## 2 Description of the Systems Under Investigation and Experimental Setups
### Random Vibration Testing
#### 4.2.3 Random Vibration Testing: Discussion on the Influence of the Central-Cut Width  
Table 7 shows a comparison of results between the random vibration data and the FEA, found by comparing results by looking at the responses from primarily the RC and side accelerometers in the Y- and Z-directions. These data were taken from the lowest input excitation since these data should minimize the nonlinear effects. It follows from the tabulated values in this table that the FEA results are a little higher than those of their random counterparts. Again, this is because FEA considers ideal conditions, and it is impossible to attain these conditions during testing. It should be mentioned that similar trends are observed in both tests. The frequency continues to decrease as the cut width decreases. These trends agree with data previously seen and discussed. Note that mode 2 of the no-cut case is not listed in the table because it is difficult to determine an accurate frequency at this low input excitation level. Figure 13: Random vibration results using the RC accelerometer in the Z-direction: (**a**) 0.5\({}^{\prime\prime}\) cut, (**b**) 0.25\({}^{\prime\prime}\) cut, (**c**) 0.1\({}^{\prime\prime}\) cut, and (**d**) no-cut BARC systems. In order to fully understand the influence that the central-cut width has on the dynamics of the BARC system, a comparison between all cut width configurations must take place. Of particular interest is the RC accelerometer, since it displays a lot of motion in all three directions, as shown in Table 2. A comparison of all central-cut width configurations for the side and RC accelerometers can be found in Figure 14 using the results for \(1\times 10^{-4}\) V\({}^{2}\)/Hz. This figure will be compared with the impact data to determine the influence of the central-cut width and to determine whether similar trends are seen in relation to peaks at certain modes by comparing the random vibration data to the mode shapes in Table 2. In comparing all systems with cuts, no mode switching is expected for the first six modes of vibration, according to the FEA, which is seen here in the random vibration data. This also agrees with what was seen in the impact data, as shown in Figure 8. Potential mode switching between the non-zero central-cut and no-cut configurations (mode 6 in the non-zero-cut configurations and mode 4 in the no-cut configuration) may occur in the systems, as previously discussed when analyzing the FEA. Finally, a direct comparison between all central-cut width configurations is presented in Figure 15 using the \(1\times 10^{-4}\) V\({}^{2}\)/Hz data from random testing for the side Y-direction, RC Y-direction, and RC Z-direction accelerometers. Trends similar to what was discussed previously are obtained, especially what was found in the tables depicting the frequencies of the dominant peaks (Tables 5-7). Especially in the second dominant peak, notice how as the central-cut width decreases from the 0.5\({}^{\prime\prime}\) cut case, the frequency decreases. In addition, it follows from the plots in Figure 15 that the 0.1\({}^{\prime\prime}\) cut system has the highest amplitude, while the 0.5\({}^{\prime\prime}\) cut system has the lowest amplitude when looking at the second dominant peak. This trend is similar for other accelerometers and directions, so for brevity, they are