Exact nonlinear model reduction for a von Kármán beam

Slow-fast decomposition and spectral submanifolds

Journal article (2018)

Authors

S. Jain ETH Zürich
Paolo Tiso ETH Zürich
G. Haller ETH Zürich
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Published Date

2018

Language

English

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Abstract

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Kármán beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow manifold in the full system which attracts solutions at rates faster than typical rates within the manifold. An SSM, the smoothest nonlinear continuation of a linear modal subspace, is then used to further reduce the beam equations within the slow manifold. This two-stage, mathematically exact procedure results in a drastic reduction of the finite-element beam model to a one-degree-of freedom nonlinear oscillator. We also introduce the technique of spectral quotient analysis, which gives the number of modes relevant for reduction as output rather than input to the reduction process.