# Exact Nonlinear Model Reduction for a von Karman beam: Slow-Fast Decomposition and Spectral Submanifolds

arXiv: https://arxiv.org/abs/1703.03001 · HTML: https://mlsanity.com/paper/1703.03001/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2017.

## Built on by (most cited first, 2 of 2)

- [Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds](https://mlsanity.com/paper/2201.04976/) (2022)
- [Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems](https://mlsanity.com/paper/2110.01929/) (2021)

## Abstract (arXiv)

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Karman 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.