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Some recent results on MDGKN‐systems
Author(s) -
Hagedorn P.,
Heffel E.,
Lancaster P.,
Müller P.C.,
Kapuria S.
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300270
Subject(s) - eigenvalues and eigenvectors , matrix (chemical analysis) , variety (cybernetics) , equations of motion , type (biology) , vibration , damping matrix , mathematics , gyroscope , classical mechanics , physics , engineering , finite element method , stiffness matrix , structural engineering , materials science , ecology , statistics , quantum mechanics , composite material , biology
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.