convergence are studied in three example problems. The method turns out to be more efficient than subspace iteration.
Issue Date:1979-06
Publisher:University of Illinois Engineering Experiment Station. College of Engineering. University of Illinois at Urbana-Champaign.
Series/Report:Civil Engineering Studies SRS-462
Genre:Technical Report
Sponsor:Office of Naval Research. Department of the Navy.
Contract No. N00014-75-C-0164
Project NR 064-183
Date Available in IDEALS:2009-10-26

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