### Abstract

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 language | English (US) |
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Title of host publication | Topics in Nonlinear Dynamics - Proceedings of the 30th IMAC, A Conference on Structural Dynamics, 2012 |

Pages | 287-299 |

Number of pages | 13 |

DOIs | |

State | Published - Jun 6 2012 |

Event | 30th IMAC, A Conference on Structural Dynamics, 2012 - Jacksonville, FL, United States Duration: Jan 30 2012 → Feb 2 2012 |

### Publication series

Name | Conference Proceedings of the Society for Experimental Mechanics Series |
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Volume | 3 |

ISSN (Print) | 2191-5644 |

ISSN (Electronic) | 2191-5652 |

### Other

Other | 30th IMAC, A Conference on Structural Dynamics, 2012 |
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Country | United States |

City | Jacksonville, FL |

Period | 1/30/12 → 2/2/12 |

### Fingerprint

### Keywords

- 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

### Cite this

*Topics in Nonlinear Dynamics - Proceedings of the 30th IMAC, A Conference on Structural Dynamics, 2012*(pp. 287-299). (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 3). https://doi.org/10.1007/978-1-4614-2416-1_23

**Nonlinear system identification of the dynamics of a vibro-impact beam.** / Chen, H.; Kurt, M.; Lee, Y. S.; McFarland, D. M.; Bergman, Lawrence; Vakakis, Alexander F.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Topics in Nonlinear Dynamics - Proceedings of the 30th IMAC, A Conference on Structural Dynamics, 2012.*Conference Proceedings of the Society for Experimental Mechanics Series, vol. 3, pp. 287-299, 30th IMAC, A Conference on Structural Dynamics, 2012, Jacksonville, FL, United States, 1/30/12. https://doi.org/10.1007/978-1-4614-2416-1_23

}

TY - GEN

T1 - Nonlinear system identification of the dynamics of a vibro-impact beam

AU - Chen, H.

AU - Kurt, M.

AU - Lee, Y. S.

AU - McFarland, D. M.

AU - Bergman, Lawrence

AU - Vakakis, Alexander F

PY - 2012/6/6

Y1 - 2012/6/6

N2 - 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.

AB - 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.

KW - Empirical mode decomposition

KW - Intrinsic mode oscillation

KW - Nonlinear interaction model

KW - Nonlinear system identification

KW - Vibro-impact beam

UR - http://www.scopus.com/inward/record.url?scp=84861737748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861737748&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-2416-1_23

DO - 10.1007/978-1-4614-2416-1_23

M3 - Conference contribution

AN - SCOPUS:84861737748

SN - 9781461424154

T3 - Conference Proceedings of the Society for Experimental Mechanics Series

SP - 287

EP - 299

BT - Topics in Nonlinear Dynamics - Proceedings of the 30th IMAC, A Conference on Structural Dynamics, 2012

ER -