Multiparameter Quadratic Eigenproblems

[+] Author and Article Information
D. L. Taylor, T. R. Kane

Department of Applied Mechanics, Stanford University, Stanford, Calif.

J. Appl. Mech 42(2), 478-483 (Jun 01, 1975) (6 pages) doi:10.1115/1.3423602 History: Received August 01, 1974; Online July 12, 2010


This paper contains an analytical theory for the study of the eigensystem of a multi-parameter quadratic eigenproblem. Previous work in this general area has focused mainly on first order eigenproblems. In the present work, eigenvalues and eigenvectors are expressed in the form of infinite series in which parameters entering the elements of various matrices play the roles of independent variables, and it is shown how the coefficients may be evaluated. The methods of derivation are given in sufficient detail to allow extension to either higher derivatives or higher order eigenproblems. Among the results presented are formulae for the second derivatives of eigenvectors, which have not been presented previously. Formulae applicable to special cases of first order eigenproblems are given also.

Copyright © 1975 by ASME
Topics: Eigenvalues
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