Matrix analysis of coupled damped vibrations: two degree-of-freedom analytic solution
2007 (English)In: International journal of pure and applied mathematics, ISSN 1311-8080, Vol. 36, 115-146 p.Article in journal (Refereed) Published
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.
trix analysis, coupled damped vibrations, oscillations, analytic solution, two degree-of-freedom
IdentifiersURN: urn:nbn:se:kth:diva-48061OAI: oai:DiVA.org:kth-48061DiVA: diva2:456730
QC 201111162011-11-152011-11-152011-11-16Bibliographically approved