# Metaconcrete: An Experimental Study on the Impact of the Core-Coating Inclusions on Mechanical Vibration

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. A Short Review of TMD

#### 1.2. Multi-TMD Setup: A Solution to the Tuning Error

- (1)
- The frequency of the target mode of the main system is not always easy to be determined, particularly when the main system is a complex structure.
- (2)
- The equivalent mass of the main system in the mode under consideration is hard to compute too.

#### 1.3. Scope and Outline of the Work

## 2. The Core-Coating Inclusions

#### 2.1. Mechanism of the Inclusions

#### 2.2. Estimation of the Inclusions’ Natural Frequency

## 3. Functioning as a Single TMD

#### 3.1. Description of the Test Setup

#### 3.2. Procedure of the Free Vibration Test

#### 3.3. Tuning the Inclusions

#### 3.4. Results and Discussion

## 4. Functioning as Multiple TMDs

#### 4.1. Description of the Numerical Model

#### 4.2. Boundary Conditions and Applied Load

#### 4.3. Analysis Procedure

#### 4.4. Tuning the Inclusions

#### 4.5. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A single-span beam with a TMD at the mid-span. (

**a**) Frahm’s vibration absorber (TMD without a self-damping). (

**b**) TMD with a self-damping.

**Figure 2.**A single-span beam in a multi-TMD setup. (

**a**) multiple TMDs distributed across the span. (

**b**) distributed core-coating inclusions in concrete forming a multi-TMD setup.

**Figure 3.**The core-coating inclusion and the oscillations of the core. (

**a**) Core-Coating inclusion (

**b**) translational oscillation of the core. (

**c**) rotational oscillation of the core.

**Figure 4.**The core-coating inclusion and its equivalent models. (

**a**) SDOF mass-spring system. (

**b**) 3D FE-Model.

**Figure 6.**Boundary conditions of the 3D FE-Model (

**a**,

**b**): illustrative presentation, (

**c**) Model in Abaqus.

**Figure 8.**Alignment of the supports, (

**a**) the 1st mode shape of beam with free ends; (

**b**) point-supported beam with a core-coating element at mid-span.

**Figure 11.**Decaying free vibration of the beams without the damper and their FFT diagrams (first step of the free vibration test). (

**a**) P670: free vibration without damper. (

**b**) P670: FFT of signal in a. (

**c**) P600: free vibration without damper. (

**d**) P600: FFT of signal in c.

**Figure 12.**Decaying free vibration of the beams with the dampers (second step of the free vibration test). (

**a**) P670: free vibration with damper 2 × K2. (

**b**) P600: free vibration with damper 2 × K3.

Component | Material | Density (kg/m^{3}) | E (MPa) |
---|---|---|---|

Core | Stainless-Steel | 8000 | 200,000 |

Coating | Silicone | 1040 | 1 |

Cube | Concrete | 2400 | 38,000 |

Configuration | Steel Core | Silicone Coating | Overall | Analysis Result | ||
---|---|---|---|---|---|---|

Diameter (mm) | m (g) | Thickness (mm) | Diameter (mm) | m (g) | f ^{1} (Hz) | |

K2 | 20 | 34 | 11 | 42 | 70 | 370 |

K3 | 20 | 34 | 7 | 34 | 51 | 460 |

K4 | 8 | 2.1 | 3 | 14 | 3.4 | 1015 |

K5 | 10 | 4.2 | 3 | 16 | 5.9 | 892 |

^{1}The translational natural frequency of the core.

Specimen | Length (mm) | Section (Width × Height) | m (g) | f ^{1} (Hz) |
---|---|---|---|---|

P670 | 670 | 60 × 40 | 3800 | 373 |

P600 | 600 | 60 × 40 | 3410 | 465 |

^{1}The first natural frequency of the beam.

