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arXiv · 1610.02252

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

Robert Szalai·David Ehrhardt·George Haller
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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.

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Robert Szalai, David Ehrhardt, George Haller. 2016-10-07. Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations. https://doi.org/10.1098/rspa.2016.0759

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