Exact nonlinear model reduction for a von Kármán beam: Slow-fast decomposition and spectral submanifolds. (9th June 2018)

• Record Type: Journal Article
• Authors: Jain, Shobhit; Tiso, Paolo; Haller, George
• Is Part Of: Journal of sound and vibration. Volume 423(2018)
• Page Start: 195
• Page End: 211
• Publication Date: 2018-06-09
• Subjects: Model order reduction (MOR) -- von Kármán beam -- Spectral submanifolds (SSM) -- Slow-fast decomposition (SFD); Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2018.01.049
• Languages: English
• ISSNs: 0022-460X

Abstract

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.