## 3 Test Results
### Dynamic Test Results at Different Damage Levels
The beam is then subjected to further damage, with modal frequencies estimated at the D\({}_{2}\) damage level. Figure 15 illustrates the variation in modal frequency ratios in both directions. Initially, as a bare beam, Beam_CFRP_PostStr experiences a reduction in modal frequencies at the D\({}_{1}\) damage level. After strengthening with CFRP, there is a recovery in modal frequencies, especially in the horizontal direction, reflecting the effectiveness of CFRP in restoring stiffness. However, as damage progresses to the D\({}_{2}\) damage level, a general decrease in modal frequency ratios is observed across all modes in both directions, signaling a reduction in stiffness as the beam's structural integrity continues to degrade. In the vertical direction, the third mode shows a noticeable reduction in frequency at the D\({}_{1}\) damage level, prior to strengthening. After strengthening with CFRP, there is a slight improvement at the D\({}_{1}\) damage level, but the modal frequencies do not fully recover to the undamaged state. At the D\({}_{2}\) damage level, all modes show further reductions, with the third mode being the most affected. In the horizontal direction, CFRP strengthening leads to a more pronounced recovery in modal frequencies at the D\({}_{1}\) damage level. The first and second mode exceed their undamaged state values after strengthening, indicating a significant enhancement in stiffness due to CFRP strengthening. However, as the beam \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{\multirow{2}{*}{**Damage Level**}} & \multicolumn{4}{c}{**Vertical Direction**} & \multicolumn{4}{c}{**Horizontal Direction**} \\ \cline{2-9}  & **f\({}_{1}\)/f\({}_{1}\)und** & **f\({}_{2}\)/f\({}_{2}\)und** & **f\({}_{3}\)/f\({}_{3}\)und** & **f\({}_{1}\)/f\({}_{1}\)und** & **f\({}_{2}\)/f\({}_{2}\)und** & **f\({}_{3}\)/f\({}_{3}\)und** \\ \hline \multirow{2}{*}{Bare} & Undamaged & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 \\  & D\({}_{1}\) & 0.937 & 0.911 & 0.738 & 0.628 & 0.952 & 0.830 \\ \hline \multirow{2}{*}{Strengthened} & D\({}_{1}\) & 0.948 & 0.934 & 0.831 & 1.047 & 1.105 & 0.732 \\  & D\({}_{2}\) & 0.865 & 0.907 & 0.785 & 0.795 & 0.900 & 0.728 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Modal frequency ratios at different damage levels for Beam_CFRP_PostStr. Figure 15: Variation in modal frequency ratios at different damage levels for Beam_CFRP_PostStr in (**a**) the vertical direction and (**b**) the horizontal direction. reaches the D\({}_{2}\) damage level, all modes experience reductions in modal frequency estimates, with the third mode showing the most substantial decrease. Despite the decrease, the vertical direction remains more resilient to damage compared to the horizontal direction, indicating the effectiveness of CFRP in enhancing the beam's dynamic behavior in the vertical direction. Figure 16 presents the modal frequency ratios for all beams in the vertical direction across different damage levels. Note that these ratios represent the proportional changes in frequencies relative to each beam's undamaged state, enabling a comparative analysis of how each beam responds to damage in relative terms. In the vertical direction, Beam_GFRP_PreStr displays a relatively stable frequency ratio for all modes. This indicates that GFRP contributes to maintaining the frequency ratios more consistently, with smaller proportional decreases as the damage level increases. Beam_CFRP_PreStr exhibits a larger decrease in the first and second modes compared to the other beams, reflecting a greater sensitivity to damage in these modes. After strengthening, Beam_CFRP_PostStr shows an increase in modal frequency values, while Beam_GFRP_PostStr exhibits a decrease. This difference in behavior can be attributed to the effects of transporting during the strengthening process and the week-long curing period for the strengthening material under the beam's own weight, potentially leading to additional damage, especially in the vertical direction.