Model reduction to spectral submanifolds and forced-response calculation in high-dimensional mechanical systems

Journal article (2020)

Authors

Sten Ponsioen ETH Zürich
S. Jain ETH Zürich
George Haller ETH Zürich
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Model-order reduction Spectral submanifolds Forced-response curves
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Published Date

2020

Language

English

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Abstract

We show how spectral submanifold (SSM) theory can be used to extract forced-response curves without any numerical simulation in high-degree-of-freedom, periodically forced mechanical systems. We use multivariate recurrence relations to construct the SSMs, achieving a major speed-up relative to earlier autonomous SSM algorithms. The increase in computational efficiency promises to close the current gap between studying lower-dimensional academic examples and analyzing larger systems obtained from finite-element modeling, as we illustrate on two different discretized damped-forced beam models. Using the exact reduction procedure via SSMs for obtaining forced response curves, we further demonstrate speed gains of several orders in magnitude relative to the available state-of-the-art continuation packages, while retaining accuracy.