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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 4/2018

30-11-2017 | Original

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

Authors: Wolfgang E. Weber, Peter C. Müller, Bernd Anders

Published in: Archive of Applied Mechanics | Issue 4/2018

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Abstract

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.
previous article Thermal post-buckling and vibration analysis of a symmetric sandwich beam with clamped and simply supported boundary conditions
next article Nonlinear dynamic analysis of cable-stayed arches under primary resonance of cables

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Metadata
Title
The remarkable structure of the mode shapes and eigenforces of a special multibody oscillator
Authors
Wolfgang E. Weber
Peter C. Müller
Bernd Anders
Publication date
30-11-2017
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 4/2018
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-017-1327-9

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