## 4 Booming Noise Reduction
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Parameters Doubled in Value**} & \multirow{2}{*}{**Mode No.**} & \multicolumn{2}{c}{**Natural Frequency (Hz)**} \\ \cline{3-4}  & & & **Simulation Results** & **Difference** \\ \hline \multirow{3}{*}{\(1\)} & [PERSON]’s modulus of the structurally & 1 st & 21.6 & 0.1 \\  & weak area of the inner panel & 2 nd & 28.1 & 0.3 \\  & weak area of the inner panel & 3 rd & 34.7 & 0 \\ \hline \multirow{3}{*}{\(2\)} & \multirow{3}{*}{Young’s modulus of the outer panel.} & 1 st & 22.2 & 0.7 \\  & & 2 nd & 29.4 & 1.6 \\  & & 3 rd & 36.1 & 1.4 \\ \hline \multirow{3}{*}{\(3\)} & \multirow{3}{*}{Guide bumper stiffness} & 1 st & 21.5 & 0 \\  & & 2 nd & 30.2 & 2.4 \\ \cline{1-1}  & & 3 rd & 39.3 & 4.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Increases in the natural frequencies when the tailgate model parameters are doubled. Figure 16: Structurally weak area of the inner panel (indicated by the dotted lines). aligning with the findings in Section 2. Instead, attention should be given to the significant 2.4 Hz increase in the second natural frequency, which has the potential to contribute significantly to booming noise. A comparison with other cases highlighted the need to develop improvement strategies based on this increase. Second, comparing the changes in the natural frequencies in the model when [PERSON]'s modulus of the entire outer panel was increased (as shown in Table 4), the first, second, and third natural frequencies of the tailgate increased by 0.7, 1.6, and 1.4 Hz, respectively. It was feasible to expect an effect here due to an increase in the second natural frequency. Finally, when examining the changes in the first, second, and third modes of the tailgate owing to an increase in [PERSON]'s modulus of the structurally weak area of the inner panel (as shown in Table 4), the effects of the modulus increase were found to be minimal, contrary to expectations. Summarizing the specific improvement strategies for the tailgate, considering the impact of the analyzed key design factors, the following points can be noted. First, increasing the stiffness of the guide bumper can be effectively implemented by increasing its contact area, providing a corresponding effect without the need for complex changes in the components' properties or significant alterations in the design. On the other hand, increasing [PERSON]'s modulus of the outer panel improved the first and second modes. However, practically doubling [PERSON]'s modulus of the entire outer panel, which would require drastic changes in the panel's properties or thickness, is unrealistic because of concerns regarding increases in the cost and weight. Additionally, the outer panel is associated with the tailgate spoiler, lamps, and garnish and contributes to the overall design of the vehicle's rear. Consequently, implementing improvements using features such as reinforcements similar to the inner panel is challenging due to various design constraints. Because applying improvement measures to the outer panel presents difficulties, a viable approach would be to focus on design changes near the central area of the inner panel, which is relatively free from design constraints within the vehicle. However, based on previous analysis results, increasing the Young moduli in this area did not result in a significant improvement. Therefore, alternative solutions are required to address this issue. Furthermore, we analyzed the changes in natural frequencies of the tailgate when the inner panel shape shown in Figure 17a was modified to the shape shown in Figure 17b. The modified shape was obtained by introducing the form of a long horizontal rectangle located at the bottom, where deformation occurred in the tailgate modes. This shape, which fills some of the existing holes in the inner panel, connects the previously disconnected parts of the panel horizontally, thereby enhancing the stiffness of the panel against bending.