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. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.

32 pages, 4 figures

References in corpus (2)

• Experimental continuation of periodic orbits through a fold
• A spectral characterization of nonlinear normal modes

Cited by in corpus (15)

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