# The Research on the Damping of Prestressed Membrane Structure Subjected to the Impact Load

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Test Settings

#### 2.1. Experiment Characteristic

^{2}and 1050 g/m

^{2}, respectively.

#### 2.2. Equipment of the Test

## 3. FEM Model

#### 3.1. The Simulation Model without Air

#### 3.2. The Simulation including Air

## 4. Results

#### 4.1. Vibration Results

#### 4.2. The Results of Displacement in Case 1

#### 4.3. The results of Displacement in Case 2

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**FEM model. (

**a**) Structure of bracket. (

**b**) The details of catapult. (

**c**) The speedometer. (

**d**) The manual windlass. (

**e**) The data acquisition card. Non-English word in the figure mean the care belong to school (

**f**) Laser displacement sensor. Non-English word in figure shows the sensor type.

**Figure 6.**Initial stress of prestressed membrane structure. (

**a**) The initial effective stress at T = 6 kN/m. (

**b**) The initial effective stress at T = 7 kN/m.

**Figure 7.**The velocity contour of air velocity in case 1. (

**a**) The velocity contour of air at T = 6 kN (time = 0.02 s). (

**b**) The velocity contour of air at T = 7 kN (time = 0.02 s).

**Figure 8.**The contour of effective stress of membrane at 0.04 s with case 1 and case 2. (

**a**) The contour of effective stress in case 1 at time = 0.04 s. (

**b**) The contour of effective stress in case 2 at time = 0.04 s.

**Figure 9.**Numerical and experimental displacement time history curves. (

**a**) The displacement curve at 1 kN/m. (

**b**) The displacement curve at 2 kN/m. (

**c**) The displacement curve at 3 kN/m. (

**d**) The displacement curve at 4 kN/m. (

**e**) The displacement curve at 5 kN/m. (

**f**) The displacement curve at 6 kN/m. (

**g**) The displacement curve at 7 kN/m. (

**h**) The displacement curve at 8 kN/m.

**Figure 10.**The comparison of displacement in case 1 and case 2. (

**a**) The displacement curve at 1 kN/m. (

**b**) The displacement curve at 2 kN/m. (

**c**) The displacement curve at 3 kN/m. (

**d**) The displacement curve at 4 kN/m. (

**e**) The displacement curve at 5 kN/m. (

**f**) The displacement curve at 6 kN/m. (

**g**) The displacement curve at 7 kN/m. (

**h**) The displacement curve at 8 kN/m.

Strength (N/dtex) | Warp Count (yarn/cm) | Density of Fabric (g/m ^{2}) | Density of Membrane (g/m ^{2}) | Tensile Strength (N/5 cm) | Tear Strength (N) | Seam Strength (N/cm) |
---|---|---|---|---|---|---|

1100 | 1212 | 270 | 1050 | 4200/4500 | 550/500 | >120/5 |

Case 1 (m/s) | Case 2 (m/s) | Case 3 (m/s) | Average (m/s) | |
---|---|---|---|---|

Velocity | 10.21 | 9.95 | 10.35 | 10.17 |

Velocity | 15.12 | 15.32 | 15.16 | 15.20 |

Membrane | Ball | Case 1 | Case 2 | |
---|---|---|---|---|

Young’s Modulus/Mpa | 200 | 2e6 | / | / |

Density/(kg/m^{3}) | 1050 | 7850 | 1.29 | 1.29 |

Poisson’s ratio | 0.11 | 0.3 | / | / |

Bulk modulus/Mpa | / | / | 0.101 | 0.101 |

Tension Force (kN/m) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Damping | 3.34 | 4.39 | 6.02 | 7.73 | 8.77 | 9.99 | 10.86 | 11.89 |

Damping ratio | 0.098 | 0.111 | 0.108 | 0.122 | 0.128 | 0.122 | 0.134 | 0.133 |

Tension Force (kN/m) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Case 1 | 1.390 | 0.836 | 0.558 | 0.438 | 0.334 | 0.411 | 0.228 | 0.226 |

Experiment | 1.568 | 0.804 | 0.580 | 0.473 | 0.314 | 0.2500 | 0.236 | 0.245 |

Tension Force (kN/m) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Case 1 | 7.35 | 5.52 | 5.05 | 4.22 | 4.19 | 2.56 | 2.38 | 1.97 |

Experiment | 7.20 | 4.96 | 4.80 | 4.16 | 4.00 | 2.56 | 2.40 | 2.88 |

Tension Force (kN/m) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Case 1 | 12.99 | 15.63 | 21.74 | 25.00 | 26.32 | 29.41 | 31.25 | 35.71 |

Case 2 | 11.63 | 17.24 | 22.72 | 25.00 | 27.78 | 27.78 | 31.25 | 35.71 |

Test | 12.87 | 15.10 | 21.37 | 24.15 | 26.28 | 29.76 | 31.15 | 34.33 |

mean | 12.50 | 16.00 | 21.94 | 24.72 | 26.80 | 28.99 | 31.22 | 35.25 |

Tension Force (kN/m) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Case 1 | 0.110 | 0.123 | 0.145 | 0.120 | 0.143 | 0.114 | 0.141 | 0.146 |

Case 2 | 0.097 | 0.115 | 0.118 | 0.103 | 0.129 | 0.105 | 0.144 | 0.139 |

Test | 0.098 | 0.111 | 0.108 | 0.122 | 0.128 | 0.122 | 0.134 | 0.133 |

mean | 0.102 | 0.116 | 0.124 | 0.115 | 0.133 | 0.114 | 0.140 | 0.140 |

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**MDPI and ACS Style**

Shu, Z.-F.; Ma, Y.; Zhang, A.; Liu, P.
The Research on the Damping of Prestressed Membrane Structure Subjected to the Impact Load. *Sustainability* **2022**, *14*, 6196.
https://doi.org/10.3390/su14106196

**AMA Style**

Shu Z-F, Ma Y, Zhang A, Liu P.
The Research on the Damping of Prestressed Membrane Structure Subjected to the Impact Load. *Sustainability*. 2022; 14(10):6196.
https://doi.org/10.3390/su14106196

**Chicago/Turabian Style**

Shu, Zhe-Feng, Yue Ma, Anqi Zhang, and Ping Liu.
2022. "The Research on the Damping of Prestressed Membrane Structure Subjected to the Impact Load" *Sustainability* 14, no. 10: 6196.
https://doi.org/10.3390/su14106196