# Experimental Evaluation of the Driving Parameters in Human–Structure Interaction

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

- Intra-subject variability: the AM curve of the same person in a given posture is affected by a natural dispersion;
- Inter-subject variability: the AM curves of different people in the same posture are different;

## 2. Passive Pedestrian Contribution

#### 2.1. Motion Analysis

#### 2.2. Number and Types of Tests

#### 2.3. Measurement of AM Curves

#### 2.3.1. Set-Up Description

#### 2.3.2. Description of the Test

#### 2.3.3. Post-Processing of Data

## 3. Reference Structure

## 4. Pedestrian–Structure Coupling

#### 4.1. Analytical Model and Its Implementation

#### 4.2. Statistical Treatment

## 5. Tests and Results

#### 5.1. Passive HSI Effect

#### 5.1.1. Change in Eigenfrequencies

#### 5.1.2. Change in Non-Dimensional Damping Ratio

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Measured AM curves for the five test subjects for postures 1af, 2af and 3af (list of the postures in Table 2). Top plots, amplitude; bottom plots, phase. (

**a**,

**b**): Subject 1; (

**c**,

**d**): Subject 2; (

**e**,

**f**): Subject 3; (

**g**,

**h**): Subject 4; (

**i**,

**j**): Subject 5.

**Figure A2.**Measured AM curves for the five test subjects for postures 1at, 2at and 3at (list of the postures in Table 2). Top plots, amplitude; bottom plots, phase. (

**a**,

**b**): Subject 1; (

**c**,

**d**): Subject 2; (

**e**,

**f**): Subject 3; (

**g**,

**h**): Subject 4; (

**i**,

**j**): Subject 5.

**Figure A3.**Measured AM curves for the five test subjects for postures 1d, 2d and 3d (list of the postures in Table 2). Top plots, amplitude; bottom plots, phase. (

**a**,

**b**): Subject 1; (

**c**,

**d**): Subject 2; (

**e**,

**f**): Subject 3; (

**g**,

**h**): Subject 4; (

**i**,

**j**): Subject 5.

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**Figure 1.**Motion analysis of subject 3 ascending and descending a staircase. The numbered green squares are in correspondence of the selected positions for the ascent (1a, 2a, 3a) and for the descent (1d, 2d, 3d).

**Figure 2.**Set-up for the measurement of the AM curve. It includes an electro-dynamic shaker, a force plate and accelerometers.

**Figure 3.**Subject 5 during the tests for the measurement of the AM curves in different postures. Letter “d” indicates the postures related to the descent, while “af” and “at” are related to the ascent.

**Figure 4.**AM curve of subject 5 (position 3af, left foot). Dashed line, frequency resolution of 0.5 Hz; solid line, frequency resolution of 0.01 Hz; (

**a**) AM magnitudes; (

**b**) AM phases.

**Figure 5.**AM curves: two measurements of the same AM curve of subject 1 in position 2d in terms of magnitude (

**a**) and phase (

**b**), comparison with subject 3 (

**c**,

**d**), comparison between posture 2d with posture 1at (

**e**,

**f**) and posture 2af (

**g**,

**h**). The solid curves are always related to the same test.

**Figure 7.**Convention of sign adopted for the PGRF ${F}_{k}^{\mathrm{PGR}}$ applied to the structure for the k-th subject, the structural displacement x and the generic external force F (

**a**) and passive HSI block diagram (

**b**).

**Figure 8.**Co-located numerical FRF at node 12 of the empty structure (dashed line) and co-located numerical FRF of the structure occupied by subject 3 in position 2af (solid line): magnitude (

**a**) and phase (

**b**).

**Figure 9.**First eigenfrequency of the occupied structure. (■): $\overline{\mu}$; (▲): $\overline{\mu}+\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}};$ (▼): $\overline{\mu}-\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}}$; $\left(+\right)$: single values; dash-dotted line: first eigenfrequency of the empty structure.

**Figure 10.**Second eigenfrequency of the occupied structure. (■): $\overline{\mu}$; (▲): $\overline{\mu}+\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}};$ (▼): $\overline{\mu}-\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}}$; $\left(+\right)$: single values; dash-dotted line: second eigenfrequency of the empty structure.

**Figure 11.**AM curves of subject 1 in postures 3af and 3at. (

**a**) Magnitudes of the AM curves; (

**b**) phases of the AM curves. The dash-dotted line in plot (

**b**) indicates −90°.

**Figure 12.**First non-dimensional damping ratio of the occupied structure. (■)$:\overline{\mu}$; (▲)$:\overline{\mu}+\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}};$ (▼)$:\overline{\mu}-\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}}$; $\left(+\right)$: single values; dash-dotted line: first non-dimensional damping ratio of the empty structure.

**Figure 13.**Second non-dimensional damping ratio of the occupied structure. (■)$:\overline{\mu}$; (▲)$:\overline{\mu}+\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}};$ (▼)$:\overline{\mu}-\frac{{t}_{\alpha ,\nu}s}{\sqrt{n}}$; $\left(+\right)$: single values; dash-dotted line: second non-dimensional damping ratio of the empty structure.

Subject | Gender | Height (cm) | Mass (kg) |
---|---|---|---|

1 | male | 175 | 85 |

2 | male | 185 | 90 |

3 | female | 165 | 55 |

4 | male | 185 | 80 |

5 | male | 180 | 70 |

Direction | Foot-Step Contact | Position Labels | ||
---|---|---|---|---|

ascent | full | 1af | 2af | 3af |

ascent | tip | 1at | 2at | 3at |

descent | full | 1d | 2d | 3d |

Mode | ${\mathit{\xi}}_{\mathit{i}}(\%)$ | ${\mathit{f}}_{\mathit{i}}\left(\mathbf{Hz}\right)$ |
---|---|---|

1st | 0.38 | 7.81 |

2nd | 0.35 | 8.87 |

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**MDPI and ACS Style**

Lucà, F.; Berardengo, M.; Manzoni, S.; Scaccabarozzi, D.; Vanali, M.; Drago, L.
Experimental Evaluation of the Driving Parameters in Human–Structure Interaction. *Vibration* **2022**, *5*, 121-140.
https://doi.org/10.3390/vibration5010008

**AMA Style**

Lucà F, Berardengo M, Manzoni S, Scaccabarozzi D, Vanali M, Drago L.
Experimental Evaluation of the Driving Parameters in Human–Structure Interaction. *Vibration*. 2022; 5(1):121-140.
https://doi.org/10.3390/vibration5010008

**Chicago/Turabian Style**

Lucà, Francescantonio, Marta Berardengo, Stefano Manzoni, Diego Scaccabarozzi, Marcello Vanali, and Loris Drago.
2022. "Experimental Evaluation of the Driving Parameters in Human–Structure Interaction" *Vibration* 5, no. 1: 121-140.
https://doi.org/10.3390/vibration5010008