# Comparing Bol Implementation Methods in Vibration Testing for Accurate Dynamic Behavior Analysis
## 3 Results  
Figure 7 shows the changes in acceleration and phase angle measured in the jig during the vibration test. The first natural frequency of the jig is 493.2 Hz, with an acceleration peak of 17.1 g and a phase angle change of 85\({}^{\circ}\) at this frequency. This result varied significantly from the analysis result of the bonded connection method. The natural frequency of the jig with the bonded connection method was 544.1 Hz, approximately 10.3% higher than the vibration test result.  
Figure 8 shows the natural frequencies and mode shapes observed in the first mode for different bolt connection methods. The colors in Figures 8 and 9 indicate the relative mode shape deformations across the structure. Four methods (adaptive bonded, beam, screw, joint) exhibited lower natural frequencies and distinct mode shapes compared to the bonded connection method. For example, the adaptive bonded method showed a local bending mode (Local Mode) along the \(y\)-axis in the ribs, with a natural frequency of 324.7 Hz. The beam method also exhibited local bending along the \(y\)-axis in the ribs, with the lowest natural frequency of 301.8 Hz. The screw method showed local bending in the ribs, with a natural frequency of 388.2 Hz. The joint method exhibited bending deformation along the \(x\)-axis at the Top Head, with a natural frequency of 500.8 Hz. By contrast, the fixed bolt method showed a higher natural frequency (881.9 Hz) compared to the bonded connection method, with a local mode displaying bending along the \(y\)-axis in specific ribs.  
Figure 9 illustrates the mode shapes and natural frequencies observed at the Top Head for different bolt connection methods. The Top Head position was specifically selected because it corresponds to the location where the accelerometer sensor was attached during the vibration test. This verifies that the analysis aligns with the actual experiment setup. The bolt connection method with the highest frequency was the bonded connection method, which exhibited a frequency of 544.1 Hz in the first mode. The method with the lowest frequency was the beam connection method, which showed a frequency of 349.8 Hz in the fifth mode. However, the bolt connection method with results most similar to those of the vibration test was the joint connection method, which exhibited a frequency of 500.8 Hz in the first mode, showing only a 7.6 Hz difference from the test result. The fixed bolt  
Figure 7: Acceleration and phase response with natural frequency identification.  
connection method, which exhibited the highest frequency in the first mode, did not show a mode occurring at the Top Head among the six modes analyzed.  
Table 2 summarizes the preprocessing time, CP Time, and memory usage for each bolt connection method. Preprocessing times were averaged over five trials conducted by experts to enhance the reliability of the analysis. The analysis efficiency and resource consumption varied significantly depending on the bolt connection method. Preprocessing time was particularly influenced by the number of bolts created and fastened. The adaptive bonded and joint methods required the longest times, each exceeding 6000 s (more than one hour), whereas the bonded, screw, and fixed bolt methods completed preprocessing in just 30 s. The beam method showed intermediate results, requiring approximately 3000 s. For CP Time, the adaptive bonded method took the longest, at 598 s, while the bonded method was the fastest, at 91.65 s. In terms of memory usage, the bonded method consumed the most memory at 37,393 MB, whereas the screw method was the most efficient, using only 25,590 MB.  
Figure 8: Natural frequencies and mode shapes based on different bolt connection methods: First mode.  
Figure 9: Natural frequencies and mode shapes based on different bolt connection methods: Top Head mode.