# 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

- Steiner, R.; Lammer, G.; Spiel, C.; Jandl, C. Refractories 4.0. BHM Berg-Hüttenmännische Monatshefte
**2017**, 162, 514–520. [Google Scholar] [CrossRef] - Tomsu, F.; Palco, S. Refractory monolithics versus shaped refractory products. Interceram Int. Ceram. Rev.
**2017**, 66, 20–23. [Google Scholar] [CrossRef] - Lee, W.; Zhang, S.; Karakus, M. Refractories: Controlled microstructure composites for extreme environments. J. Mater. Sci.
**2004**, 39, 6675–6685. [Google Scholar] [CrossRef] - Jin, J.; Rivière, J.; Ohara, Y.; Shokouhi, P. Dynamic acousto-elastic response of single fatigue cracks with different microstructural features: An experimental investigation. J. Appl. Phys.
**2018**, 124, 075303. [Google Scholar] [CrossRef] - Ankay, B.; Zhang, C. Acoustoelastic evaluation of ultra-high performance concretes. In AIP Conference Proceedings; AIP Publishing LLC.: Melville, NY, USA, 2019; Volume 2102, p. 110002. [Google Scholar] [CrossRef]
- Gutiérrez-Vargas, G.; Ruiz, A.; Kim, J.Y.; Jacobs, L.J. Characterization of thermal embrittlement in 2507 super duplex stainless steel using nonlinear acoustic effects. NDT E Int.
**2018**, 94, 101–108. [Google Scholar] [CrossRef] - Kwaśniewki, J.; Dominik, I.; Lalik, K.; Holewa, K. Influence of acoustoelastic coefficient on wave time of flight in stress measurement in piezoelectric self-excited system. Mech. Syst. Signal Process.
**2016**, 78, 143–155. [Google Scholar] [CrossRef] - Masurkar, F.; Tse, P.W.; Yelve, N.P. Theoretical and experimental measurement of intrinsic and fatigue induced material nonlinearities using Lamb wave based nonlinearity parameters. Meas. J. Int. Meas. Confed.
**2020**, 151, 107148. [Google Scholar] [CrossRef] - Yang, Y.; Ng, C.T.; Mohabuth, M.; Kotousov, A. Finite element prediction of acoustoelastic effect associated with Lamb wave propagation in pre-stressed plates. Smart Mater. Struct.
**2019**, 28, 095007. [Google Scholar] [CrossRef][Green Version] - Pei, N.; Bond, L.J. Comparison of acoustoelastic Lamb wave propagation in stressed plates for different measurement orientations. J. Acoust. Soc. Am.
**2017**, 142, EL327–EL331. [Google Scholar] [CrossRef][Green Version] - Chen, P.; He, X.; Wang, X. Ultrasonic Measurement of Axial Stress Using High-frequency Cylindrical Guided Wave. IEEE Sens. J.
**2020**, 21, 6691–6697. [Google Scholar] [CrossRef] - Bompan, K.F.; Haach, V.G. Ultrasonic tests in the evaluation of the stress level in concrete prisms based on the acoustoelasticity. Constr. Build. Mater.
**2018**, 162, 740–750. [Google Scholar] [CrossRef] - Shokouhi, P.; Zoëga, A.; Wiggenhauser, H.; Fischer, G. Surface wave velocity-stress relationship in uniaxially loaded concrete. ACI Mater. J.
**2012**, 109, 131–139. [Google Scholar] [CrossRef][Green Version] - Lott, M.; Remillieux, M.C.; Garnier, V.; Le Bas, P.Y.; Ulrich, T.J.; Payan, C. Nonlinear elasticity in rocks: A comprehensive three-dimensional description. Phys. Rev. Mater.
**2017**, 1, 023603. [Google Scholar] [CrossRef][Green Version] - Pau, A.; Vestroni, F. The role of material and geometric nonlinearities in acoustoelasticity. Wave Motion
**2019**, 86, 79–90. [Google Scholar] [CrossRef] - Muñoz, C.Q.G.; Márquez, F.P.G. A new fault location approach for acoustic emission techniques in wind turbines. Energies
**2016**, 9, 40. [Google Scholar] [CrossRef][Green Version] - Perugia, I.; Schöberl, J.; Stocker, P.; Wintersteiger, C. Tent pitching and Trefftz-DG method for the acoustic wave equation. Comput. Math. Appl.
**2020**, 79, 2987–3000. [Google Scholar] [CrossRef][Green Version] - Carcione, A.; Blanloeuil, P.; Rose, L.R.; Wang, C.H.; Veidt, M. Modulated high frequency excitation approach to nonlinear ultrasonic NDT. J. Sound Vib.
