# Experimental Investigation on Vibration Control of a Suspended Particle-Tuned Liquid Damper

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Configuration of SPTLD and Experimental Setup

#### 2.1. Configuration of SPTLD

^{2}); and ${V}_{\mathrm{p}}$ represents the volume of the particle (m

^{3}). ${\rho}_{\mathrm{p}}$ is the overall density of the particle (kg/m

^{3}). For each particle suspended in water, the sand filled in the gap needs to be adjusted so that ${\rho}_{\mathrm{p}}$ is equal to the density of water ${\rho}_{\mathrm{w}}=1\times {10}^{3}\mathrm{kg}/{\mathrm{m}}^{3}$.

#### 2.2. Experimental Setup

## 3. Test Results and Discussion

^{2}); and ${A}_{\mathrm{p}}$ and ${A}_{\mathrm{r}}$ are for the structure under the control of the damper, correspondingly (m/s

^{2}).

#### 3.1. Control Effectiveness of SPTLD

#### 3.2. Parametric Analysis

#### 3.2.1. Particle Numbers

#### 3.2.2. Excitations with Various Amplitudes

#### 3.2.3. Suspended vs. Floating Particles

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Acceleration response of the primary structure under harmonic excitation: (

**a**) time history; (

**b**) frequency spectrum.

**Figure 6.**Acceleration time histories of the primary structure under different excitations: (

**a**) sweep wave; (

**b**) CPM wave; (

**c**) H-E wave; (

**d**) SYL wave.

**Figure 7.**Vibration reduction effects of SPTLD under different excitations: (

**a**) peak acceleration; (

**b**) RMS acceleration.

Case | Acceleration Response (μg) | Reduction Ratio (%) | ||
---|---|---|---|---|

Peak | RMS | η_{p} | η_{r} | |

Uncontrolled | 795.3 | 422.5 | / | / |

TLD | 606.7 | 306.2 | 23.7 | 27.5 |

SPTLD | 583.0 | 262.4 | 26.7 | 37.9 |

**Table 2.**Structural response and reduction ratio with various particle numbers under harmonic excitation.

Number of Particles | μ_{p} (%) | Acceleration Response without Control (μg) | Acceleration Response under SPTLD (μg) | Reduction Ratio (%) | |||
---|---|---|---|---|---|---|---|

Peak | RMS | Peak | RMS | η_{p} | η_{r} | ||

1 | 0.91 | 795.3 | 422.5 | 664.3 | 351.4 | 16.5 | 16.8 |

2 | 1.82 | 586.1 | 250.7 | 26.3 | 40.7 | ||

3 | 2.73 | 583.0 | 262.4 | 26.7 | 37.9 | ||

4 | 3.64 | 620.2 | 264.2 | 22.0 | 37.5 | ||

5 | 4.55 | 646.4 | 287.4 | 18.7 | 32.0 | ||

6 | 5.46 | 653.8 | 300.6 | 17.8 | 28.9 | ||

7 | 6.37 | 668.0 | 321.8 | 16.0 | 23.8 | ||

8 | 7.28 | 678.6 | 323.1 | 14.7 | 23.5 |

Reduction Ratio (%) | Sweep Wave | CPM Wave | H-E Wave | SYL Wave | |||||
---|---|---|---|---|---|---|---|---|---|

Amplitude of the Excitation (cm) | η_{p} | η_{r} | η_{p} | η_{r} | η_{p} | η_{r} | η_{p} | η_{r} | |

1.0 | 48.4 | 54.2 | 42.0 | 27.2 | 6.7 | 43.8 | 19.1 | 48.4 | |

1.5 | 57.7 | 60.9 | 34.7 | 28.8 | 29.0 | 61.5 | 35.3 | 57.7 | |

2.0 | 56.5 | 65.0 | 41.7 | 29.9 | 55.5 | 73.9 | 67.4 | 56.4 | |

2.5 | 60.2 | 68.4 | 51.9 | 75.9 | 34.2 | 66.8 | 30.8 | 60.2 | |

3.0 | 63.5 | 69.7 | 39.3 | 66.5 | 29.4 | 61.0 | 27.7 | 63.5 |

Wave | Excitation Amplitude (cm) | Damper | Acceleration Response under SPTLD (μg) | Reduction Ratio (%) | ||
---|---|---|---|---|---|---|

Peak | RMS | η_{p} | η_{r} | |||

Harmonic excitation | 1.7 | FPTLD-12 | 589.5 | 266.4 | 25.9 | 36.9 |

SPTLD-2 | 586.1 | 250.7 | 26.3 | 40.7 | ||

Sweep wave | 2.0 | FPTLD-12 | 2058.5 | 487.6 | 41.2 | 49.7 |

SPTLD-2 | 1597.1 | 349.7 | 54.3 | 63.9 | ||

CPM wave | 2.0 | FPTLD-12 | 2009.3 | 915.6 | 43.3 | 32.5 |

SPTLD-2 | 1941.9 | 891.3 | 45.2 | 34.3 | ||

H-E wave | 2.0 | FPTLD-12 | 673.1 | 156.4 | 47.8 | 72.1 |

SPTLD-2 | 661.9 | 137.9 | 48.7 | 75.4 | ||

SYL wave | 2.0 | FPTLD-12 | 591.4 | 162.8 | 65.8 | 59.1 |

SPTLD-2 | 571.2 | 141.9 | 66.9 | 64.3 |

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**MDPI and ACS Style**

Lu, Z.; Zhou, M.; Ren, H.
Experimental Investigation on Vibration Control of a Suspended Particle-Tuned Liquid Damper. *Sustainability* **2022**, *14*, 13085.
https://doi.org/10.3390/su142013085

**AMA Style**

Lu Z, Zhou M, Ren H.
Experimental Investigation on Vibration Control of a Suspended Particle-Tuned Liquid Damper. *Sustainability*. 2022; 14(20):13085.
https://doi.org/10.3390/su142013085

**Chicago/Turabian Style**

Lu, Zheng, Mengyao Zhou, and Hongmei Ren.
2022. "Experimental Investigation on Vibration Control of a Suspended Particle-Tuned Liquid Damper" *Sustainability* 14, no. 20: 13085.
https://doi.org/10.3390/su142013085