# Experimental Study on Impact Force Identification on a Multi-Storey Tower Structure Using Different Transducers

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

#### 2.1. Single Impact Force Reconstruction

- one impact is being applied at a time,
- structural responses are linear,
- the impact location is known.

**f**is the vector of impact force which is to be reconstructed, and ${\mathbf{T}}_{s}$ is the impulse response matrix, which is a lower triangular toeplitz matrix, given by

**f**through the following penalized least-squares problem:

#### 2.2. Transfer Function

#### 2.3. Impact Force Location

## 3. Experimental Set-Up

## 4. Results and Discussion

#### 4.1. Effect of Regularization

#### 4.2. Establishing the Transfer Function

#### 4.3. Influence of Sensor Type and Location

#### 4.4. Impact Force Location

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 2.**Experimentalset-up showing the multi-storey tower and primary response transducers including (1) laser Doppler vibrometer, (2) laser triangulation sensor, and (3) accelerometer.

**Figure 3.**The effect of regularization in establishing the transfer function and reconstructing the impact force.

**Figure 5.**Impact force reconstruction using transfer functions (TF) established by different hammer tips.

Parameter | Value |
---|---|

Beam length | 2 m |

Beam cross-section | 65.3 × 35 mm${}^{2}$ |

Beam thickness | 2.5 mm |

Lumped masses dimension | 128× 98 × 50 mm${}^{3}$ |

Lumped masses weight | 4 kg |

Lumped masses distances | 250 mm |

Impact Location | Measured Response | ||
---|---|---|---|

Vel. at Level 3 | Acc. at Level 3 | Acc. at Level 8 | |

Level 1 | 0.0219 | 0.2448 | 0.0956 |

Level 2 | 0.0141 | 0.0182 | 0.0682 |

Level 3 | 0.0053 | 0.0551 | 0.0323 |

Level 4 | 0.0140 | 0.0342 | 0.0290 |

Level 5 | 0.1644 | 0.0908 | 0.0157 |

Level 6 | 0.5969 | 0.0223 | 0.0157 |

Level 7 | 0.3779 | 0.0518 | 0.0125 |

Level 8 | 0.7738 | 0.3177 | 0.0108 |

**Table 3.**Accuracy errors of the reconstruction of impact forces applied by rubber tip hammers at different levels.

Hammer Tip | Impact Location | |||||||
---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |

Soft rubber | 0.0974 | 0.0516 | 0.0339 | 0.0576 | 0.0482 | 0.0642 | 0.0563 | 0.0604 |

Medium rubber | 0.0863 | 0.0502 | 0.0590 | 0.0563 | 0.0967 | 0.0902 | 0.1031 | 0.0932 |

Hard rubber | 0.0472 | 0.0239 | 0.0558 | 0.0404 | 0.0558 | 0.3282 | 0.0464 | 0.0421 |

**Table 4.**Accuracy errors of the reconstruction of actual impact force using different traducers at each individual level.

Measured Response | Impact Location | |||||||
---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |

Vel. at level 3 | 0.9581 | 0.9370 | 0.2522 | 0.9395 | 0.9608 | 1.0389 | 0.9821 | 1.0117 |

Acc. at level 3 | 0.9303 | 0.8922 | 0.4225 | 0.8439 | 0.9145 | 0.9701 | 0.9706 | 0.9883 |

Acc. at level 8 | 1.0055 | 0.9861 | 0.9868 | 1.0233 | 0.9899 | 0.9831 | 0.9164 | 0.1559 |

Vel. at l3 and Acc. at l8 | 1.0093 | 0.9842 | 0.9934 | 1.0149 | 0.9992 | 1.0375 | 0.9067 | 0.1163 |

Acc. at l3 and Acc. at l8 | 0.8947 | 0.8839 | 0.3038 | 0.7664 | 0.8968 | 0.9948 | 0.8844 | 0.0991 |

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**MDPI and ACS Style**

Kalhori, H.; Tashakori, S.; Halkon, B.
Experimental Study on Impact Force Identification on a Multi-Storey Tower Structure Using Different Transducers. *Vibration* **2021**, *4*, 101-116.
https://doi.org/10.3390/vibration4010009

**AMA Style**

Kalhori H, Tashakori S, Halkon B.
Experimental Study on Impact Force Identification on a Multi-Storey Tower Structure Using Different Transducers. *Vibration*. 2021; 4(1):101-116.
https://doi.org/10.3390/vibration4010009

**Chicago/Turabian Style**

Kalhori, Hamed, Shabnam Tashakori, and Benjamin Halkon.
2021. "Experimental Study on Impact Force Identification on a Multi-Storey Tower Structure Using Different Transducers" *Vibration* 4, no. 1: 101-116.
https://doi.org/10.3390/vibration4010009