# Comparing Bol Implementation Methods in Vibration Testing for Accurate Dynamic Behavior Analysis
## 4 Discussion  
This study analyzed the natural frequencies, mode shapes, and efficiency of various bolt implementation methods in a vibration test jig to propose the optimal connection method. To this end, the natural frequency and mode shape of the vibration test jig applied with six-bolt connection methods were compared to the natural frequency (493.2 Hz) derived from the Top Head in an actual vibration experiment. The joint connection method was found to produce the results most similar to the vibration test, with a difference of only 7.6 Hz, indicating high accuracy. Through the results of this study, the discrepancy between vibration test results and bonded connection analysis was quantitatively assessed. The bonded connection method showed a natural frequency of 544.1 Hz, approximately 10.3% higher than the vibration test result (493.2 Hz). This is because the bonded contact exhibits greater stiffness than the bolt connections. Whereas bolt connections only connect specific points with gaps between joint surfaces, bonded connection assumes complete bonding between nodes, resulting in stronger coupling [35]. Therefore, although the bonded connection method is effective for simulating welded connections, it has limitations in representing the dynamic characteristics of bolt connections. To determine whether the proposed bolt connection methods could simulate actual bolts, the differences in natural frequencies among the connection methods were examined. The two types of connections differed in structural stiffness, with bolt connection methods (except for fixed bolts) exhibiting relatively lower natural frequencies than bonded connections. This is because, unlike bonded connections, bolt connection methods involve smaller contact areas and account for nonlinear behavior in their coupling characteristics [36]. Additionally, the fixed bolt method exhibited a natural frequency of 881.9 Hz, which was 337.8 Hz higher than the natural frequency of 544.1 Hz for the bonded connection. This is because the fixed bolt method was based on Inspire's functionality, which treats the bolt head and endpoints of the threads as fixed points, restricting displacement and rotation degrees of freedom at both points. In other words, the fixed bolt method exhibits excessive rigidity, making it unsuitable for reproducing the dynamic characteristics of actual bolts. However, the fixed bolt method can be effectively utilized in designs requiring maximum structural coupling rigidity, such as heavy equipment, bridge structures, or stationary machinery. A comparison of the modes among the analyzed bolt connection methods showed that the bonded connection method exhibited a global mode where the entire jig moved, while the bolt connection methods (except for the joint method) showed local modes with maximum deformation occurring in the ribs. This is because bolt connection methods have insufficient contact area and bonding strength, with nonlinear behavior influencing vibration characteristics [37; 38; 39]. On the other hand, the joint method, similar to the bonded connection, exhibited a global mode where the entire jig moved. This is because the joint method, based on ANSYS's joint functionality, rigidly connects two surfaces or points, providing high contact stiffness. As a result, relatively high contact stiffness in the rib connections occurs, effectively dispersing vibrations in local areas. Therefore, the \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Bonded** & **Adaptive Bonded** & **Joint** & **Beam** & **Screw** & **Fixed Bolt** \\ \hline Average time required & & & & & & \\ preprocessing [s] & 30 & 6000 & 6000 & 3000 & 30 & 30 \\ CP Time [s] & 95 & 598 & 97 & 345 & 209 & 274 \\ Memory usage [MB] & 37,393 & 35,731 & 32,671 & 30,044 & 25,590 & 25,985 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of preprocessing time, analysis time, and memory usage for different bolt connection methods.