## Abstract

Nonlinear Normal Modes (NNMs) offer tremendous insight into the dynamic behavior of a nonlinear system, extending many concepts that are familiar in linear modal analysis. Hence there is interest in developing methods to experimentally and numerically determine a system's NNMs for model updating or simply to characterize its dynamic response. Previous experimental work has shown that a mono-harmonic excitation can be used to isolate a system's dynamic response in the neighborhood of a NNM along the main backbones of a system. This work shows that a multi-harmonic excitation is needed to isolate a NNM when well separated linear modes of a structure couple to produce an internal resonance. It is shown that one can tune the multiple harmonics of the input excitation using a plot of the input force versus the response velocity until the area enclosed by the force-velocity curve is minimized. Once an appropriated NNM is measured, one can increase the force level and retune the frequency to obtain a NNM at a higher amplitude or remove the excitation and measure the structure's decay down a NNM backbone. This work explores both methods using simulations and measurements of a nominally-flat clamped-clamped beam excited at a single point with a magnetic force. Numerical simulations are used to validate the method in a well defined environment and to provide comparison with the experimentally measured NNMs. The experimental results seem to produce a good estimate of two NNMs along their backbone and part of an internal resonance branch. Full-field measurements are then used to further explore the couplings between the underlying linear modes along the identified NNMs.

Original language | English (US) |
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Pages (from-to) | 612-633 |

Number of pages | 22 |

Journal | Mechanical Systems and Signal Processing |

Volume | 76-77 |

DOIs | |

State | Published - Aug 1 2016 |

Externally published | Yes |

## Keywords

- Continuous-scan laser Doppler vibrometry
- Experimental force appropriation
- Nonlinear normal mode

## ASJC Scopus subject areas

- Control and Systems Engineering
- Signal Processing
- Civil and Structural Engineering
- Aerospace Engineering
- Mechanical Engineering
- Computer Science Applications