Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations
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Open access
Date
2017-06Type
- Journal Article
ETH Bibliography
yes
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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. This model identification utilizes Taken’s delay-embedding theorem, as well as a least square fit to the Taylor expansion of the sampling map associated with that embedding. The SSMs are then constructed for the sampling map using the parametrization method for invariant manifolds, which assumes that the manifold is an embedding of, rather than a graph over, a spectral subspace. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000190469Publication status
publishedExternal links
Journal / series
Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesVolume
Pages / Article No.
Publisher
Royal SocietySubject
nonlinear vibrations; model identification; nonlinear normal modes; invariant manifoldsOrganisational unit
03973 - Haller, George / Haller, George
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ETH Bibliography
yes
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