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Matrix analysis of coupled damped vibrations: two degree-of-freedom analytic solution
KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
2007 (English)In: International journal of pure and applied mathematics, ISSN 1311-8080, E-ISSN 1314-3395, Vol. 36, 115-146 p.Article in journal (Refereed) Published
Abstract [en]

The linear coupled damped free oscillator problem is solved bymeans of matrix analysis. The solution can be written by means of exponentialsof time evolution matrices multiplied by time. These time evolution matricesare determined as the solutions of quadratic matrix equations. The intricaciesof non-proportional damping become particularly clear in this treatment. Forthe two degree-of-freedom problem an explicit analytic solution is given in termsof a root of a cubic equation. The existence of an algebraically simpler specialcase (other than proportional damping) is pointed out.

Place, publisher, year, edition, pages
2007. Vol. 36, 115-146 p.
Keyword [en]
trix analysis, coupled damped vibrations, oscillations, analytic solution, two degree-of-freedom
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:kth:diva-48061OAI: oai:DiVA.org:kth-48061DiVA: diva2:456730
Note
QC 20111116Available from: 2011-11-15 Created: 2011-11-15 Last updated: 2017-12-08Bibliographically approved

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http://www.ijpam.eu/contents/2007-36-1/10/10.pdf

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