Main Mass | Damper | Current Tuning Parameters | Equation (5) | |||||
---|---|---|---|---|---|---|---|---|

Beam | ${\mathit{m}}_{\mathit{m}}$ | ${\mathit{f}}_{\mathit{m}}$ | Configuration | ${\mathit{m}}_{\mathit{d}}$ ^{1} | ${\mathit{f}}_{\mathit{d}}$ | $\mathit{\mu}$ | $\mathit{\kappa}$ | ${\mathit{\kappa}}_{\mathit{o}\mathit{p}\mathit{t}}$ |

P670 | 950 | 373 | 2 no. of K2 | 68 | 370 | 0.07 | 0.99 | 0.93 |

P600 | 853 | 465 | 2 no. of K3 | 68 | 460 | 0.08 | 0.99 | 0.93 |

^{1}The mass of the core multiplied with the no. of inclusions.

Test # | Damping Ratio—P670 | Damping Ratio—P600 | ||||
---|---|---|---|---|---|---|

Without Damper | With 2 × K2 | Change | Without Damper | With 2 × K3 | Change | |

1 | 0.44% | 0.56% | 0.51% | 0.59% | ||

2 | 0.39% | 0.57% | 0.48% | 0.58% | ||

3 | 0.40% | 0.65% | 0.40% | 0.57% | ||

4 | 0.40% | 0.57% | - | 0.62% | ||

5 | 0.46% | - | - | 0.59% | ||

6 | 0.46% | - | - | - | ||

mean value | 0.43% | 0.59% | +37% | 0.46% | 0.59% | +28% |

Model | Length (mm) | Section (Width × Height) | m (g) | V (cm^{3}) | f ^{1} (Hz) |
---|---|---|---|---|---|

P480 | 480 | 40 × 60 | 2640 | 1152 | 373 |

P510 | 510 | 40 × 60 | 2800 | 1224 | 465 |

^{1}The first natural frequency of the beam.

Phase | Component | Volume Fraction (%) | E (GPa) | Density (kg/m^{3}) | |
---|---|---|---|---|---|

Model without the Inclusions | Model with the Inclusions | ||||

Mortar Matrix | Cement | 11.6 | 38 | 2360 | |

Water | 15.8 | ||||

Air | 2 | ||||

Aggregate 0/2 | 23.4 | ||||

Aggregate 2/8 | 19.2 | ||||

Particles | Aggregate 8/16 | 28.4 | 23.4 | 63.5 | 2600 |

Core-Coating | 0 | 5 | - | - | |

sum | 100 | 100 |

Main Mass | Damper | Current Tuning Parameters | Equation (5) | |||||
---|---|---|---|---|---|---|---|---|

Beam | ${\mathit{m}}_{\mathit{m}}$ | ${\mathit{f}}_{\mathit{m}}$ | Configuration | ${\mathit{m}}_{\mathit{d}}$ ^{1} | ${\mathit{f}}_{\mathit{d}}$ | $\mathit{\mu}$ | $\mathit{\kappa}$ | ${\mathit{\kappa}}_{\mathit{o}\mathit{p}\mathit{t}}$ |

P480 | 2640 | 1070 | 40 no. of K4 | 84 | 1015 | 0.032 | 0.95 | 0.97 |

P510 | 2800 | 950 | 30 no. of K5 | 126 | 892 | 0.045 | 0.94 | 0.96 |

^{1}The mass of the core multiplied with the no. of inclusions.

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**MDPI and ACS Style**

Ansari, M.; Zacharias, C.; Koenke, C.
Metaconcrete: An Experimental Study on the Impact of the Core-Coating Inclusions on Mechanical Vibration. *Materials* **2023**, *16*, 1836.
https://doi.org/10.3390/ma16051836

**AMA Style**

Ansari M, Zacharias C, Koenke C.
Metaconcrete: An Experimental Study on the Impact of the Core-Coating Inclusions on Mechanical Vibration. *Materials*. 2023; 16(5):1836.
https://doi.org/10.3390/ma16051836

**Chicago/Turabian Style**

Ansari, Meisam, Christin Zacharias, and Carsten Koenke.
2023. "Metaconcrete: An Experimental Study on the Impact of the Core-Coating Inclusions on Mechanical Vibration" *Materials* 16, no. 5: 1836.
https://doi.org/10.3390/ma16051836