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Some Recent Results on MDGKN-Systems

Hagedorn, P. and Heffel, Eduard and Lancaster, P. and Müller, P. C. and Kapuria, S. (2013):
Some Recent Results on MDGKN-Systems.
In: Zeitschrift für Angewandte Mathematik und Mechanik - ZAMM, WILEY-VCH, ISSN 1521-4001, [Article]

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Abstract

The linearized equations of motion of finite dimensional autonomous mechanical systems are normally written as a second order system and are of the MDGKN type, where the different n × n matrices have certain characteristic properties. These matrix properties have consequences for the underlying eigenvalue problem. Engineers have developed a good intuitive understanding of such systems, particularly for systems without gyroscopic terms (G-matrix) and circulatory terms (N-matrix, which may lead to self-excited vibrations). A number of important engineering problems in the linearized form are described by this type of equations. It has been known for a long time, that damping (D-matrix) in such systems may either stabilize or destabilize the system depending on the structure of the matrices. Here we present some new results (using a variety of methods of proof) on the influence of the damping terms, which are quite general. Starting from a number of conjectures, they were jointly developed by the authors during recent months.

Item Type: Article
Erschienen: 2013
Creators: Hagedorn, P. and Heffel, Eduard and Lancaster, P. and Müller, P. C. and Kapuria, S.
Title: Some Recent Results on MDGKN-Systems
Language: English
Abstract:

The linearized equations of motion of finite dimensional autonomous mechanical systems are normally written as a second order system and are of the MDGKN type, where the different n × n matrices have certain characteristic properties. These matrix properties have consequences for the underlying eigenvalue problem. Engineers have developed a good intuitive understanding of such systems, particularly for systems without gyroscopic terms (G-matrix) and circulatory terms (N-matrix, which may lead to self-excited vibrations). A number of important engineering problems in the linearized form are described by this type of equations. It has been known for a long time, that damping (D-matrix) in such systems may either stabilize or destabilize the system depending on the structure of the matrices. Here we present some new results (using a variety of methods of proof) on the influence of the damping terms, which are quite general. Starting from a number of conjectures, they were jointly developed by the authors during recent months.

Journal or Publication Title: Zeitschrift für Angewandte Mathematik und Mechanik - ZAMM
Publisher: WILEY-VCH
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)
Zentrale Einrichtungen
Date Deposited: 02 Jun 2014 13:53
Identification Number: doi:10.1002/zamm.201300270
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