Some recent results on MDGKN‐systems. Issue 7 (4th April 2014)

• Record Type: Journal Article
• Authors: Hagedorn, P.; Heffel, E.; Lancaster, P.; Müller, P.C.; Kapuria, S.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 95:Issue 7(2015)
• Page Start: 695
• Page End: 702
• Publication Date: 2014-04-04
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201300270
• Languages: English
• ISSNs: 0044-2267

Abstract

<abstract abstract-type="graphical" xml:lang="en" id="zamm201300270-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p>The linearized equations of motion of finite dimensional autonomous mechanical systems are normally written as a second order system and are of the <bold>MDGKN</bold> type, where the different <italic>n</italic> × <italic>n</italic> 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 (<bold>G</bold>‐matrix) and circulatory terms (<bold>N‐</bold>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 (<bold>D</bold>‐matrix) in such systems may either stabilize or destabilize the system depending on the structure of the matrices. <graphic position="anchor" mimetype="image" xlink:href="ark:/27927/pgj1m9qc5mr" orientation="portrait" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /></p> </abstract>