# Self-Excited Acoustical System Frequency Monitoring for Refractory Concrete under Uniaxial Compression

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## Abstract

**:**

## 1. Introduction

## 2. The Self-Excited Acoustical System (SAS) for Indirect Stress Changes Monitoring

- ${V}_{\sigma}$—wave velocity of the stresses sample [$\frac{m}{s}$],
- ${V}_{0}$—wave velocity of unstressed sample [$\frac{m}{s}$],
- $\beta $—acoustoelastic coefficient [${Pa}^{-1}$],
- $\sigma $—stress [$Pa$].

- the energy source (constant),
- oscillating object,
- energy supply regulator for an oscillating object,
- positive feedback loop.

## 3. Research Methodology

## 4. Experimental

#### 4.1. Materials Preparation and Characterization Techniques

#### 4.2. SAS Resonance Frequency Monitoring for Concrete Samples with Different Thermal History

#### 4.3. Introduction of Alumina Waveguide to SAS

## 5. Results

#### 5.1. Load and Resonance Frequency Characteristics of Materials with Different Thermal History

#### 5.2. Resonance Frequency Monitoring with SAS Working in Conjunction with Alumina Waveguide

## 6. Discussion

#### 6.1. Influence of the Thermal History on the Load and Resonance Frequency Characteristics

#### 6.2. Introduction of Alumina Waveguide to SAS

- ${\omega}_{0}$—frequency of the SAS system [$\frac{rad}{s}$],
- ${T}_{0}$—time constant for the measurement stand [s],
- $\tau $—delay time for wave transmission between the emitter and receiver [s],
- $\zeta $—dumping coefficient [−].

#### 6.3. Limitations of the Study

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**SEM images of (

**a**,

**b**) concrete sample before sintering and (

**c**,

**d**) concrete sample after sintering emitter.

**Figure 8.**Dependence of the resonance frequency in the function of load for non-sintered sample determined with the use of acoustic emitter.

**Figure 9.**Dependence of the resonance frequency in the function of load for sintered sample determined with the use of acoustic emitter.

**Figure 10.**Dependence of the resonance frequency in the function of load for non-sintered and sintered sample determined with the use of piezo-emitter. Green and blue curves correspond to the subsequent measurements.

**Figure 11.**Dependence of the resonance frequency in the function of load determined by SAS working in three configurations: without alumina waveguide; with one alumina waveguide connecting the emitter and the sample; with two alumina waveguides connecting both emitter and receiver with the sample. Green and blue curves correspond to the subsequent measurements.

**Figure 12.**Dependence of the resonance frequency for different sample load determined by SAS using a piezoelectric actuator.

**Figure 13.**Dependence of the resonance frequency in the function of sample load determined by SAS working with three emitters.

**Figure 14.**Energy flows during vibrations for (

**a**) one stability point; (

**b**) multiple stability points.

Parameter | Piezo: PS-X-03-6/500 | Piezo: PS-X-03-6/1000 | Electromechanical | |
---|---|---|---|---|

1 | Weight | 40 [g] | 35 [g] | 10 [g] |

2 | Flat frequency range | 50 [kHz] | 100 [kHz] | 115 [kHz] |

3 | Capacity | <250 [nF] | <30 [nF] | - |

4 | Stroke | 2.4 [µm] | 1,2 [µm] | 2.5 [mm] |

5 | Preload on piezo | 400 [N] | 500 [N] | - |

6 | Blocking force | 5 [kN] | 5 [kN] | 1 [kN] |

7 | Piezoelectric modulus (d33) | 1.22 × 10${}^{-5}$ [m/V] | 1.22 × 10${}^{-5}$ [m/V] | - |

**Table 2.**Parameters of the unloaded material determined by the Resonance Frequency and Damping Analyzer (RFDA), the resonance frequency technique and the Self-Excited Acoustical System (SAS).

Sample | Volumetric Density [g/cm${}^{3}$] | RFDA | Resonance | SAS | ||||
---|---|---|---|---|---|---|---|---|

Frequency | Acoustic | Piezo- | ||||||

E | ${\mathit{f}}_{\mathit{r}}$ | ${\mathit{Q}}^{-1}$ | E | ${\mathit{f}}_{\mathit{r}}$ | Emitter | Emitter | ||

[GPa] | [Hz] | ($\times {10}^{-3}$) | [GPa] | [Hz] | ${\mathit{f}}_{\mathit{r}}$ [Hz] | ${\mathit{f}}_{\mathit{r}}$ [Hz] | ||

Non-sintered | 2.47 | 34.8 | 3151 | 4.23 | 35.9 | 7150 | 1543 | 3404 |

Sintered | 2.49 | 45.5 | 3505 | 5.08 | 46.5 | 8050 | 6945 | 14,350 |

**Table 3.**Relative change of resonant frequency versus load determined by SAS working in two configurations with acoustic and piezo-emitter.

$\mathbf{\Delta}\mathit{f}/{\mathit{f}}_{\mathbf{in}}$ | Acoustic Emitter | Piezo-Emitter | |
---|---|---|---|

100–1500 [kg] | 100–800 [kg] | 100–800 [kg] | |

Non-sintered | $0.06\pm 0.004$ | $0.05\pm 0.002$ | $0.16\pm 0.01$ |

Sintered | $0.22\pm 0.02$ | $0.21\pm 0.02$ | $0.19\pm 0.01$ |

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**MDPI and ACS Style**

Kieliba, I.; Dominik, I.; Lalik, K.; Tonnesen, T.; Szczerba, J.; Telle, R.
Self-Excited Acoustical System Frequency Monitoring for Refractory Concrete under Uniaxial Compression. *Energies* **2021**, *14*, 2222.
https://doi.org/10.3390/en14082222

**AMA Style**

Kieliba I, Dominik I, Lalik K, Tonnesen T, Szczerba J, Telle R.
Self-Excited Acoustical System Frequency Monitoring for Refractory Concrete under Uniaxial Compression. *Energies*. 2021; 14(8):2222.
https://doi.org/10.3390/en14082222

**Chicago/Turabian Style**

Kieliba, Ilona, Ireneusz Dominik, Krzysztof Lalik, Thorsten Tonnesen, Jacek Szczerba, and Reiner Telle.
2021. "Self-Excited Acoustical System Frequency Monitoring for Refractory Concrete under Uniaxial Compression" *Energies* 14, no. 8: 2222.
https://doi.org/10.3390/en14082222