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Variational characterization of real eigenvalues in linear viscoelastic oscillators
Publikationstyp
Journal Article
Date Issued
2018-10-01
Sprache
English
Author(s)
Voß, Heinrich
Institut
TORE-URI
Volume
23
Issue
10
Start Page
1377
End Page
1388
Citation
Mathematics and Mechanics of Solids 10 (23): 1377-1388 (2018-10-01)
Publisher DOI
Scopus ID
This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.