The Derivatives of Repeated Eigenvalues and Their Associated Eigenvectors

[+] Author and Article Information
M. I. Friswell

Department of Mechanical Engineering, University of Wales Swansea, Swansea SA2 8PP, United Kingdom

J. Vib. Acoust 118(3), 390-397 (Jul 01, 1996) (8 pages) doi:10.1115/1.2888195 History: Received April 01, 1994; Online February 26, 2008


This paper considers the calculation of eigenvalue and eigenvector derivatives when the eigenvalues are repeated. An extension to Nelson’s method is used to calculate the first order derivatives of eigenvectors when the derivatives of the associated eigenvalues are also equal. The continuity of the eigenvalues and eigenvectors is discussed, and the discontinuities in the eigenvectors, when they are regarded as functions of two or more design parameters, is demonstrated. The validity of Taylor series for the eigenvalues and eigenvectors is examined and the use of these series critically assessed.

Copyright © 1996 by The American Society of Mechanical Engineers
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