# Effects of Central Cut Width on the Dynamical Characteristics of Box Assembly Structure
## 2 Box Assembly Configurations and Experimental Techniques  
To investigate the effects of the width of the central cut of the BA structure on the dynamical responses of the system, four configurations of the central cut were considered, as presented in Figure 1. These configurations included the original BA structure with a 0.5\" cut shown in Figure 1a, and three modified designs (Figure 1b-d), namely, BA with a 0.25\", 0.1\", and 0\" central cut. The 0\" central cut was named as no-cut configuration, as shown in Figure 1d. The three width cut cases of 0.5\", 0.25\", and 0.1\" can be seen as input uncertainties in the design and manufacturing of the box assembly system. To gain a further understanding of the influence of the central cut on the dynamics of the box assembly systems under investigation, finite element analysis (FEA) was carried out through the 3 DEperience's ABAQUS software (3 DEXPERIENCE R2023x, Dassault Systemes). The computational outcomes from FEA are valuable and can be used as a reference for the identification of the linear properties (natural frequencies and mode shapes) of the systems under consideration. This is beneficial in terms of guiding the experiments, particularly harmonic testing, to be performed near resonances where most of the important characteristics can be identified. Because two accelerometers were attached to the box assembly in the experimental measurements, it was important to computationally model the accelerometers in their specific locations so a better quantitative comparison could be performed between the FEA and experimental results. For this reason, finite element simulations were conducted on both assembly systems with and without accelerometers. For the FEA with the presence of accelerometers, two accelerometers weighing 6.3 g each were placed on every system in the respective locations as in the experiments, as shown in Figures 2 and 3. These accelerometers are defined as the \"top\" and \"side\" accelerometers for the remainder of this study. Previous research in the literature, as well as FEA, have shown these locations for the accelerometers to be the ideal locations to capture high dynamic responses of the system [24]. A structural simulation was selected to focus on purely the structural dynamics of the system. Next, a mesh was manually initialized in the software. A tetrahedron mesh was selected with the initial elements of 10 mm and of quadratic order. The order allows for an additional node between the standard vertices used in a tetrahedron model. A sag  
Figure 1: Box assembly configurations under consideration: (**a**) 0.5” cut, (**b**) 0.25” cut, (**c**) 0.1” cut, and (**d**) 0” cut. ratio of 0.1 was selected to minimize the distance between the elements and the edge of the model. Then, this finite element model (FEM) was subjected to a frequency step analysis. Restrictions were imposed on the translation in X-, Y-, and Z-directions within the holes of the BA's base plate. A mesh convergence analysis was carried out by iteratively reducing element size and maintaining a sag ratio of about an order of magnitude. It was determined that 400,000 elements are enough to accurately estimate the natural frequencies and mode shapes of the box assembly systems. The dominant frequencies of the box assembly systems under consideration were estimated through a free vibration test by hitting the system with a modal impact hammer with a blue soft tip. In order to excite the first mode of each system, the BA was impacted in the Y-direction, as indicated in Figure 2. It should be mentioned that spacers were used at the bolted connections on the base of each system to accurately explore the dynamics of the systems with the considered set of boundary conditions [24]. In fact, the inclusion of the space nuts prevented any interference between the box assembly base motion and the table holding it. In this way, the box assembly could freely vibrate beyond the horizontal plane.