## 3 Results and Discussion
### Discussion
The passage between the two holes has relatively poor deformation intensity. Figure 12 clearly and concisely illustrates how the sheet metal model with a V-shaped notch is less affected than the first two models. Specifically, the worst deformation only occurs on a small amount on both sides of the model's corners. According to the sheet metal model, the center and whole of the model have better deformation due to the force distribution from the notches from two sides. The results indicate that the sheet metal model with a V-shaped notch is the most effective, as shown in Figure 13.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mode Shape**} & \multicolumn{3}{c}{**Natural Frequency (Hz)**} \\ \cline{2-4}  & **Virgin** & **Hole** & **V-Notch** \\ \hline
**1** & 11.290 & 10.791 & 11.103 \\
**2** & 30.998 & 29.893 & 31.598 \\
**3** & 69.777 & 66.958 & 66.780 \\
**4** & 109.030 & 105. In this section, we will delve into the findings of an experimental prototype kit that boasts the remarkable ability to read natural frequencies. For our study, we selected three different specimens, namely the full rectangular plate, the V-shaped plate, and the perforated plate, and conducted thorough vibration tests on each. By employing an accelerometer and force sensor through Simulink as shown in Figure 14, we could accurately plot the relationship between frequency and time and force and time. To further analyze our results, we compared the natural frequencies obtained from the FE model and utilized them to make behavioral predictions [52]. By doing so, we could anticipate initiating internal damage and fracture of carbon steel during the behavioral analysis. We  
Figure 12: Natural frequencies of low carbon steel material on different models. Figure 13: Contours of total deformation from mode 5 V notch. utilized a frequency testing machine equipped with an accelerometer and force sensor through Simulink to test carbon steel vibrations on the above three workpieces. During the test, we set the force range to 20-25 Newtons and carefully collected the frequency when the vibration was stationary. These results have been instrumental in enhancing our understanding of the behavior of carbon steel under varying conditions and will undoubtedly serve as a valuable resource in future studies. The unilaterally reinforced perimeter conditions of [PERSON] et al. (2018) and [PERSON] et al. (2019) have consistent results with both studies, as shown in Table 7.  
Determining the modal constraint frequency of a workpiece is a complex process that involves various factors. These factors include the positional characteristics of grooving and the workpiece's geometric parameters and material properties. In Table 8, experimental data are compared with the FE model to obtain accurate results, allowing for a comparison of natural frequencies. The research findings indicate that the experimental natural frequency and FE modeling were similar across modes 1-4, with an average tolerance of 1.47%. Moreover, the vibration values of workpiece distortion in various modes were also found to be comparable. Although modes 5-7 had higher workpiece values, the difference of 5.538% between the experimental natural frequency and FE modeling was considered acceptable, as it did not significantly affect the overall accuracy of the results. The results are consistent with the research of [PERSON] et al. (2018). Moreover, [PERSON] et al. (2018) \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mode Shape**} & \multicolumn{3}{c}{**Natural Frequency (Hz)**} \\ \cline{2-4}  & **Virgin** & **Hole** & **V-Notch** \\ \hline
**1** & 10 & 11 & 11 \\
**2** & 39 & 33 & 49 \\
**3** & 65 & 46 & 59 \\
**4** & 98 & 95 & 107 \\
**5** & 121 & 109 & 137 \\
**6** & 189 & 195 & 202 \\
**7** & 225 & 213 & 278 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Natural frequencies of low carbon steel experiment.