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Stability of weakly damped MDGKN-systems: The role of velocity proportional terms

Jekel, Dominic and Hagedorn, Peter (2017):
Stability of weakly damped MDGKN-systems: The role of velocity proportional terms.
97, In: ZAMM - Z. Angew. Math. Mech., (9), John Wiley and Sons, pp. 1128-1135, ISSN 0044-2267, DOI: 10.1002/zamm.201600288,
[Online-Edition: http://onlinelibrary.wiley.com/doi/10.1002/zamm.201600288/fu...],
[Article]

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Abstract

Many problems in mechanical engineering, in the linearized case, can be modeled as a second order system of differential equations of type MDGKN, where the matrices correspond to inertia, damping, gyroscopic, stiffness, and circulatory forces. The latter may lead to self-excited vibrations which in general are unwanted and sometimes dangerous. It is well known that circulatory systems are very sensitive to damping and their stability behavior may strongly depend on the structure of the damping matrix. Moreover, it has been known for a long time, that the addition of (even infinitesimally small) damping may also destabilize such systems. The present note studies in more detail some of the effects of velocity proportional terms on the stability of mechanical systems of this type. The aim is to extend the findings recently presented by HAGEDORN et al. Therefore, the analytically derived stability boundary of an MDGKN-system with two degrees of freedom is analyzed with regard to infinitesimally small, incomplete, and indefinite damping matrices as well as the role of gyroscopic terms and the spacing of the eigenfrequencies.

Item Type: Article
Erschienen: 2017
Creators: Jekel, Dominic and Hagedorn, Peter
Title: Stability of weakly damped MDGKN-systems: The role of velocity proportional terms
Language: English
Abstract:

Many problems in mechanical engineering, in the linearized case, can be modeled as a second order system of differential equations of type MDGKN, where the matrices correspond to inertia, damping, gyroscopic, stiffness, and circulatory forces. The latter may lead to self-excited vibrations which in general are unwanted and sometimes dangerous. It is well known that circulatory systems are very sensitive to damping and their stability behavior may strongly depend on the structure of the damping matrix. Moreover, it has been known for a long time, that the addition of (even infinitesimally small) damping may also destabilize such systems. The present note studies in more detail some of the effects of velocity proportional terms on the stability of mechanical systems of this type. The aim is to extend the findings recently presented by HAGEDORN et al. Therefore, the analytically derived stability boundary of an MDGKN-system with two degrees of freedom is analyzed with regard to infinitesimally small, incomplete, and indefinite damping matrices as well as the role of gyroscopic terms and the spacing of the eigenfrequencies.

Journal or Publication Title: ZAMM - Z. Angew. Math. Mech.
Volume: 97
Number: 9
Publisher: John Wiley and Sons
Uncontrolled Keywords: circulatory system, non-conservative system, damping, stability
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Dynamics and Vibrations
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 27 Oct 2017 08:35
DOI: 10.1002/zamm.201600288
Official URL: http://onlinelibrary.wiley.com/doi/10.1002/zamm.201600288/fu...
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