## Abstract

This work reports new approaches for order reduction of nonlinear systems with time periodic coefficients. First, the equations of motion are transformed using the Lyapunov-Floquet (LF) transformation, which makes the linear part of new set of equations time invariant. At this point, either linear or nonlinear order reduction methodologies can be applied. The linear order reduction technique is based on classical technique of aggregation and nonlinear technique is based on 'Time periodic invariant manifold theory'. These methods do not assume the parametric excitation term to be small. The nonlinear order reduction technique yields superior results. An example of two degrees of freedom system representing a magnetic bearing is included to show the practical implementation of these methods. The conditions when order reduction is not possible are also discussed.

Original language | English (US) |
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Pages | 2041-2048 |

Number of pages | 8 |

State | Published - 2003 |

Event | Proceedings of the Tenth International Congress on Sound and Vibration - Stockholm, Sweden Duration: Jul 7 2003 → Jul 10 2003 |

### Other

Other | Proceedings of the Tenth International Congress on Sound and Vibration |
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Country/Territory | Sweden |

City | Stockholm |

Period | 7/7/03 → 7/10/03 |

## ASJC Scopus subject areas

- Engineering(all)