# Assessment of Novel Modal Testing Methods for Structures Rotating in Water
## 4 Results
### Detection of Natural Frequencies through a Transient Ramp-Up  
A transient rotating speed ramp-up from 0 to 300 rpm was employed to excite the structure. Figure 18 shows the spectra measured in air by the accelerometer mounted on the disk during the ramp-up, in orange, and during the chirp excitation using the PZT patch, in blue. The spectra show that all the natural frequencies of the disk, 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 were excited by the mechanical imbalance or its harmonics and were accurately measured by the onboard accelerometer. The natural frequencies in the low-frequency band presented higher amplitudes than those in the high-frequency band because they were excited by the first harmonics of the mechanical imbalance, which have a higher level of energy. Other natural frequencies in the low-frequency band, associated with the supporting structure, were also excited during the ramp-up. These natural frequencies were not excited when using a localized excitation on the disk, such as with the PZT patch.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Mode** & \multicolumn{2}{c}{**Numerical**} & \multicolumn{2}{c}{**Experimental**} & \multicolumn{2}{c}{**FRR**} & \multicolumn{2}{c}{**FRR**} \\ \cline{2-6}
**Shape** & **Air** & **Water** & **Air** & **Water** & **Numerical** & **Experimental** \\ \hline
1 ND & 37.5 Hz & 12.9 Hz & 39.8 Hz & 13.1 Hz & 65.55\% & 67.10\% \\
0 NC & 57.3 Hz & 13.0 Hz & 41.2 Hz & 12.1 Hz & 77.27\% & 70.66\% \\
2 ND & 67.3 Hz & 24.3 Hz & 69.1 Hz & 22.0 Hz & 63.91\% & 68.11\% \\
3 ND & 140.8 Hz & 55.8 Hz & 147.1 Hz & 51.8 Hz & 60.34\% & 64.80\% \\
4 ND & 246.2 Hz & 104.9 Hz & 246.5 Hz & 101.0 Hz & 57.38\% & 59.02\% \\
1 NC & 329.3 Hz & 110.6 Hz & 277.1 Hz & 122.6 Hz & 66.41\% & 55.75\% \\
1 NC+1 ND & 355.1 Hz & 128.2 Hz & 292.3 Hz & 128.9 Hz & 63.90\% & 55.91\% \\ \(1\) & & & & & \\ \hline \end{tabular}  
* Combined mode with 1 nodal circle (1 NC) and 1 nodal diameter (1 ND).  
\end{table}
Table 3: Frequency reduction ratios (FRRs) obtained from numerical and experimental modal analyses of the non-rotating disk in air and water.  
Figure 17: 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 in air and water.  
Figure 19 shows the spectra measured in water by the accelerometer mounted on the lower bearing in a radial direction, ALBy, during a ramp-up, in orange, and during a chirp excitation using the PZT patch, in blue. These spectra show that most of the natural frequencies of the disk corresponding to the 1 ND and 0 NC at around 13 Hz, the 2 ND at 22 Hz, the 3 ND at 51.8 Hz and the 1 NC+1 ND at 128.9 Hz were accurately measured by the off-board accelerometer. It is probable that the other natural frequencies of the disk, corresponding to the 4 ND and 1 NC, were also excited by the mechanical imbalance and its harmonics, but they were not measured with precision from the bearing housing. Additional natural frequencies associated with the supporting structure were also excited and measured from the bearing housing.