Archive of Applied Mechanics

, Volume 88, Issue 4, pp 563–571 | Cite as

The remarkable structure of the mode shapes and eigenforces of a special multibody oscillator

  • Wolfgang E. Weber
  • Peter C. Müller
  • Bernd Anders


This contribution deals with Mikota’s oscillator, a linear vibration chain with arbitrary n degrees of freedom. Of special interest are both the left- and right-eigenvectors of the undamped system. Investigating the first two right-eigenvectors leads to a conjecture concerning the general structure of the remaining \(n-2\) right-eigenvectors. This general structure is proven, and an analytical expression is found which provides an efficient possibility to calculate all left- and right-eigenvectors in a successive manner. Additionally, it is revealed that the mode shapes of this special vibration chain are (partly) orthogonal to each other with respect to the standard scalar product.


Eigenfrequency Eigenvalue Mode shape Mikota Multibody dynamics 

Mathematics Subject Classification (2000)

15A18 33C45 37F10 37K20 74H05 74H25 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Wolfgang E. Weber
    • 1
  • Peter C. Müller
    • 2
  • Bernd Anders
    • 3
  1. 1.Helmut-Schmidt-University/University of the Federal Armed ForcesHamburgGermany
  2. 2.Safety Control EngineeringUniversity of WuppertalWuppertalGermany
  3. 3.WuppertalGermany

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