## 5 Experimental Test
### Mode Shape Decomposition of the Diametrical Modes for the Standing Disk-Blades-Disk Structure
These differences can be attributed to the experimental fact that rough surfaces and misalignment can cause a loss of the returned light to the Laser lens. These effects, known as speckle noise and pseudo-vibrations, have been discussed in many references [50; 51; 52; 53]. To quantify these effects, the predominant component of each of the analyzed modes is considered, and the amplitudes experimentally detected with the Laser and those ones analytically predicted are compared. In this case, the average amplitude detected with the Laser is around 20% less than the amplitude analytically predicted. Therefore, in this section, the utility of the mode shape decomposition has been demonstrated to predict the natural frequencies observed by a sensor on the stationary frame, when the rotating disk-blades-disk structure is under resonance condition of a diametrical mode. Limitation of Standard Numerical Codes For Non-Axisymmetric Rotating Structures Analyzed in the Stationary Frame  
It is important to mention that such behavior is not well predicted when using commercial software that restrict rotating structures to be axisymmetric around the rotating axis (ANSYS(r), Canonsburg, PA [37], MSC NASTRAN(r), Newport Beach, CA [38]). For this reason, frequencies from the stationary frame of simple axisymmetric disk structures have been successfully predicted in the past [54], while for non- axisymmetric structures, such as the structure analyzed here, this is not possible if the same kind of numerical simulations are performed. This is shown in Figure 17, where the prediction of peaks and relative amplitudes detected with a stationary sensor, when a resonance of the first diametrical mode of the rotating structure occurs, is compared for different methods. Two cases are considered here: the first diametrical mode shape of a simple disk with \(n=2\) (and no nodal diameters) [19] and the first diametrical mode shape of the present disk-blades-disk structures (with main component \(n=2\)). The different methods are compared with experimental results. Simple disk theory means that in Equation (14), only the main diametrical component \(n\) is considered and therefore only two peaks, with half amplitude and modulated \(n\cdot\Omega\), are predicted. Direct simulation means to introduce a rotating speed to the disk or disk-blades-disk structure and obtain the frequencies from the stationary frame (using ANSYS standard code [37]). The mode shape decomposition is applied to decompose the mode shape obtained in the standing case by means of experimental modal analysis and numerical modal analysis, as explained in this paper. As seen in this figure, for the simple disk, all the predictions accurately determine the amplitude and frequency of the peaks of the stationary sensor and, therefore, the proposed method in this paper does not offer extra relevant information for simple disk structures. Nevertheless, for the disk-blade-disk assembly, the simple disk theory predicts only two peaks with higher amplitude, as the description of the mode shape is incomplete. Direct simulation with a standard code also fails, as axisymmetric structures are required. In this case, only the mode-shape decomposition, proposed in this paper, approaches the experimental results obtained. Validity of the Relationship between the Mode Shape Decomposition and the Frequencies Detected from the Stationary Frame and Future Work  
In this section, we have shown that the proposed method allows to predict the frequencies and relative amplitudes of the different peaks seen by a stationary sensor, for the typical range of rotating speeds of prototypes consisting of a disk-blade-disk assembly. The effects of the relative rotation of a surrounding heavy fluid, such as water (the normal fluid in the operation of hydropower units), which have been discussed in previous papers [19; 43; 55], are not considered in this case and will be analyzed in a future paper.