Exact nonlinear model reduction for a von Kármán beam: Slow-fast decomposition and spectral submanifolds

Shobhit Jain*, Paolo Tiso, George Haller

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

42 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)195-211
Number of pages17
JournalJournal of Sound and Vibration
Volume423
DOIs
Publication statusPublished - 2018
Externally publishedYes

Funding

We would like to thank Sten Ponsioen and Tiemo Pedergnana for catching typos in an earlier draft of the manuscript. The support of the Air Force Office of Scientific Research , Air Force Material Command , USAF under Award No. FA9550-16-1-0096 is acknowledged.

Keywords

  • Model order reduction (MOR)
  • Slow-fast decomposition (SFD)
  • Spectral submanifolds (SSM)
  • von Kármán beam

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