**2019**, 446, 238–248. [Google Scholar] [CrossRef] - Abbasi, Z.; Ozevin, D. The influence of ultrasonic frequency on shear stress measurement using acoustoelasticity. In AIP Conference Proceedings; AIP Publishing LLC.: Melville, NY, USA, 2016. [Google Scholar] [CrossRef][Green Version]
- Dubuc, B.; Ebrahimkhanlou, A.; Salamone, S. Higher order longitudinal guided wave modes in axially stressed seven-wire strands. Ultrasonics
**2018**, 84, 382–391. [Google Scholar] [CrossRef] - Dominik, I.; Lalik, K.; Flaga, S. Modeling of self-excited stress measurement system. J. Low Freq. Noise Vib. Act. Control
**2020**, 146134842092945. [Google Scholar] [CrossRef] - Lalik, K.; Dominik, I.; Ćwia̧kała, P.; Kwaśniewski, J. Integrated stress measurement system in tower crane mast. Meas. J. Int. Meas. Confed.
**2017**, 102, 47–56. [Google Scholar] [CrossRef] - Skrzypkowski, K.; Korzeniowski, W.; Zagórski, K.; Dominik, I.; Lalik, K. Fast, non-destructive measurement of roof-bolt loads. Studia Geotech. Mech.
**2019**, 41. [Google Scholar] [CrossRef][Green Version] - Kwaśniewski, J.; Dominik, I.; Lalik, K. A Self-Excited Acoustical System for Stress Measurement in a Cement Plant. Mech. Control
**2012**, 31, 29. [Google Scholar] [CrossRef] - Kwaśniewki, J.; Dominik, I.; Lalik, K. Application of self-oscillating system for stress measurement in metal. J. Vibroeng.
**2012**, 14, 1429–2955. [Google Scholar] - Roebben, G.; Bollen, B.; Brebels, A.; Van Humbeeck, J.; der Biest, O. Impulse excitation apparatus to measure resonant frequencies, elastic moduli, and internal friction at room and high temperature. Rev. Sci. Instrum.
**1997**, 68, 4511–4515. [Google Scholar] [CrossRef] - Bradt, R.C.; Alton, N. Elastic properties of refractories- their role and characterization. Refract. Appl. News
**2007**, 12. [Google Scholar] - Etzold, S.; Tarabeux, J.; Porada, R.; Tonnesen, T.; Telle, R. Thermomechanical behavior of high-alumina refractory castables containing partially stabilized zirconia with different grain shapes. In Proceedings of the 15th Biennial Worldwide Congress UNITECR, Santiago, Chile, 26–29 September 2017; pp. 54–57. [Google Scholar]
- Huger, M.; Fargeot, D.; Gault, C. High-temperature measurement of ultrasonic wave velocity in refractory materials. High Temp.-High Press.
**2002**, 34, 193–201. [Google Scholar] [CrossRef] - Lundqvist, P.; Rydén, N. Acoustoelastic effects on the resonance frequencies of prestressed concrete beams—Short-term measurements. NDT E Int.
**2012**, 50, 36–41. [Google Scholar] [CrossRef] - Shokouhi, P.; Zoëga, A.; Wiggenhauser, H. Nondestructive investigation of stress-induced damage in concrete. Adv. Civ. Eng.
**2010**, 2010, 740189. [Google Scholar] [CrossRef][Green Version] - Popovics, S.; Popovics, J.S. Effect of stresses on the ultrasonic pulse velocity in concrete. Mater. Struct.
**1991**, 24, 15–23. [Google Scholar] [CrossRef] - Berthaud, Y. Damage measurements in concrete via an ultrasonic technique. Part I experiment. Cem. Concr. Res.
**1991**, 21, 73–82. [Google Scholar] [CrossRef] - Chaix, J.F.; Lillamand, I.; Ploix, M.A.; Garnier, V.; Corneloup, G. Study of acoustoelasticity behavior of concrete material under uniaxial compression. J. Acoust. Soc. Am.
**2008**, 123, 3847. [Google Scholar] [CrossRef] - Larose, E.; Hall, S. Monitoring stress related velocity variation in concrete with a 2 × 10
^{-5}relative resolution using diffuse ultrasound. J. Acoust. Soc. Am.**2009**, 125, 1853–1856. [Google Scholar] [CrossRef][Green Version] - Ghassemi Kakroudi, M.; Yeugo-Fogaing, E.; Huger, M.; Gault, C.; Chotard, T. Influence of the thermal history on the mechanical properties of two alumina based castables. J. Eur. Ceram. Soc.
**2009**, 29, 3197–3204. [Google Scholar] [CrossRef] - Tonnesen, T.; Telle, R. Thermal shock damage in castables: Microstructural changes and evaluation by a damping method. CFI Ceram. Forum Int.
**2007**, 84, E131–E136. [Google Scholar] - Skrzypkowski, K.; Korzeniowski, W.; Zagórski, K.; Dudek, P. Application of long expansion rock bolt support in the underground mines of legnica-głogów copper district. Studia Geotech. Mech.
**2017**, 39, 47–57. [Google Scholar] [CrossRef][Green Version]

**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