On the extension of global vibration modes with Ritz-vectors needed for local effects

  • Karim Sherif
  • Wolfgang Witteveen
  • Hans Irschik
  • Helmut Holl
  • Karl Mayrhofer
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


In Ritz-vector based model reduction techniques, the problem-oriented combination of different kind of Ritz-vectors may significantly influence the quality of the reduction base. It is common to combine global vibration modes with Ritz-vectors, which are necessary to characterize local effects. Even if the global vibration modes and the local Ritz-vectors may be separately orthogonal with respect to the mass and stiffness matrix, the combined reduced system is usually not decoupled. By using common decoupling strategies the separation of the two mode groups is lost. In this contribution, we will present a transformation procedure in order to obtain a combined and decoupled mode base, which is still separable into global vibration modes and Ritz-vectors due to local effects. Due to the clear separation of the two kinds of modes it is possible to give a frequency limit for the relevance of the inertia effects of the second mode group. In case the inertia effects of the second mode group may be neglected, the dimension of the differential equation of motion can be reduced once more again. At our theoretical considerations, an example is presented for the sake of illustration.


Contact Problem Component Mode Reduction Base Nonlinear Spring AIAA Journal 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Karim Sherif
    • 1
  • Wolfgang Witteveen
    • 2
  • Hans Irschik
    • 3
  • Helmut Holl
    • 3
  • Karl Mayrhofer
    • 4
  1. 1.Linz Center of Mechatronics GmbHLinzAustria
  2. 2.University of Applied Science - WelsWelsAustria
  3. 3.Johannes Kepler University - LinzLinzAustria
  4. 4.Siemens VAI Metals Technologies GmbHLinzAustria

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