## 3 Results and Discussion
This second frequency peak is not affected by changes in defect size. This may be explained by the fact that our defect is placed on the neutral line, which has no major impact on frequency. This suggests that Peak 2 may be related to the location of the defect, which had no real impact on Peak 2's frequency. In contrast, defect  
Figure 11: Effect of damping on defect square size. Figure 10: Variation in frequency peak with defect square size. detection is more pronounced at the amplitude of the second peak. At this point, the data obtained remain consistent with bending behavior. Nevertheless, amplitude variations allow us to formulate a complementary hypothesis concerning the possible intervention of an additional stress mode such as torsion or a combination of the two. As the defect size rises, nonetheless, the amplitude of Peak 2 typically decreases. Another explanation is that larger defects (7 and 10 mm) exhibit delamination around the edges of the defect, which generates internal friction, creating a local loss of energy and therefore a loss of amplitude. In order to analyze the contribution of each vibration peak to the overall signal and amplitude and their impact on defect size, the sum of the peak frequencies and the integrated amplitude of these two peaks are presented in Table 7. Specifically, the total values of Peak 1 and Peak 2 show that the no-defect samples have a higher integrated amplitude of 583.826 \(\times\) 10\({}^{3}\) Hz.mV and a lower combined peak frequency of 1466.16 Hz. As there are no internal losses, acoustic waves propagate without being reflected, scattered, or absorbed. As a result, the structure retains all its energy, resulting in a low peak frequency and maximum integral amplitude. Samples with 7 and 10 mm defects, on the other hand, have a lower integrated amplitude values and higher sum of peak frequencies values. This indicates that concentrating vibrations on a smaller zone enhances the modal frequency detected. Moreover, for a smaller integrated amplitude, concentration in a reduced area minimizes the displacement of the normal surface and the energy transmitted to the air, resulting in a lower acoustic amplitude. Figure 12: _Cont._  
* Vibration detector  
Average values of peak frequency and damping, as well as their standard deviations, in relation to defect size, are presented in Table 8. A 3 mm defect shows an enhanced peak frequency. This suggests that local hardening results in little radiation disturbance and therefore elevated peak frequencies. Samples free of defects also show a higher damping value and lower frequency peak. This is due to internal manufacturing stress, which slows down vibration compared to defective parts. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Defect Size**} & \multicolumn{3}{c}{**Acoustic**} \\ \cline{2-4}  & \multicolumn{2}{c}{**Sum of Peak Frequencies**} & \multicolumn{2}{c}{**Integrated Amplitude**} \\  & \multicolumn{2}{c}{**(Hz)**} & \multicolumn{2}{c}{**(Hz.mV)**} \\ \hline No defect & 1466.16 & 583.826 \(\times\) 10\({}^{3}\) \\
3 mm & 1495.96 & 542.406 \(\times\) 10\({}^{3}\) \\
5 mm & 1489.85 & 577.280 \(\times\) 10\({}^{3}\) \\
7 mm & 1500.54 & 538.052 \(\times\) 10\({}^{3}\) \\
10 mm & 1502.06 & 542.079 \(\times\) 10\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sum of peak frequencies and integrated amplitude for different defect sizes. Figure 12: Comparison of the MATLAB-calculated average FFT spectra of three samples with various internal defects. Figure 13 shows the peak frequency as a function of the defect size in the flexion test. The results display that the vibration sensor detects defects as small as 3 mm, where a frequency of 1436.66 Hz is recorded, indicating that there is a high detection threshold for identifying internal defects associated with local hardening.