Nonlinear system identification of the dynamics of a vibro-impact beam

H. Chen, M. Kurt, Y. S. Lee, D. M. McFarland, L. A. Bergman, A. F. Vakakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We study the dynamics of a cantilever beam with two rigid stops of certain clearances by performing nonlinear system identification (NSI) based on the correspondence between analytical and empirical slow-flow dynamics. First, we perform empirical mode decomposition (EMD) on the acceleration responses measured at ten, almost evenly-spaced, spanwise positions along the beam leading to sets of intrinsic modal oscillators governing the vibroimpact dynamics at different time scales. In particular, the EMD analysis can separate any nonsmooth effects caused by vibro-impacts of the beam and the rigid stops from the smooth (elastodynamic) response, so that nonlinear modal interactions caused by vibro-impacts can be explored only with the remaining smooth components. Then, we establish nonlinear interaction models (NIMs) for the respective intrinsic modal oscillators, where the NIMs invoke slowly-varying forcing amplitudes that can be computed from empirical slow-flows. By comparing the spatio-temporal variations of the nonlinear modal interactions for the vibro-impact beam and those of the underlying linear model (i.e., the beam with no rigid constraints), we demonstrate that vibro-impacts significantly influence the lower frequency modes introducing spatial modal distortions, whereas the higher frequency modes tend to retain their linear dynamics in between impacts.

Original languageEnglish (US)
Title of host publicationTopics in Nonlinear Dynamics - Proceedings of the 30th IMAC, A Conference on Structural Dynamics, 2012
Number of pages13
StatePublished - 2012
Event30th IMAC, A Conference on Structural Dynamics, 2012 - Jacksonville, FL, United States
Duration: Jan 30 2012Feb 2 2012

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652


Other30th IMAC, A Conference on Structural Dynamics, 2012
Country/TerritoryUnited States
CityJacksonville, FL


  • Empirical mode decomposition
  • Intrinsic mode oscillation
  • Nonlinear interaction model
  • Nonlinear system identification
  • Vibro-impact beam

ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mechanics
  • Mechanical Engineering


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