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

Robert Szalai, David Ehrhardt, George Haller

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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.
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
Publication statusPublished - Jun 2017

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