## 2 Description of the Systems Under Investigation and Experimental Setups
### Random Vibration Testing
#### 4.2.2 RC Accelerometer  
As shown in the impact testing results, the RC accelerometer data should be more useful in examining the influence of the central-cut width on the dynamical characteristics of the system due to its capability to clearly detect oscillations in the X- and Z-directions. The plotted curves in Figure 12 show the results from random vibration when four levels of input excitation are considered. Again, it follows from these plots that nonlinear softening is present. As the input excitation increases, the peak frequencies decrease. This is true \begin{table}
\begin{tabular}{c|c c c c c c c} \hline  & \multicolumn{2}{c}{**0.5\({}^{\prime\prime}\) Cut (Hz)**} & \multicolumn{2}{c}{**0.25\({}^{\prime\prime}\) Cut (Hz)**} & \multicolumn{2}{c}{**0.1\({}^{\prime\prime}\) Cut (Hz)**} & \multicolumn{2}{c}{**No Cut (Hz)**} \\  & **Mode 1** & **Mode 2** & **Mode 1** & **Mode 2** & **Mode 1** & **Mode 2** & **Mode 1** \\ \cline{2-8}
**1 \(\times\) 10\({}^{-7}\) V\({}^{2}\)/Hz** & 106.25 & 285.156 & 101.562 & 279.297 & 101.172 & 275.781 & 155.078 \\
**1 \(\times\) 10\({}^{-6}\) V\({}^{2}\)/Hz** & 104.297 & 284.766 & 101.172 & 278.516 & 101.562 & 275.391 & 149.609 \\
**1 \(\times\) 10\({}^{-5}\) V\({}^{2}\)/Hz** & 103.125 & 283.984 & 99.609 & 277.344 & 101.172 & 274.609 & 148.047 \\
**1 \(\times\) 10\({}^{-4}\) V\({}^{2}\)/Hz** & 101.562 & 283.594 & 98.828 & 276.172 & 99.609 & 274.609 & 153.516 \\
**\% Change** & 4.41\% & 0.55\% & 2.69\% & 1.12\% & 1.54\% & 0.42\% & 1.01\% \\ \hline \end{tabular}
\end{table} 
Table 5: Dominant peaks found from mode 1 and mode 2 of the side accelerometer through random vibration testing in the Y-direction. especially in the lower modes, as seen previously with the side accelerometer, but, in this instance, it is more evident in the higher modes as compared to the Y-direction of the side-accelerometer results. Since the peaks are around 100 Hz, 275 Hz, and 300 Hz (a smaller peak), it is reasonable to assume that these modes are mode 1, mode 2, and mode 3 based on the FEA found in Table 3. Notice that the quality of data in the no-cut case is not as high as it is in the other cut cases. This adds some uncertainty when analyzing the data, and that is seen when looking at the results in Table 6.  
An investigation into the \(Z\)-direction took place for the RC accelerometer to determine the presence of potential coupling between the box assembly and the removable component, evidence of which has already been observed in the Y-direction section of this study. The random vibration results from the RC accelerometer in the Z-direction are shown in Figure 13. Referring to Tables 2 and 3, it can be reasonably assumed that the dominant peaks around 100 Hz and 275 Hz are mode 1 and mode 2, since the RC accelerometer moves in the Z-direction and the frequencies found in random testing are similar to those \begin{table}
\begin{tabular}{c|c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**0.5\({}^{\prime\prime}\) Cut (Hz)**} & \multicolumn{2}{c}{**0.25\({}^{\prime\prime}\) Cut (Hz)**} & \multicolumn{2}{c}{**0.7\({}^{\prime\prime}\) Cut (Hz)**} & \multicolumn{2}{c}{**No Cut (Hz)**} \\  & **Mode 1** & **Mode 2** & **Mode 1** & **Mode 2** & **Mode 1** & **Mode 2** & **Mode 1** \\ \hline \(\mathbf{1\times 10^{-7}}\)**V\({}^{2}\)/Hz** & 106.641 & 284.766 & 101.562 & 278.906 & 102.344 & 275.781 & 154.688 \\ \hline \(\mathbf{1\times 10^{-6}}\)**V\({}^{2}\)/Hz** & 104.297 & 284.375 & 101.172 & 278.125 & 101.562 & 275.391 & 150.0 \\ \hline \(\mathbf{1\times 10^{-5}}\)**V\({}^{2}\)/Hz** & 103.125 & 283.594 & 99.609 & 276.953 & 100.781 & 274.219 & 153.516 \\ \hline \(\mathbf{1\times 10^{-4}}\)**V\({}^{2}\)/Hz** & 101.172 & 281.641 & 99.219 & 275.0 & 100.0 & 273.828 & 153.906 \\ \hline \% Change & 5.13\% & 1.10\% & 2.31\% & 1.40\% & 2.29\% & 0.71\% & 0.51\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Dominant peaks found from mode 1 and mode 2 of the RC accelerometer through random vibration testing in the \(Z\)-direction.