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  4. Reduction of dynamic cable stiffness to linear matrix polynomial
 
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Reduction of dynamic cable stiffness to linear matrix polynomial

Citation Link: https://doi.org/10.15480/882.323
Publikationstyp
Journal Article
Date Issued
1993
Sprache
English
Author(s)
Starossek, Uwe 
Institut
Baustatik B-4  
TORE-DOI
10.15480/882.323
TORE-URI
http://tubdok.tub.tuhh.de/handle/11420/325
Journal
Journal of engineering mechanics  
Citation
Journal of Engineering Mechanics, Vol. 119, No. 10, 1993, pp. 2132-2136
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. When considering such functions in stiffness matrices of composed structures, however, these matrices become frequency dependent, too - a troublesome fact, especially in regards to the eigenvalue difficulties is described whereby an analytic dynamic stiffness function is reduced to a linear matrix polynomial; the matrices of this polynomial are of any desired order. The reduction corresponds to a mathematically performed transition from a continuum to a discrete-coordinate vibrating system. In structural dynamic applications (dynamic cable stiffness), the two resultant matrices correspond to a static stiffness matrix and a mass matrix. Beyond the particular problem focused on, the method may be applied to all kinds of analytic impedance functions. In every case, the resultant matrices can easily be considered within the scope of a linear matrix-eigenvalue problem.
DDC Class
620: Ingenieurwissenschaften
Lizenz
http://doku.b.tu-harburg.de/doku/lic_ohne_pod.php
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