## 3 Dynamic Modeling
### Tailgate Model Mounted on the Vehicle  
After successfully validating the tailgate model under free-free conditions, the final version was developed by incorporating the connecting components with the actual vehicle. In the previous section describing the tailgate structure, various connections and their functions between the vehicle and the tailgate were detailed. In summary, from the top to the bottom of the tailgate are the hinges, gas lifts and spindles, guide bumpers, over-slam bumpers, and latches. Additionally, there is a weather strip that wraps around the entire contact surface between the tailgate and the vehicle body. Determining the specific method to apply this in the final model requires careful consideration. These boundary conditions can be broadly classified into two categories based on their characteristics. By evaluating their impact using these attributes, it is possible to simplify the boundary conditions and achieve efficient modeling. It is conceivable to consider models that encompass all of the various structures between the vehicle body and the tailgate; using a model with numerous parts for analysis can demand excessive time and might pose challenges for practical use in the intermediate stages of the design process, diminishing the utility of the model. Hence, simplification is feasible within limits that do not compromise the accuracy of the model, thereby maximizing the advantages of the model. From this perspective, when categorizing the boundary conditions, the essential elements for the tailgate attachment include hinges and latches. The remaining components, such as gas lifts, spindles, guide bumpers, over-slam bumpers, and weather strips, can be utilized considering their detachability. Following the procedures outlined in Section 2, the influence of these components was compared and analyzed. It was experimentally determined that among the various structures connecting the tailgate and the vehicle, the guide bumper significantly influenced the dynamic characteristics of the tailgate. In addition, within a range that did not significantly compromise the accuracy of the model, other elements were simplified or excluded to simplify the boundary conditions. A foundation was then established for modeling, with the guide bumper as the focal point. Considering these results, the final tailgate model, validated through previous experiments under free-free conditions, was completed in the form of a tailgate model with an attached guide bumper. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mode No.**} & \multicolumn{3}{c}{**Natural Frequency (Hz)**} \\ \cline{2-4}  & **Simulation** & **Experiment** & **Difference** \\ \hline
1 st & 20.8 & 19 & \(-\)1.8 \\
2 nd & 36.0 & 36 & 0 \\
3 rd & 44.0 & 45 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the natural frequencies obtained via the simulation and experiment under free-free boundary conditions. Figure 13: Mode shapes of the tailgate under free-free boundary conditions: (a) 19.1 Hz; (b) 35.7 Hz; and (c) 45.2 Hz. As shown in Figure 14, the guide bumper consists of parts connected to the vehicle body and the tailgate. The portion connected to the vehicle body is composed of steel, fixed to the body, and surrounded by rubber. The section attached to the tailgate is made of plastic. Before simplifying the intricate structure of the guide bumper, a local coordinate system was defined based on the guide bumper, as shown in Figure 14d. Given the impact of the guide bumper's structure on the dynamic characteristics of the tailgate, our strategy for simplifying the intricately shaped guide bumper while considering the elements affecting the tailgate's dynamic behavior is outlined as follows.