## 2 Experimental Implementation of DIC  
### Experimental Set-Up  
The structure chosen for carrying out an experimental modal analysis using DIC is an aluminum beam of width \(b=30\) mm and thickness \(h=6\) mm. The Young's modulus and the density of the beam were experimentally determined and are respectively equal to \(E=71.8\) GPa and \(\rho=2760\) kg\(\cdot\)m\({}^{-3}\). The boundary conditions are either clamped-clamped,with length \(L\) = 505 mm, or cantilever, with length \(L\) = 570 mm. The beam is subjected to a shock produced with an instrumented impact hammer system. This system consists of a hammer head (Bruel & Kjaer type 8200) mounted with a spring like a pinball plunger. In this way, double shocks are avoided and the impact duration can be adjusted. This kind of excitation leads to the solicitation of a maximum number of modes. Moreover, we are able to measure the excitation signal. In order to isolate, as much as possible, the experimental set-up from external disturbances, the latter one is mounted on a breadboard. The vibratory response of the beam is recorded using a JAI SP-12000M-CXP4 fast camera that directly records images within the RAM of the host computer. This camera, equipped with a macro lens from Zeiss (DISTAGON T 2/35 ZF-I), is set above the beam by means of a gantry mounted on the same breadboard at a distance such that the whole beam is observed within the width of the field of view. The frame rate of the image acquisition is limited by the internal data processing of the camera and the speed of the bus that transfers them to the host computer. At full definition (4096 \(\times\) 3072 px\({}^{2}\)), it reaches 190 frames per second (fps). However, such a definition is useless for a slender structure such as our beam. An image definition of 4096 \(\times\) 80 px\({}^{2}\) is sufficient to image the whole system, with the same image resolution, and permits a much larger frame rate of 5439 fps. In order to avoid images being blurred by motion during the shooting, the integration time of the camera is set to its minimal value: 15 \(\upmu\)s. Therefore, sufficient light is required for the object to be imaged with the best signal-to-noise ratio of the camera. In our case, the beam was illuminated using four pulsed LED spots (developed by R&D Vision), which light the scene with pulses having a duration of 8 \(\upmu\)s, i.e., slightly more than half of the integration time. This system is synchronized with the camera using an external trigger box (EG, synchronization electronics developed by R&D Vision). For the chosen image resolution, this illumination system restrains the maximum fps we can choose for the camera since the maximum reachable light pulse frequency for the system is about 4500 Hz due to the cyclic pulse duration limit of the LED. The acquisition of the frames is therefore performed at this sampling frequency. This allows us to record sequences of typically 10 to 15 thousand images, from which displacement data need to be extracted.  
In addition, ten accelerometers are installed on the beam in order to compare the results of the modal analysis performed using the DIC measurements with those obtained with such more conventional sensors. Data acquisition of the accelerometers and the force sensor is carried out using NI CompactDAQ equipment (housing 9174 with three modules 9234). For this system, the sampling frequency is chosen equal to 10,240 Hz so as, on one hand, to investigate the presence of other modes beyond the range of frequencies studied by the optical system [0-4500] Hz and, on the other hand, to quantify precisely the loading sequence. The experimental setup is pictured in Figure 1.  
Figure 1: Experimental set-up.