# Sideband Peak Count in a Vibro-Acoustic Modulation Method for Crack Detection

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Configuration of the Experimental Setup

## 3. Results

## 4. Bilinear Crack Model of Multiple Sideband Peak Interpretation

_{0}+ Dk(q), where the nonlinear part of the stiffness coefficient Dk(q) << K

_{0}.

_{1}and P

_{2}.

_{1}= P

_{2}= 1.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schema of the experimental VAM setup (

**left**) and a picture of the sample with glued transducers (

**right**).

**Figure 2.**Spectra in the frequency window of 60 Hz around the probe frequency f = 175 kHz for Sample #3: (

**a**) after 11,252 load cycles, no damage initiation; (

**b**) after 47,139 cycles, initial damage accumulation; (

**c**) after 51,219 cycles, visible crack. The number of cycles to failure was 52,106 (see Table 2).

**Figure 4.**Spectra in the frequency window of 2000 Hz around the probe frequency f = 175 KHz for Sample #3: (

**a**) after 11,252 load cycles, no damage initiation; (

**b**) after 47,139 cycles, initial damage accumulation; (

**c**) after 51,219 cycles, visible crack. The number of cycles to failure was 52,106 (see Table 2).

**Figure 6.**Spectra in the frequency window of 60 Hz around the probe frequency f = 195 kHz for Sample #5: (

**a**) after 0 normalized cycles, no visible crack; (

**b**) after 0.69 normalized cycles, initial damage accumulation; (

**c**) after 0.9 normalized cycles, visible crack.

**Figure 7.**Spectra in the frequency window of 2000 Hz around the probe frequency f = 195 kHz for Sample #5: (

**a**) after 0 normalized cycles, no visible crack; (

**b**) after 0.69 normalized cycles, initial damage accumulation; (

**c**) after 0.9 normalized cycles, visible crack.

**Figure 8.**Three specimens failed after being examined by the MI versus the number of cycles ratio for average frequencies.

**Figure 9.**Three specimens were successfully examined by the SPN versus the number of cycles ratio for average frequencies.

**Figure 10.**Variations of parameter MI (

**upper**) and SPN (

**lower**) for Sample #4 for different probe frequencies.

**Figure 12.**Examples of bilinear (red line) and quadratic (blue line) force–displacement spring relationship. The nonlinear parameter here is $\alpha =0.5,$ which is much larger than for the considered case.

**Figure 14.**Dependence of the first sideband peak (A+) on (

**a**) the probe wave amplitude and (

**b**) the pump wave amplitude calculated from the bilinear model. The dotted lines show the same dependences from the quadratic model.

**Figure 15.**Examples of the spectra calculated from the bilinear crack models: (

**a**) probe wave 0 dB and pump wave 10 dB; (

**b**) probe wave 10 dB and pump wave 0 dB.

Mechanical Properties | Value |
---|---|

Density | 0.284 Ib/in3 |

Ultimate Tensile Strength | 63,800 psi |

Yield Tensile Strength | 53,700 psi |

Shear Strength | 43,500 psi |

Melting Point | 2590–2670 °F |

Sample | Number of Cycles to Failure |
---|---|

Sample #1 | 46,102 |

Sample #2 | 120,074 |

Sample #3 | 52,106 |

Sample #4 | 67,637 |

Sample #5 | 67,712 |

Sample #6 | 70,603 |

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**MDPI and ACS Style**

Alnutayfat, A.; Hassiotis, S.; Liu, D.; Sutin, A.
Sideband Peak Count in a Vibro-Acoustic Modulation Method for Crack Detection. *Acoustics* **2022**, *4*, 74-86.
https://doi.org/10.3390/acoustics4010005

**AMA Style**

Alnutayfat A, Hassiotis S, Liu D, Sutin A.
Sideband Peak Count in a Vibro-Acoustic Modulation Method for Crack Detection. *Acoustics*. 2022; 4(1):74-86.
https://doi.org/10.3390/acoustics4010005

**Chicago/Turabian Style**

Alnutayfat, Abdullah, Sophia Hassiotis, Dong Liu, and Alexander Sutin.
2022. "Sideband Peak Count in a Vibro-Acoustic Modulation Method for Crack Detection" *Acoustics* 4, no. 1: 74-86.
https://doi.org/10.3390/acoustics4010005