## 2 Description of the Systems Under Investigation and Experimental Setups
### Free Vibration Testing
#### 4.1.3 Free Vibration Testing: Discussions on the Influence of the Central-Cut Width  
A comparison of the FEA and impact frequencies is shown in Table 4, giving valuable insight into how all the frequencies compare to one another. Notice that the impact testing data are consistently lower than what was found in the FEA, especially as the frequencies increase. This is because the FEA considers ideal conditions, and, although conditions can be as near ideal as possible, nothing will match the precision of computational analysis. Indeed, the FEA simulations considered the stiffest representation for the boundary conditions and bolted-joint connections. Further work should be conducted on accurately modeling bolted-joint connections, which is not in the scope of this study. It should be mentioned that the idealistic considerations of FEA have been extensively studied by [PERSON] et al. [33]. Nonetheless, there is still significant confidence in the results. Some takeaways from this table include that a higher frequency is seen for the no-cut system. This is expected since that is the most rigid system. Further, it can be observed that the 0.25\({}^{\prime\prime}\) cut system shows higher frequencies as compared to the other two cut systems, namely, 0.5\({}^{\prime\prime}\) and 0.1\({}^{\prime\prime}\). This trend will be considered when analyzing data from random vibration testing. In order to understand the importance of each accelerometer in characterizing the dynamics of the BARC system, a comparison of the locations is shown in Figure 9. This depicts the strength of each response from the respective accelerometer, showing how different responses are stronger at different locations on the BARC system under investigation and how the choice of the location of the accelerometer or measurement is important and may change the characterization of complex coupled systems, such as the BARC system. For example, looking at Figure 9c, there are dominant peaks around 250 Hz and 275 Hz. These peaks are most distinct when looking at the RC accelerometer in the Z-direction. Indeed, the top and side accelerometers are mostly useful for movement in the Y- and X-directions, depending on the mode of vibration. Similar trends are shown for other dominant peaks in the other directional plots. Focusing on the third mode of vibration near 275 Hz, it is clear that the top and RC accelerometers have similar behaviors in the X-direction, as presented in Figure 9a. Indeed, it is clear from the mode shape of this third mode that both accelerometers have similar motion in the X-direction. On the other hand, these top and RC accelerometers do not have similar motion in the Y- and Z-directions near mode 3 due to the coupling between the removable component and the box assembly, as \begin{table}
\begin{tabular}{c|c c c c c c c c} \hline  & \multicolumn{2}{c}{**0.5\({}^{\prime\prime}\) Cut**} & \multicolumn{2}{c}{**0.25\({}^{\prime\prime}\) Cut**} & \multicolumn{2}{c}{**0.1\({}^{\prime\prime}\) Cut**} & \multicolumn{2}{c}{**No Cut**} \\ \cline{2-9}  & **Impact** & **FEA** & **Impact** & **FEA** & **Impact** & **FEA** & **Impact** & **FEA** \\ \hline
**Mode 1** & 93.75 & 106.89 & 96.875 & 105.63 & 92.5 & 104.7 & 148.03 & 165.29 \\
**Mode 2** & 248.44 & 290.87 & 265.63 & 287.58 & 257.5 & 284.38 & 337.99 & 395.39 \\ \hline
**Mode 3** & 275.0 & 331.63 & 293.75 & 322.34 & 266.25 & 314.27 & 544.0 & 649.25 \\ \hline
**Mode 4** & 328.13 & 379.11 & 343.75 & 364.3 & 315.0 & 353.89 & 660.04 & 728.92 \\ \hline
**Mode 5** & 398.44 & 450.47 & 390.63 & 443.72 & 386.25 & 438.09 & 742.97 & 846.72 \\ \hline
**Mode 6** & 448.44 & 511.62 & 453.13 & 493.46 & 431.25 & 480.92 & - & 1073.2 \\ \hline \end{tabular}
\end{table} 
Table 4: A comparison of dominant frequencies found using FEA and impact testing. shown in Table 2 and Figure 9b,c. For brevity, only the 0.5\({}^{\prime\prime}\) cut system is shown, since all other BARC systems show similar trends.