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

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 manifol

SUBMITTER: Szalai R 

PROVIDER: S-EPMC5493940 | biostudies-literature | 2017 Jun

REPOSITORIES: biostudies-literature