## 5 Discussion  
The increase in natural frequencies using key design parameters of the tailgate is related to the fore-aft behavior of the tailgate, which induces booming noise. Firstly, increasing the stiffness of the tailgate guide bumper reduces the booming noise level by suppressing the rigid-body behavior in the fore-aft direction, thereby inhibiting the related natural vibration modes. Additionally, improvements such as increases in the outer panel's stiffness and structural modifications near the lower central part of the inner panel, where deformation dominantly occurs, reinforce the stiffness of vulnerable regions in the deformation modes of the tailgate. This, in turn, reduces the booming noise caused by the tailgate.  
Comparing the results of our random vibration analysis with the first and second natural modes of the tailgate yields important findings. Figure 18b, in which the red color represents a large deformation, shows the deformed shape of the tailgate. It is observed in this figure that the central lower part of the tailgate has the maximum deformation. This is closely related to the second mode shape of the tailgate. Therefore, structural improvements to the inner panel, which can directly affect the region in which deformation predominantly occurs, are effective. As observed earlier, these improvements significantly increased the second natural frequency when compared to the first natural frequency. On the other hand, considering the guide bumper's proximity to the upper part of the tailgate, it can be expected that applying direct structural improvements may not have a significant impact on reducing the deformation occurring in the lower part. This expectation was confirmed through our analysis results.  
On the other hand, the behavior related to the third mode of the tailgate is unrelated to the occurrence of booming noise, as observed in Section 2. According to the mechanism of booming noise, the tailgate generates noise by compressing and expanding the vehicle cabin in the fore-aft direction, causing changes in air pressure. However, in the frequency associated with this mode, the results from road tests, ODS analysis, EMA, and various other experimental findings, analyzed collectively, indicate that the overall behavior of the tailgate shows characteristics of torsional deformation. Based on this observation, it can be concluded that such behavior does not generate booming noise.  
When compared to other studies, our proposed solutions for the tailgate model, as presented in Section 4, may be somewhat lacking in terms of their quantitative effectiveness. However, the distinctiveness lies not only in providing potential improvements through analyzing the impact of parameters constituting the system and utilizing them for practical applications, but also in avoiding the complexity and cost escalation associated with using additional systems. By modeling only essential targets and offering a simplified model through reasonable simplifications, the utility of the model is increased, enabling an improved problem-solving process compared to previous approaches.  
Analyzing the primary behaviors of the tailgate based on experimental data and utilizing a simplified tailgate model focused on essential aspects has several advantages compared to existing methods. If a model reflects key elements and allows for the analysis of dynamic characteristics, it becomes possible to analyze booming noise in an environment similar to actual vehicle conditions. Furthermore, by utilizing a model with a high utility in the early design stages compared to other existing ones, it becomes feasible to analyze and evaluate booming noise in advance, allowing for design considerations. Additionally, rather than using additional systems such as sound absorbers, which have been widely employed in previous research efforts, to address booming noise caused by the tailgate, this study extracts key design factors through analyzing the characteristics of parameters constituting the tailgate system.