# Stereo-DIC Measurements of a Vibrating Bladed Disk: In-Depth Analysis of Full-Field Deformed Shapes
## 1 Introduction  
The experimental characterization of bladed disks (or blisks) dynamics is a critical task in turbomachinery for avoiding potential resonances and harsh startup and shutdown [1]. Bladed disks are usually characterized by many vibration modes which need to be recognized and investigated both with Finite Element (FE) analysis and through a dedicated experimental analysis [2]. These modes can be critically excited by different engine orders which induce resonances [3]. Any bladed disk has a nominal shape which is in principle perfectly cyclic. However, small deviations of this symmetry property are unavoidable, due to small manufacturing imperfections or even material inhomogeneities [4]. This deviation from the nominal shape is usually referred to as \"mistuning\" and can be distinguished into just random mistuning and intentional mistuning, and this latter is introduced to mitigate the vibrations of the random mistuning itself [4, 5]. A dedicated modeling is therefore required, usually based on reduced-order models [6, 7, 5], and this can provide a tool for the optimization of the intentional mistuning pattern [8, 9]. The mistuning can even be obtained by applying a coating on the blades with an intentional different thickness on each blade, which can be easily controlled at the manufacturing stage [6]. Even two coating layers can be applied on each blade for a more effective intentional mistuning [10]. The main role of these coatings is to introduce a damping effect, indeed damping hard coating materials are employed, and damping mistuning is obtained, which can be modeled and ultimately optimized. However, the coating affects also the mass and the stiffness of the blades, which can be more accurately considered, as pointed out by [PERSON] et al. [11]. FE investigation on blisks efficiently models the nominal vibration modes and their frequencies, regardless of any mistuning, and the FE modal analysis is run to provide the Singh's Advanced Frequency Evaluation (SAFE) diagram. This tool allows one to find the shape matching between the load harmonics and the modes and finally try to avoid the resonance matches [12]. This diagram was recently extended to the actual dynamic behavior of the blisks, by considering any possible mistuning, as proposed by [PERSON] et al. [13]. However, a tailored experimental investigation is required to find the angular harmonic content of the bladed disks [14; 15]. The proposed experimental technique requires a Laser Doppler Vibrometer (LDV), which measures the vibrating surface velocity along the specific direction of the laser beam and at the laser spot, thus providing just a point measurement though quite accurate. The use of accelerometers or strain gauges, providing either the acceleration or the local deformation of the structure, respectively, are valid alternative techniques. However, they are still measuring a single point of the structure. Multiple measurement points can be alternatively recorded with a traveling LDV, as proposed by [PERSON] et al. [14], such as by using a robotic station for the accurate positioning of the laser beam with respect to the complex bladed disk geometry. Other techniques are obviously available for posing the LDV in a defined position with respect to the component, for example, by combining a camera and the CAD model, as proposed by [PERSON] et al. [16]. However, after considering the number of blisk blades, if several measurement points are dedicated to each sector, the total number of positioning steps is too large, thus the whole procedure is quite time consuming. Scanning LDV (SLDV), or Continuously Scanning LDV (CSLDV), could provide another similar approach, by performing a scan along a linear path [17] or a circular path by means of two mirrors aligned according to a specific arrangement [18; 19]. However, SLDV signal is much stronger when the beam direction is approximately aligned with the surface normal, which is not feasible in complex 3D blisks geometry.