### Abstract

We describe a new method for identifying mechanical systems with strongly nonlinear attachments using measured transient response data. The procedure is motivated by the desire to quantify the degree of nonlinearity of a system, with the ultimate goal of updating a finite-element or other mathematical model to capture the nonlinear effects accurately. Our method relies on the proper orthogonal decomposition to extract proper orthogonal mode shapes (POMs), which are inherently energy dependent, directly from the measured transient response. Using known linear properties, the system’s frequencies are estimated using the Rayleigh quotient and an estimated frequency-energy plot (FEP) is created by them as functions of the system’s mechanical energy. The estimated FEP reveals distinct linear and nonlinear regimes which h are characterized by constant frequency (horizontal lines) and large frequency changes, respectively. The nonlinear regimes also contain spikes that connect different modes and indicate strongly nonlinear modal interactions. The nonlinearity is identified by plotting the estimated frequencies as functions of characteristic displacement and fitting a frequency equation based on the model of the nonlinearity. We demonstrate the method on the response of a cantilevered, model airplane wing with a nonlinear energy sink attached at its free end.

Original language | English (US) |
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Title of host publication | Nonlinear Dynamics - Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018 |

Editors | Gaetan Kerschen |

Publisher | Springer New York LLC |

Pages | 23-25 |

Number of pages | 3 |

ISBN (Print) | 9783319742793 |

DOIs | |

State | Published - Jan 1 2019 |

Event | 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018 - Orlando, United States Duration: Feb 12 2018 → Feb 15 2018 |

### Publication series

Name | Conference Proceedings of the Society for Experimental Mechanics Series |
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Volume | 1 |

ISSN (Print) | 2191-5644 |

ISSN (Electronic) | 2191-5652 |

### Other

Other | 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018 |
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Country | United States |

City | Orlando |

Period | 2/12/18 → 2/15/18 |

### Keywords

- Frequency-energy plot
- Nonlinear energy sink
- Nonlinear normal modes
- Nonlinear system identification
- Proper orthogonal decomposition

### ASJC Scopus subject areas

- Engineering(all)
- Computational Mechanics
- Mechanical Engineering

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## Cite this

*Nonlinear Dynamics - Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018*(pp. 23-25). (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 1). Springer New York LLC. https://doi.org/10.1007/978-3-319-74280-9_3