## 4 Results and Discussion
### Cantilever Beam  
Figure 22 shows the averages and standard deviations over the ten tests for the mode shapes, while Tables 4 and 5, respectively, report the frequencies and the modal damping ratios determined using the full-field measurement and the accelerometer data set.  
DIC measurements are obtained after a numerical processing performed on each image. The time signal being obtained after a numerical post-processing and not in an analogue way, as for accelerometers, the signal is therefore necessarily subjected to aliasing because no analogue filter can be applied. Thus, the eighth mode observed from DIC measurements, at the frequency of 2178 Hz (see Table 4), is a folding frequency of the frequency obtained with the accelerometer measurements for this mode, which is equal to 2327 Hz.  
As for the previous case of the clamped-clamped beam, the tests for the cantilever beam show a good repeatability and both sets of data lead to similar eigen frequencies and modal damping ratios. As in the previous case, the mode shapes were determined with a good accuracy for modes with frequencies up to almost the Nyquist frequency, equal to 2250 Hz in this study.  
Figure 21: Components of the MAC matrix calculated from measurements: (**a**) auto-MAC of mode shapes obtained from DIC measurements and (**b**) MAC of mode shapes obtained from accelerometer and DIC measurements.  
Figure 22: First eight mode shapes obtained from the DIC measurements for the cantilever beam.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c} \hline \multirow{2}{*}{**Test**} & \multicolumn{3}{c}{**Mode 1**} & \multicolumn{3}{c}{**Mode 2**} & \multicolumn{3}{c}{**Mode 3**} & \multicolumn{3}{c}{**Mode 4**} & \multicolumn{3}{c}{**Mode 5**} & \multicolumn{3}{c}{**Mode 6**} & \multicolumn{3}{c}{**Mode 7**} & \multicolumn{3}{c}{**Mode 8**} \\ \cline{2-13}  & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** \\ \hline
1 & 15.05 & 15.05 & 93.09 & 93.08 & 259.0 & 259.0 & 509.3 & 509.3 & 844.3 & 844.3 & 1255.3 & 1255.2 & 1752.9 & 1753.5 & 2178.2 & 2327.0 \\
2 & 15.04 & 15.05 & 93.09 & 93.08 & 259.1 & 259.1 & 509.4 & 509.4 & 844.4 & 844.2 & 1255.2 & 1255.2 & 1753.2 & 1753.5 & 2178.2 & 2326.9 \\
3 & 15.04 & 15.05 & 93.08 & 93.10 & 259.1 & 259.1 & 509.3 & 509.3 & 844.5 & 844.2 & 1255.5 & 1255.3 & 1753.0 & 1753.3 & 2178.0 & 2326.9 \\
4 & 15.04 & 15.05 & 93.09 & 93.09 & 259.0 & 259.1 & 509.2 & 509.3 & 844.0 & 844.3 & 1254.8 & 1255.3 & 1753.0 & 1753.1 & 2177.9 & 2326.4 \\
5 & 15.05 & 15.05 & 93.09 & 93.09 & 259.1 & 259.1 & 509.4 & 509.4 & 844.0 & 844.5 & 1255.3 & 1255.5 & 1753.3 & 1753.5 & 2176.9 & 2327.0 \\
6 & 15.04 & 15.05 & 93.08 & 93.09 & 259.1 & 259.1 & 509.4 & 509.3 & 844.7 & 844.3 & 1255.4 & 1255.4 & 1753.1 & 1753.6 & 2177.8 & 2327.0 \\
7 & 15.04 & 15.04 & 93.09 & 93.09 & 259.0 & 259.1 & 509.5 & 509.5 & 844.5 & 844.4 & 1255.5 & 1255.6 & 1753.3 & 1753.6 & 2178.2 & 2326.9 \\
8 & 15.07 & 15.07 & 93.13 & 93.16 & 259.0 & 259.2 & 509.6 & 509.7 & 844.6 & 844.8 & 1253.2 & 1256.0 & 1753.8 & 1754.1 & 2176.2 & 3238.1 \\
9 & 15.04 & 15.04 & 93.08 & 93.08 & 259.1 & 259.0 & 509.3 & 509.4 & 844.1 & 844.2 & 1254.9 & 1255.1 & 1753.0 & 1753.1 & 2177.7 & 2326.7 \\
10 & 15.03 & 15.04 & 93.09 & 93.09 & 259.0 & 259.0 & 509.2 & 509.3 & 844.3 & 844.3 & 1255.2 & 1255.1 & 1753.0 & 1753.1 & 2177.7 & 2326.8 \\ \hline Mean & 15.04 & 15.05 & 93.09 & 93.10 & 259.1 & 259.1 & 509.4 & 509.4 & 844.3 & 844.4 & 1255.0 & 1255.4 & 1753.2 & 1753.4 & 21753.4 & 2327.0 \\ RSD (\%) & 0.08 & 0.07 & 0.02 & 0.02 & 0.01 & 0.02 & 0.02 & 0.02 & 0.03 & 0.02 & 0.05 & 0.02 & 0.01 & 0.02 & 0.02 & 0.02 \\ \hline \end{tabular}
\end{table}
Table 4: Frequencies of the cantilever beam determined for the different tests from DIC measurements and accelerometers (in Hz).