# Assessment of Novel Modal Testing Methods for Structures Rotating in Water
## 4 Results
### Results in Air
#### 4.1.3 Influence of Rotation on the Natural Frequencies of the Disk in Air  
Figure 12 shows the spectra in the range of 5 to 100 Hz of the structural response measured by the on-board accelerometer at different rotating frequencies. The spectrum at 0 rpm presented three frequency peaks corresponding to the 1 ND at 39.8 Hz, the 0 NC at 41.2 Hz and the 2 ND at 69.1 Hz. All these modes were also detected at higher rotating frequencies, from 50 rpm to 300 rpm, at the same frequencies. Similar to the conclusions of [17], the current results suggest that the natural frequency detected from an on-board position, \(f_{on-board}\), is independent of the rotating speed. This also agrees with the observations of [12; 13; 14], who concluded that the rotating speed influences the natural frequencies, but this influence begins at higher rotating speeds than those tested in the present study. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Mode Shape**} & **Numerical** & **Experimental** & \multirow{2}{*}{**Discrepancy**} \\  & **Simulation** & **Modal Test** & \\ \hline
1 ND & 37.5 Hz & 39.8 Hz & 6.2\% \\
0 NC & 57.3 Hz & 41.2 Hz & 28.0\% \\
2 ND & 67.3 Hz & 69.1 Hz & 2.7\% \\
3 ND & 140.8 Hz & 147.1 Hz & 4.5\% \\
4 ND & 246.2 Hz & 246.5 Hz & 0.1\% \\
1 NC & 329.3 Hz & 277.1 Hz & 15.9\% \\
1 NC+1 ND 1 & 355.1 Hz & 292.3 Hz & 17.7\% \\ \hline \end{tabular} \({}^{1}\) Combined mode with 1 nodal circle (1 NC) and 1 nodal diameter (1 ND).  
\end{table} 
Table 1: Natural frequencies obtained from numerical and experimental modal analyses of the non-rotating disk in air. Figure 13 shows the spectra in the ranges of 16 to 100 Hz (a), 100 to 200 Hz (b) and 200 to 300 Hz (c) measured by the D0 mounted off board and pointing directly at the disk. The spectra at 0 rpm presented seven frequency peaks corresponding to the 1 ND at 39.8 Hz, the 0 NC at 41.2 Hz, the 2 ND at 69.1 Hz, the 3 ND at 147.1 Hz, the 4 ND at 246.5 Hz, the 1 NC at 277.1 Hz and the 1 NC+1 ND at 292.3 Hz. When the rotating speed was increased, the single frequency peaks corresponding to the 1 ND, 2 ND, 3 ND, 4 ND and 1 NC+1 ND were split into two frequency peaks: one with a higher value and the other with a lower value. The higher and lower frequency values increased and decreased, respectively, when the rotating speed of the disk increased. Moreover, this increase or decrease in frequency depended on the number of NDs of the mode shape. On the other hand, the single frequency peaks corresponding to 0 NC and 1 NC were not split, and they always presented the same frequency value. As also observed by [23; 24; 25], the natural frequency detected by the D0, \(f_{laser}\), of an ND mode has been found to be dependent on the rotating speed of the disk, \(\omega_{rot}\), and the number of nodal diameters, \(ND_{number}\), based on the following expression:  
\[f_{laser}=f_{on-board}\pm ND_{number}\cdot\omega_{rot} \tag{1}\]  
Figure 11: Maximum normalized spectra of the STFT measured from several sensors when the disk was excited with a chirp in the range of 0–100 Hz. Figure 12: Maximum spectra of the STFT of the on-board accelerometer when the disk was excited in air with a chirp in the range of 0 to 100 Hz at different rotating speeds. Figure 13: (**a**) Maximum spectra of the STFT of the D0 when the disk was excited with chirps in air in the ranges of 0 to 100 Hz (**a**), 100 to 200 Hz (**b**) and 200 to 300 Hz (**c**) at different rotating speeds. Figure 14 shows the spectra in the range of 200 to 320 Hz measured by the off-board accelerometer mounted on the upper bearing in the radial direction, AUB\({}_{y}\), at different rotating speeds. The spectrum at 0 rpm presented three frequency peaks corresponding to the 4 ND at 246.5 Hz, the 1 NC at 277.1 Hz and the 1 NC+1 ND at 292.3 Hz. When the rotating speed was increased, the single frequency peak corresponding to the 4 ND was split into two frequency peaks: one with a higher value and the other with a lower value.