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Reduktion analytischer Impedanzfunktionen auf lineare Matrizenpolynome am Beispiel der dynamischen Seilsteifigkeit
Citation Link: https://doi.org/10.15480/882.351
Other Titles
Reduction of analytic impedance function to linear matrix polynomial - exemplified for dynamic cable stiffness
Publikationstyp
Journal Article
Date Issued
1992-06
Sprache
German
Author(s)
Starossek, Uwe
Institut
TORE-DOI
Journal
Volume
62
Issue
6
Start Page
428
End Page
434
Citation
Archive of applied mechanics 62 (1992) 6, pp 428-34
Publisher DOI
Publisher
Springer-Verlag
For the dynamic stiffness of a sagging cable subject to harmonic boundary displacements, frequency-dependent closed-form analytic functions can be derived from the corresponding continuum equations. By consideration of such functions in stiffness matrices of composed systems, however, these matrices become frequency-dependent, too a troublesome fact, especially with regard to the eigenvalue problem which becomes nonlinear. In this paper a method for avoiding such difficulties is described: A complex analytic impedance function is reduced to two constant matrices of any desired dimension. This reduction corresponds to a mathematically performed transition from a continuum to a discrete-coordinate vibrating system. In structural dynamics applications such as for dynamic cable stiffness the two resultant matrices correspond to a static stiffness matrix and a mass matrix. In every case, these matrices can easily be considered within the scope of a linear eigenvalue problem.
DDC Class
620: Ingenieurwissenschaften
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