# Stereo-DIC Measurements of a Vibrating Bladed Disk: In-Depth Analysis of Full-Field Deformed Shapes
## 4 Results  
In order to assess the advantages of the proposed method, with respect to the conventional single-point systems, the harmonic response testing was performed on a blisk having eleven sectors, with a main blade and a splitter blade in each sector, and a maximum diameter of 220 mm. The blisk was painted in white, and a black speckle pattern was sprayed on the blade surface. A picture of the blisk, as acquired by the left camera during the acquisition, is shown in Figure 2a, and a number was assigned to each blade for easier referencing. As evident from the figure and due to the short shutter time, no blur is present in the image despite the high-frequency vibration of the blades (6357 Hz in this example). The figure also shows two reference frames: the Cartesian coordinate system of the camera and the cylindrical coordinate system of the blisk, which was introduced for a better understanding of the results, as shown below. To define this latter reference frame, three points of the point cloud were selected on the maximum diameter of the disk, placed at approximately 120\({}^{\circ}\) as shown in Figure 2b with red dots: the circle through these points was then computed, in order to obtain the center of the reference frame, which is placed on the axis of the blisk. Additionally, the normal to the plane defined by the three reference points was computed, which is aligned with the blisk axis (red arrow in Figure 2b). The counterclockwise direction was chosen for the rotational direction of the cylindrical reference system. Finally, the radial direction (i.e., the 0\({}^{\circ}\) location) was conventionally defined by the vector difference between the first two reference points. The hub of the blisk was directly mounted on the plate of an electrodynamic shaker, and with this device it was possible to precisely set a sinusoidal excitation to the blisk. Different frequencies were tested to prove the effectiveness of the setup in the kHz range. As discussed in the literature, the kHz range represents a challenge even for those setups exploiting high-speed cameras. A preliminary analysis was performed by applying a sine sweep to the blisk, in the range 1-7 kHz, measuring the response of Blade 1 with an LDV sensor. This allowed researchers to find the main response peaks of the blisk, and thus to select some resonance frequencies, as shown in Figure 3.  
Figure 2: (**a**) Acquisition of the tested blisk, by the left camera, during a high-frequency sine excitation. (**b**) Reference to three points on the disk outer diameter for the determination of the base plane and the axial direction as orthogonal to this plane. A relatively low peak frequency of 2568 Hz was initially tested, which is however already much higher than the maximum frame rate available with the cameras of the present setup. Figure 4 shows the measured displacement maps, considering the components along the three directions of the blisk: radial, tangential and axial (\(U_{\mathrm{r}}\), \(U_{\mathrm{0}}\) and \(U_{\mathrm{a}}\), respectively). These maps demonstrate that the 3D full-field measurements are properly achieved, despite the high vibration frequency and the low displacement amplitude, in the range of tens of microns. The full-field measurement allows for the reconstruction of the complete deformed shape of the blisk just with a single acquisition configuration, without requiring the movement of a single-point sensor in different locations. The images highlight that the higher response amplitude is measured at Blades 2, 3, 9 and 11, while the other blades experience much smaller displacements, thus denoting a certain mistuning level. Since a relatively low frequency is considered, the blade deformed shape has a low complexity level. This is evident because all the points of the blade move in phase to each other and with low gradients. The test was then repeated at higher frequencies, to investigate the response of the modes to sinusoidal excitation of the hub in the range 6200-6400 Hz.