Nonlinear Dynamics

, Volume 51, Issue 4, pp 529–539 | Cite as

Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts

  • Frank Schilder
  • Jan Rübel
  • Jens Starke
  • Hinke M. Osinga
  • Bernd Krauskopf
  • Mizuho Inagaki
Original Paper

Abstract

We present a numerical method for the investigation of quasiperiodic oscillations in applications modeled by systems of ordinary differential equations. We focus on systems with parts that have a significant rotational speed. An important element of our approach is that it allows us to verify whether one can neglect gravitational forces after a change of coordinates into a corotating frame. Specifically, we show that this leads to a dramatic reduction of computational effort. As a practical example, we study a turbocharger model for which we give a thorough comparison of results for a model with and without the inclusion of gravitational forces.

Keywords

Invariant tori Noise Oil-whirl Quasiperiodic oscillation Rotordynamics Turbocharger Unbalance oscillation Vibration 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Frank Schilder
    • 1
  • Jan Rübel
    • 2
  • Jens Starke
    • 3
  • Hinke M. Osinga
    • 1
  • Bernd Krauskopf
    • 1
  • Mizuho Inagaki
    • 4
  1. 1.Bristol Center for Applied Nonlinear Mathematics, Department of Engineering MathematicsUniversity of BristolBristolUK
  2. 2.Interdisciplinary Center for Scientific Computing (IWR) and Institute of Applied MathematicsUniversity of HeidelbergHeidelbergGermany
  3. 3.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark
  4. 4.Toyota Central Research and Development Laboratories, Inc.NagakuteJapan

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