Modelling of nonlinear modal interactions in the transient dynamics of an elastic rod with an essentially nonlinear attachment

S. Tsakirtzis, Y. S. Lee, A. F. Vakakis, L. A. Bergman, D. M. McFarland

Research output: Contribution to journalArticle

Abstract

We perform system identification and modelling of the strongly nonlinear modal interactions in a system composed of a linear elastic rod with an essentially nonlinear attachment at its end. Our method is based on slow/fast decomposition of the transient dynamics of the system, combined with empirical mode decomposition (EMD) and Hilbert transforms. The derived reduced order models (ROMs) are in the form of sets of uncoupled linear oscillators (termed intrinsic modal oscillators - IMOs), each corresponding to a basic frequency of the dynamical interaction and forced by transient excitations that represent the nonlinear modal interactions between the rod and the attachment at each of these basic frequencies. A main advantage of our proposed technique is that it is nonparametric and multi-scale, so it is applicable to a broad range of linear as well as nonlinear dynamical systems. Moreover, it is computationally tractable and conceptually meaningful, and it leads to reduced order models of rather simple form that fully capture the basic strongly nonlinear resonant interactions between the subsystems of the problem.

Original languageEnglish (US)
Pages (from-to)2617-2633
Number of pages17
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume15
Issue number9
DOIs
StatePublished - Sep 1 2010

Fingerprint

Elastic Rods
Transient Dynamics
Decomposition
Nonlinear dynamical systems
Reduced Order Model
Interaction
Modeling
Identification (control systems)
Decompose
Linear Dynamical Systems
Hilbert Transform
Nonlinear Dynamical Systems
System Identification
System Modeling
Subsystem
Excitation
Range of data
Form

Keywords

  • Essential nonlinearity
  • Nonlinear modal interactions
  • System identification

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Modelling of nonlinear modal interactions in the transient dynamics of an elastic rod with an essentially nonlinear attachment. / Tsakirtzis, S.; Lee, Y. S.; Vakakis, A. F.; Bergman, L. A.; McFarland, D. M.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 9, 01.09.2010, p. 2617-2633.

Research output: Contribution to journalArticle

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AU - McFarland, D. M.

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