## 2 Description of the Systems Under Investigation and Experimental Setups
### Harmonic Vibration Testing
#### 4.3.2 RC Accelerometer  
Next, the effects of the central-cut width on the BARC system's dynamics are studied, with a particular focus on the RC accelerometer data. The first direction that is examined for the RC accelerometer is the Y-direction. These results will be closely compared to what was found in the random vibration data shown in Figure 12, with the goal of finding similar nonlinear trends, such as the nonlinear softening seen in each system. Again, only the first dominant peak will be investigated for this harmonic vibration study. Figure 18 depicts the results from the RC accelerometer Y-direction. Inspecting the plotted frequency response curves in this figure, it can be concluded that similar trends to the side-accelerometer Y-direction results are observed. It should be mentioned that the quality of the experimental data is much better in the Y-direction of the RC accelerometer compared to the side-accelerometer counterpart. Concerning the 0.5\({}^{\prime\prime}\) and 0.25\({}^{\prime\prime}\) configurations, it is clear from the plots in Figure 18a,b that nonlinear softening is present. This data can be more easily seen in Table 9, depicting the actual frequencies of each dominant peak associated with each system. Again, notice that the nonlinear softening decreases as the cut width decreases. This was a trend seen previously in Table 8. Focusing on the 0.1\({}^{\prime\prime}\) central-cut system, the resonant frequencies seem to almost experience nonlinear hardening  
Figure 17: A comparison of central-cut width configurations using the side accelerometer in the Y-direction for the 50 mV and 150 mV input excitation levels. \begin{table}
\begin{tabular}{c|c c c c} \hline  & **0.5\({}^{\prime\prime}\) Cut (Hz)** & **0.25\({}^{\prime\prime}\) Cut (Hz)** & **0.1\({}^{\prime\prime}\) Cut (Hz)** & **No Cut (Hz)** \\ \hline
**50 mV** & 102.7 & 100.8 & 100.8 & 155.3 \\
**100 mV** & 102.6 & 100.5 & 100.9 & 156.4 \\
**125 mV** & 102.5 & 100.4 & 101 & 156.5 \\
**150 mV** & 102.4 & 100.2 & 101.1 & 156.6 \\ \hline
**\% Change** & 0.29\% & 0.60\% & \(-\)0.30\% & \(-\)0.84\% \\ \end{tabular}
\end{table} 
Table 8: Resonant frequencies found from mode 1 through harmonic vibration testing using the side accelerometer in the Y-direction. but revert to 100.8 Hz. Again, the system with the most nonlinear softening is the 0.5\({}^{\prime\prime}\) cut system, while the system with the most nonlinear hardening is the no-cut system. It should be mentioned that the side accelerometer has more oscillations in the Y-direction, and hence, the activation of nonlinearity should be more significant. To truly determine how the central-cut width configurations compare to each other, a side-by-side comparison is shown in Figure 19 for the RC accelerometer in the Y-direction. Compare this to Figure 15b, where a similar comparison is shown for the random vibration data. Again, the 0.1\({}^{\prime\prime}\) cut data are between the 0.5\({}^{\prime\prime}\) and 0.25\({}^{\prime\prime}\) data, especially at the higher 150 mV excitation. It follows from the plots in Figure 19 that uncertainty in the estimation  
Figure 18: Harmonic vibration results from the RC Y-direction accelerometer from the (**a**) 0.5\({}^{\prime\prime}\) cut, (**b**) 0.25\({}^{\prime\prime}\) cut, (**c**) 0.1\({}^{\prime\prime}\) cut, and (**d**) no-cut BARC systems. \begin{table}
\begin{tabular}{|c|c c c c|} \hline  & **0.5\({}^{\prime\prime}\) Cut (Hz)** & **0.25\({}^{\prime\prime}\) Cut (Hz)** & **0.1\({}^{\prime\prime}\) Cut (Hz)** & **No Cut (Hz)** \\ \hline
**50 mV** & 102.7 & 100.8 & 100.8 & 155.2 \\
**100 mV** & 102.6 & 100.5 & 101 & 1556.4 \\
**125 mV** & 102.5 & 100.4 & 101 & 156 \\
**150 mV** & 102.4 & 100.2 & 100.8 & 156.1 \\
**\% Change** & 0.29\% & 0.60\% & 0.00\% & \(-\)0.58\% \\ \hline \end{tabular}
\end{table} 
Table 9: Dominant frequencies found from mode 1 through harmonic vibration testing using the RC accelerometer in the Y-direction.