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Free and Forced Vibrations of a Linear Non‐Conservative System with Multiple Eigenvalues
Author(s) -
Kliem W.
Publication year - 1980
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.19800601104
Subject(s) - eigenvalues and eigenvectors , mathematics , constant (computer programming) , work (physics) , vibration , extension (predicate logic) , square (algebra) , linear system , mathematical analysis , mathematical physics , pure mathematics , physics , thermodynamics , quantum mechanics , geometry , computer science , programming language
The paper shows the derivation of the response of a linear system governed by the equation A \documentclass{article}\pagestyle{empty}\begin{document}$ \ddot q $\end{document} + Bq̇ + Cq = Q(t), in which the square matrices A, B and C are real and constant, but not necessary symmetric or positive definite. In addition the special case of multiple eigenvalues with an insufficient number of eigenvectors occurs. The theory is an extension of the work by Wahed and Bishop [1], which is limited to distinct eigenvalues.