On the practical use of the lanczos algorithm in finite element applications to vibration and bifurcation problems

Vibration and bifurcation analyses of structures modeled by finite elements yield a linear eigenvalue problem, Kq = λ Bq, where K and B are symmetric matrices of large dimension in practical applications. An interative reduction of the matrix size is attained by the biorthogonal Lanczos algorithm wh...

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Bibliographic Details
Main Authors: Carnoy, E. G., Geradin, M.
Format: Book Chapter
Language:English
Subjects:
Bifurcation Analysis
Eigenvalue Problem
Free Vibration Analysis
Stability Matrix
Stiffness Matrix
Online Access:Get full text
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Summary:Vibration and bifurcation analyses of structures modeled by finite elements yield a linear eigenvalue problem, Kq = λ Bq, where K and B are symmetric matrices of large dimension in practical applications. An interative reduction of the matrix size is attained by the biorthogonal Lanczos algorithm which allows extraction of the lower eigenvalue spectrum. For solving the problem when coincident eigenvalues occur, a restart procedure is implemented so that further iterations can be performed from a new arbitrary vector, yielding thus to modifications in the interaction eigenvalue problem. In addition, practical suggestions for the implementation of the method are made and efficiency of the proposed approach is demonstrated through several numerical examples.
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0062100