## 3 Dynamic Modeling
### Tailgate Model with Free-Free Boundary Conditions
Similarly, the spoiler and taillight cover was constructed with a model similar to the actual tailgate, using the corresponding masses specified in the design requirements. Each modeling element of the tailgate was applied with appropriate bonding conditions to reflect the actual structure. Before combining the inner panel with the outer panel or the outer panel with the glass, suitable bonding conditions were defined for the inner panel and reinforcements to account for their effects. As described in Section 2, the inner panel of the tailgate, with various structures for connection to the vehicle body, employs a thin panel form. Additional reinforcements were added to each structure connected to the vehicle body to reinforce the rigidity of the thin inner panel of the tailgate and reduce panel deformation. These structures include hinge reinforcements at the top of the tailgate, gas lift/spindle reinforcements, guide bumper reinforcements, and latch reinforcements at the bottom. During the actual modeling process, the modal analysis results for the panels showed significant differences in the natural frequencies and modes of the tailgate based on the presence or absence of reinforcements. Therefore, appropriate modeling of the interaction between the inner panel and the reinforcements is crucial. The reinforcements are welded to the edges of the inner panel. To reflect this, the bonding condition is imposed between the reinforcements and the inner panel (Figure 11). The inner panel, strengthened with reinforcements, is connected to the outer panel using two different techniques: hemming and spot welding. The outer and inner panels are joined along their outer edges using hemming, allowing relative motion between the panels. To appropriately model this, a condition of no separation was applied, allowing relative movement between the panel surfaces. At the inner boundaries of the panel, where hemming and spot welding were used for strong bonding, a bonded condition suitable  
Figure 11: Inner panel and reinforcement assembly with bonded contact. for welding was applied (Figure 12). The tailgate glass was strongly bonded to the outer panel using a structural adhesive along their boundaries. To represent this, the bonding condition was applied to the interface between the glass and the outer panel. Additionally, the spoiler, occupying a large area on the top of the tailgate, and the taillight covers, which extended horizontally to the bottom of the glass, were bonded in their respective positions, creating the tailgate model. Modal experiments were then conducted on the tailgate to validate the constructed model when the tailgate was suspended freely at the left and right hinge points to create a free-free condition. Near the hinges, the presence of plastic spoilers and garnishes rendered localized deformations unrelated to the structural rigidity of the tailgate panel, so to capture the overall mode shape of the tailgate, the modal tests were conducted from the glass surface below the spoiler. Following the methodology shown in Figure 8 of the previous section, accelerometers were attached to the glass, and 50 points marked with red dots were impacted with the impact hammer to obtain the FRFs. These measurements were then used to extract the mode shapes of the tailgate. The results from the tailgate experiments under free-free conditions were compared with the analytical results to validate the tailgate model. From the experiments, the natural frequencies under free-free conditions were confirmed to be 19.1, 35.7, and 45.2 Hz (Figure 13). At 19.1 Hz, the lower sides of the tailgate exhibited torsional behavior in a direction perpendicular to the surface of the tailgate, while at 35.7 Hz, bending shapes were observed on the lower and lateral parts of the tailgate.