## 5 Conclusions  
The presented experiments allowed us to demonstrate the feasibility of modal analysis using the displacement measurement with DIC. It must be emphasized that the speckle realization affects the displacement resolution. In the presented investigation, the speckle realized with a pen showed better results in terms of random and systematic errors than that realized with the spray paint. This can be partially explained by the fact that setting  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **DIC** & \multicolumn{2}{c}{**Accelerometers**} \\ \hline Frequency & Good determination & \(=\) & Good determination & \(=\) \\ Damping ratio & \
\begin{tabular}{c} Some disparity \\ (many measurements) \\ \end{tabular} & \(+/-\) &
\begin{tabular}{c} Low disparity \\ (few measurements) \\ \end{tabular} & \(+\) \\ Mode shape & Accurate description & \(+\) & Lack of points & \(-\) \\ Impact on measurement & Non-intrusive & \(+\) & Intrusive & \(-\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison between the DIC measurements and accelerometers.  
\begin{table}
\begin{tabular}{c c c c 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**} & \multicolumn{2}{c}{**Mode 7**} & \multicolumn{2}{c}{**Mode 8**} \\ \cline{2-13}  & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** & **DIC** & **Acc.** \\ \hline
1 & 0.45 & 0.50 & 0.28 & 0.28 & 0.27 & 0.28 & 0.15 & 0.15 & 0.49 & 0.49 & 0.13 & 0.14 & 0.14 & 0.17 & 0.15 \\
2 & 0.46 & 0.48 & 0.28 & 0.28 & 0.27  
the spot size with a pen is far easier at the scale of the experiment presented in the paper than with spray paint.  
The measurement quality realized with DIC has been investigated for the transverse vibratory response of a beam excited by a shock for two boundaries conditions, clamped-clamped and cantilever. To deal with the numerous and noisy signals obtained from the DIC measurements, a continuous wavelet transform method is adapted to perform a modal identification and a signal processing procedure is proposed. The identification was carried out for modes whose frequency goes up to about 2200 Hz, up to the sixth mode for the clamped-clamped beam and the eighth mode for the cantilever beam.  
The comparison with the results of modal analysis resulting from the measurement of accelerometers shows that the natural frequencies and the modal damping ratios determined using DIC are very close to those obtained with the accelerometers and that the dispersion of the results is similar. Concerning the mode shapes, the results obtained from DIC measurements are much more accurate due to the large number of points, up to three hundred in our experiments. Thus, one of the interests of using DIC for modal identification of structures is to provide a more accurate description of the mode shapes. This can therefore be very useful for damage detection methods using mode shapes and/or their derivatives, such as modal curvature methods.  
Conceptualization, X.R. and G.C.; methodology, G.C.; software, G.C.; validation, G.C.; investigation, X.R.; data curation, G.C.; writing--original draft preparation, X.R.; writing--review and editing, G.C., M.B. and M.Q.; supervision, G.C., M.B. and M.Q.; funding acquisition, G.C., M.B. and M.Q. All authors have read and agreed to the published version of the manuscript.  
This work benefited from a grant from the French government managed by the ANR in the framework of the investments of the national program for the future ANR-11-LABX-02-01.  
Not applicable.  
The data are contained within the article.  
The authors declare no conflict of interest.