## 4 Results and Discussion
### Clamped-Clamped Beam  
First, a 1D FE computation, using beam elements with two degrees of freedom, is performed and compared with the results of the test. The loading signal is taken up from the experimental measurement of the impact hammer. To fit the numerical model on the experimental configuration, the Young's modulus is adjusted in order to obtain the first numerical frequency in accordance with the experimental one. On Figure 13 the Fourier transform of both numerical and experimental data, for the neutral axis point of coordinate \(x=14.10\) cm, are shown. The first six modes are observable through the experimental displacement field. Figure 14 illustrates the comparison between numerical and experimental transverse displacements of the middle of the beam (\(x=L/2=25.25\) cm). Concerning the experimental displacements, the standard deviation before the excitation, representing the noise level, is lower than \(10^{-6}\) m, as expected. The results presented in the two previously mentioned figures show a very good agreement of the measurement with the theory, except for Mode 4, whose amplitude is higher in the experiment, possibly due to a spurious mode. Figure 12: Relative variation of the modal damping ratios of the clamped–clamped beam as a function of the modal amplitude threshold of the normalized mode shapes used to select the points to calculate the averages of the modal damping ratios. In order to quantify the noise level for each mode for the full-field measurements, the SNR is calculated for each measurement point of the neutral axis for the clamped-clamped beam. The evolution of this ratio along the beam is shown for each mode on Figure 15a for the full-field displacements and Figure 15b for the accelerometers for comparison. For the full-field displacements, it can be observed that this ratio decreases with the mode number and also at the modal nodes. These two observations can be easily explained by the fact that the higher the mode is, the less it participates in the global motion and that, close to the nodes, the motion is near to zero and thus, closer to the noise level. After evaluating the noise level for each mode, the modal parameter identification is presented. Figure 16a,d depict, for a specific test, the frequency determined at each measurement point for the second and fifth mode, respectively. Figure 16b,e show the damping ratios and Figures 16c,f the mode shapes for the same modes, respectively. From these figures, it can be observed that, apart in a few measurement points near the modal nodes and the boundary conditions, the determined frequencies and damping ratios are rather constant. In the following, the frequencies and modal damping ratios will refer to the averages of the values obtained for all measurement points. Figure 14: Comparison of numerical and experimental transverse displacement for the neutral axis, point of the clamped–clamped beam at abscissa \(x=25.25\) cm. Figure 13: Comparison of Fourier transform of numerical and experimental signals for neutral axis, point of the clamped–clamped beam at abscissa \(x=14.10\) cm. Figure 16: Modal parameters obtained from the DIC measurements for Modes 2 and 5 of the clamped–clamped beam. Figure 15: Signal-to-noise ratio (SNR), in dB, for different measurement types for the clamped–clamped beam: (**a**) full-field displacements and (**b**) accelerometers. The distributions of the frequency and the damping ratio values obtained for the second and fifth mode are shown in Figure 17a,d. It appears one more time that, apart from a few points very far from the average values, there is little deviation for all other points. One of the main advantages of a full-field measurement is to consider numerous points and thus to provide mode shapes with a high discretization. Figure 18a,f show the means and relative standard deviations (RSD) for each point of the mode shapes over ten tests.