## 4 Results and Discussion
### Clamped-Clamped Beam
Since the CWT method is an output-only method, which means that the excitation signal is not needed for modal parameter identification, the mode shapes are normalized to their maximum (\(L_{1}\)-normalization). The mode shapes obtained are consistent with those expected. Considering the standard deviation, the figures highlight that, as expected, it increases with the order of the mode, because the SNR is less important for higher modes, and also close to the modal nodes. Figure 17: Distributions of frequencies and modal damping ratios obtained from the DIC measurements for Mode 2 and 5 of the clamped–clamped beam. From results reported in the aforementioned tables, a good repeatability of the tests is observed; indeed, the standard deviations of frequencies and of modal damping ratios are low for both data sets. Secondly, it can be seen that the two kinds of measurement lead to very similar results for the natural frequencies and modal damping ratios. Figure 19 depicts the Fourier transforms of the measured displacement and acceleration for the neutral axis point of the clamped-clamped beam at abscissa \(x=14.10\) cm. The presented results clearly show that the displacement measurement emphasizes the low frequencies, while the acceleration measurement emphasizes the high frequencies, which is classical. It should also be noted that the SNR is much higher for the acceleration measurement, especially as the mode order increases. To continue the direct comparison between modal analysis based on accelerometers and full-field measurements, Figure 20 presents the first six mode shapes determined from both experimental data sets, for a single test, and those expected from the beam theory. Therefore, the graphs confirm a very good agreement between the experimental measurements and the theory, excepted for the fourth and sixth mode shapes obtained with DIC measurements. Indeed, the excitation level for the sixth mode is very weak so  
Figure 19: Fourier transforms obtained from the accelerometer and the DIC for the neutral axis point of the clamped–clamped beam at abscissa \(x=14.10\) cm. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multicolumn{2}{c}{**Mode 1**} & \multicolumn{2}{c}{**Mode 2**} & \multicolumn{2}{c}{**Mode 3**} & \multicolumn{2}{c}{**Mode 4**} & \multicolumn{2}{c}{**Mode 5**} & \multicolumn{2}{c}{**Mode 6**} \\ \cline{2-13}  & **DIC** & **Acc. ** & **DIC** & **Acc. ** & **DIC** & **Acc. ** & **DIC** & **Acc. ** & **DIC** & **Acc. ** & **DIC** & **Acc. ** \\ \hline
1 & 0.49 & 0.51 & 0.38 & 0.37 & 0.38 & 0.37 & 0.32 & 0.31 & 0.20 & 0.20 & 0.17 & 0.18 \\
2 & 0.51 & 0.50 & 0.36 & 0.36 & 0.39 & 0.39 & 0.32 &  
that the identified mode shape is very noisy and, for the fourth mode, the identification process is disturbed, especially near the modal nodes, by a spurious mode with nearly the same frequency. This spurious mode is only present in the DIC measurements. Its shape is that of a first mode but its frequency does not correspond to the first mode of the other motion components, i.e., traction and torsion. However, we found it was sensitive to the boundary conditions but not enough to uncouple this mode from the fourth mode and improve the identification process. To validate the use of the DIC to perform modal analysis, we can compare the eigen frequency and modal damping ratio values obtained to those determined using the accelerometer measurements. The mode shapes can also be compared to theoretical or numerical ones. To this end, the Modal Assurance Criterion (MAC) is commonly used [27]. This criterion is defined as the normalized scalar products of the mode shapes.