## 2 Description of the Systems Under Investigation and Experimental Setups  
The objective of this study is to investigate how changing the central-cut width affects the linear and nonlinear properties of the BARC system. This kind of investigation should be performed in order to determine whether any geometric uncertainty in the design and/or manufacturing of the box assembly's central cut may influence the overall responses of the system. This investigation was performed by looking at the influence the accelerometers and removable components have on each system's dynamics. Four total BARC assemblies were considered, beginning with the standard 0.5\({}^{\prime\prime}\) cut BARC, a 0.25\({}^{\prime\prime}\) cut BARC, a 0.1\({}^{\prime\prime}\) cut BARC, and a BARC with a 0\({}^{\prime\prime}\) cut, designated as the no-cut system. Each of these assemblies had computational simulations run on them and were also experimented on using impact testing, random testing, and harmonic testing. Each system is shown in Figure 1 as a computer-aided design (CAD) model from Dassault Systemes SOLIDWORKS. These CAD models helped aid in the finite element analysis (FEA) performed on each system by using 3 DExperience ABAQUS software (3 DEXPERIENCE R2023x, Dassault Systemes). FEA is a powerful tool allowing researchers to determine frequency ranges that should be focused on during experimentation. FEA also gives reliable mode shapes to consider during the testing and post-processing of experimental data. In order to give the best replication of each system, numerical simulations that consider the systems with an accelerometer and without an accelerometer were considered and compared. Three accelerometers weighing 6.3 g each were placed in various locations on the physical BARC  
Figure 1: Computer-aided design (CAD) models of each BARC system: (**a**) 0.5\({}^{\prime\prime}\) cut, (**b**) 0.25\({}^{\prime\prime}\) cut, (**c**) 0.1\({}^{\prime\prime}\) cut, and (**d**) no cut. systems in locations that are expected to have high oscillating responses from different modes [13; 26]. In order to replicate the accelerometers in the FEA, the accelerometers were modeled within the FEA and placed in the same locations as they would be on the physical BARC system during experimental testing. The accelerometers are designated as \"top\", \"side\", and \"RC\" and pictured in Figure 2.  
FEA was conducted using a frequency-step analysis, restricted in the X-, Y-, and Z-directions (with the coordinate system shown) within the holes of the baseplate of the BARC in both the translational and rotational frames. The bolts on the removable component were modeled using virtual bolts. Virtual bolts mimic the same configuration as the stick configuration, where the contact faces between the C-channel and the top beam and the C-channel and the box assembly are rigidly coupled [13; 30]. As [PERSON] et al. [30] mentioned, the shared faces between the components are stuck together. When considering an unrestrained case (which this study did not consider), the faces are free to detach from each other since they are not coupled together. By using the stiffer stick configuration, the computationally found natural frequencies tend to be higher than when using the less stiff unrestrained configuration. Stick configuration modeling more accurately represents the conditions expected in the laboratory setting and was therefore used in this work. It should be noted that the modeling of the bolted-joint connection is not in the scope of this study. After FEA was carried out on the systems under consideration, the BARC structures were assembled for laboratory testing. The joints of the BARC systems were fastened using hex screws in an alternating formation/pattern, as shown in Figure 3. The alternating pattern allows for a better distribution of pressure along the joint. The screws were torqued to a 20-inch-lbs specification into the box assembly, while the bolts attaching the bar to the C-brackets were torqued to a specification of 30 inch-lbs.