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Eigenpath analyses of friction induced vibrations depending on the friction coefficient
Author(s) -
Wagner N.,
Gaul L.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310342
Subject(s) - eigenvalues and eigenvectors , jacobian matrix and determinant , parameterized complexity , subspace topology , invariant subspace , vibration , invariant (physics) , mathematics , friction coefficient , mathematical analysis , control theory (sociology) , computer science , linear subspace , algorithm , pure mathematics , control (management) , physics , acoustics , artificial intelligence , materials science , quantum mechanics , composite material , mathematical physics
The tracking of eigenvalues and eigenvectors for parameterized matrices is of major importance in stability problems. A continuation method for approximating complex eigenpaths of parameter‐dependent matrices is proposed. The presence of a multiple eigenvalue (especially when it is defective) is inherently connected with an ill‐conditioned Jacobian and calls for a special treatment of the approach. Therefore, an invariant subspace is used to circumvent the difficulties of passing possible branch points. The procedure is illustrated by means of an example coming from structural dynamics.