Order reduction of nonlinear time periodic systems

S. C. Sinha, Sangram Redkar, Eric A. Butcher

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationProceedings of the Tenth International Congress on Sound and Vibration
EditorsA. Nilson, H. Boden
Pages2041-2048
Number of pages8
StatePublished - 2003
Externally publishedYes
EventProceedings of the Tenth International Congress on Sound and Vibration - Stockholm, Sweden
Duration: Jul 7 2003Jul 10 2003

Other

OtherProceedings of the Tenth International Congress on Sound and Vibration
CountrySweden
CityStockholm
Period7/7/037/10/03

Fingerprint

Time varying systems
Magnetic bearings
Equations of motion
Nonlinear systems
Agglomeration

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Sinha, S. C., Redkar, S., & Butcher, E. A. (2003). Order reduction of nonlinear time periodic systems. In A. Nilson, & H. Boden (Eds.), 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.

Proceedings of the Tenth International Congress on Sound and Vibration. ed. / A. Nilson; H. Boden. 2003. p. 2041-2048.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sinha, SC, Redkar, S & Butcher, EA 2003, Order reduction of nonlinear time periodic systems. in A Nilson & H Boden (eds), 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.
Sinha SC, Redkar S, Butcher EA. Order reduction of nonlinear time periodic systems. In Nilson A, Boden H, editors, Proceedings of the Tenth International Congress on Sound and Vibration. 2003. p. 2041-2048
Sinha, S. C. ; Redkar, Sangram ; Butcher, Eric A. / Order reduction of nonlinear time periodic systems. Proceedings of the Tenth International Congress on Sound and Vibration. editor / A. Nilson ; H. Boden. 2003. pp. 2041-2048
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