## 3 Results and Discussions
### Quantitative Analysis of Curvature Mode Difference Damage Identification  
Due to the damage to the structural sealant on the glass panel, the elastic support condition around the panel is disrupted. As a result, more pronounced changes in boundary modal characteristics are observed when structural sealant damage occurs. In this study, the experimental data for each working condition were divided into two independent datasets based on spatial characteristics. The boundary modal dataset was processed through modal extraction and renumbering procedures to analyze the vibration characteristics of the glass panel's boundary region, as shown in Figure 9. The complete dataset containing boundary nodes at structural sealant damage locations (six damage conditions, 24 nodes total) was collected for modal analysis. For comparison, data from 120 boundary nodes in the undamaged sealant regions across the same six damage conditions were synchronized to establish a baseline reference value for the undamaged state. Simultaneously, the internal modal dataset was established to record the dynamic response characteristics of the panel's internal region.  
Significant regularity was observed in the characteristic parameters of the damaged nodes. The average FCMD value for the damaged nodes was calculated as 0.194, which is significantly higher than the average value for undamaged nodes (\(-\)0.0034). A peak value of 0.11 (Condition 7, node 10) was identified in the undamaged region for the damaged scenario, whereas the minimum value for damaged nodes was measured at 0.131 (Condition 7, node 13). A nonlinear transition region was detected between these two characteristic ranges. Therefore, to establish a baseline threshold for quantitative damage identification, the peak value of the undamaged group (0.11) was combined with the minimum value of the damaged group (0.131). As presented in Table 2, the damage threshold is defined as 0.1205, calculated by taking the arithmetic mean of 0.11 and 0.131. Based on this principle, the criterion is established: structural sealant damage is considered to have occurred at that location as the FCMD of any node exceeds 0.1205.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Conditions** & **Average Value** & \begin{tabular}{c} **Maximum** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **Minimum** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Damage** \\ **Threshold** \\ \end{tabular} \\ \hline Undamaged & \(-\)0.0034 & 0.11 & \(-\)0.11 & \\ Damaged & 0.194 & 0.272 & 0.131 & 0.1205 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Critical threshold demarcation between damaged and undamaged conditions.  
Figure 7: First-order curvature mode difference under identical damage degree (**a**-**d**) of (**a**) Condition 2; (**b**) Condition 3; (**c**) Condition 4; (**d**) Condition 5.  
To comprehensively evaluate the performance of curvature mode difference (CMD) for structural sealant damage identification, the experimental results from all six damage conditions (Table 1) were systematically analyzed. The first-order curvature mode difference (FCMD) exhibited a clear correlation between damage severity and localized response magnitude. This proportional relationship aligns with the theoretical expectation that stiffness reduction amplifies curvature mode perturbations [38].  
Figure 8: First-order curvature mode difference in side A under different damage degrees of (**a**) Condition 2; (**b**) Condition 6; (**c**) Condition 7.  
Figure 9: Schematic of boundary modal sampling points.