# Full-Field Vibration Measurements by Using High-Speed Two-Dimensional Digital Image Correlation
## 3 Experiment and Result
### Measurement of Natural Frequencies and Mode Shapes of a Rectangular Cantilever Panel  
To investigate the effectiveness of an HS-2D-DIC in characterizing full-field vibrations, an experiment measuring the rectangular cantilever panel movements under the impulse load was finally performed. As shown in Figure 8, an aluminum panel with a speckle pattern was tightly installed on a vibration isolation platform. A high-speed camera (Revealer M220, Fuhuang AgileDevice Ltd., Hefei, China, maximum frame rate of 2000 _fps_ at a resolution of 1920 \(\times\) 1080 pixels) equipped with an imaging lens (Sigma Art series DG HSM(A014), Sigma Co., Ltd., Kanagawa, Japan, aperture F/1.4, and focal length of 50 mm) was placed in front of the panel to capture the speckle images during the measurement. In order to compare the reference values provided in Ref. [11], the dimensions of the rectangular aluminum panel specimen are the same as the ones measured in the reference article, i.e., 460 mm \(\times\) 200 mm \(\times\) 2 mm (W \(\times\) H \(\times\) T). Two evenly distributed holes were drilled in one short side of the rectangular aluminum panel, and the panel was prepared with contrasting speckle patterns and tightly installed onto the vibration isolation platform through a fixture. Before the measurement, the distance between the panel and the camera was set at 1250 mm, and the imaging lens was carefully adjusted to make the camera capable of capturing high-contrast speckle images. In the experiment, a rubber bullet was fired to excite the cantilever panel. The speckle images during the panel movement were continuously recorded by using the camera at a rate of 1000 _fps_. Using the captured speckle images, the in-plane displacement and virtual strain fields can first be estimated based on the 2D-DIC algorithm. After that, the out-of-plane displacement fields can be obtained using the measured virtual strain fields based on Equation (3), as shown in Figure 8. Figure 9a-i show the out-of-plane displacements corresponding to the times that they were measured: 0.28 s, 0.31 s, 0.34 s, 0.37 s, 0.40 s, 0.43 s, 0.46 s, 0.49 s, and 0.52 s, respectively. Since the left edge of the panel was fixed, the out-of-plane displacement of the edge was kept at 0 throughout the vibration. Figure 7: (**a**) Schematic of the single-frequency vibration measurement experiment and the results of the vibrational tests with reference frequencies of (**b**) 20.02 Hz (**c**) 29.08 Hz, and (**d**) 38.95 Hz. To exhibit the dynamic results better, the displacements of four different points, i.e., P1, P2, P3, and P4, on the panel are plotted as shown in Figure 10. Since points P2 and P3 are close to the free edge of the panel, it is observed that the displacement amplitudes of these two points are larger than that of points P1 and P4. By processing the displacement results using the Fourier transform (FT), the frequency spectrums of the tested aluminum panel can be calculated, as shown in Figure 10d. From the spectrums, the natural frequencies of the aluminum panel can be acquired, i.e., 8.89 Hz, 41.80 Hz, and 56.00 Hz, showing good agreement with the reference values estimated by finite element analysis (FEA) [11], i.e., 9.04 Hz, 41.90 Hz, and 56.41 Hz. The differences between the measured and reference values are only \(-\)1.5%, \(-\)0.2%, and \(-\)0.7%. Figure 8: A photograph of the cantilever aluminum panel vibration experiment. Figure 9: The out-of-plane displacement fields measured at (**a**) 0.28 s, (**b**) 0.31 s, (**c**) 0.34 s, (**d**) 0.37 s, (**e**) 0.40 s, (**f**) 0.43 s, (**g**) 0.46 s, (**h**) 0.49 s, (**i**) 0.52 s.  
In addition to extracting the natural frequencies, the mode shapes of the aluminum panel can also be estimated from the measured full-field displacements. First, transform the measured displacements from the time domain to the frequency domain. Then, extract the displacement at different natural frequencies by using band-pass filters. Finally, reversely transform the filtered displacements from the frequency domain to the time domain.