### 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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Title of host publication | Proceedings of the Tenth International Congress on Sound and Vibration |

Editors | A. Nilson, H. Boden |

Pages | 2041-2048 |

Number of pages | 8 |

State | Published - 2003 |

Externally published | Yes |

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 |
---|---|

Country | Sweden |

City | Stockholm |

Period | 7/7/03 → 7/10/03 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the Tenth International Congress on Sound and Vibration*(pp. 2041-2048)

**Order reduction of nonlinear time periodic systems.** / Sinha, S. C.; Redkar, Sangram; Butcher, Eric A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Tenth International Congress on Sound and Vibration.*pp. 2041-2048, Proceedings of the Tenth International Congress on Sound and Vibration, Stockholm, Sweden, 7/7/03.

}

TY - GEN

T1 - Order reduction of nonlinear time periodic systems

AU - Sinha, S. C.

AU - Redkar, Sangram

AU - Butcher, Eric A.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=2342425595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2342425595&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:2342425595

SP - 2041

EP - 2048

BT - Proceedings of the Tenth International Congress on Sound and Vibration

A2 - Nilson, A.

A2 - Boden, H.

ER -