Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations
![Thumbnail](/bitstream/handle/20.500.11850/234370/20160759.full.pdf.jpg?sequence=4&isAllowed=y)
Open access
Datum
2017-06Typ
- Journal Article
ETH Bibliographie
yes
Altmetrics
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. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000190469Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesBand
Seiten / Artikelnummer
Verlag
Royal SocietyThema
nonlinear vibrations; model identification; nonlinear normal modes; invariant manifoldsOrganisationseinheit
03973 - Haller, George / Haller, George
ETH Bibliographie
yes
Altmetrics