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Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

Research output: Contribution to journalArticle

Original languageEnglish
Article number20160759
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2202
Early online date14 Jun 2017
DOIs
DateSubmitted - 7 Oct 2016
DateAccepted/In press - 16 May 2017
DateE-pub ahead of print - 14 Jun 2017
DatePublished (current) - Jun 2017

Abstract

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via the Royal Society at http://rspa.royalsocietypublishing.org/content/473/2202/20160759 . Please refer to any applicable terms of use of the publisher.

    Final published version, 706 KB, PDF document

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  • Supplementary information PDF

    Rights statement: This is the final published version of the article (version of record). It first appeared online via the Royal Society at http://rspa.royalsocietypublishing.org/content/473/2202/20160759. Please refer to any applicable terms of use of the publisher.

    Final published version, 397 KB, PDF document

    Licence: CC BY

  • Supplementary information MAT - Vibration data

    Rights statement: This is the final published version of the article (version of record). It first appeared online via the Royal Society at http://rspa.royalsocietypublishing.org/content/473/2202/20160759. Please refer to any applicable terms of use of the publisher.

    Final published version, 130 KB, application/octet-stream

    Licence: CC BY

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