# Assessment of Novel Modal Testing Methods for Structures Rotating in Water
## 2 Experimental Investigation
### Methodology  
The experimental modal tests of the disk-shaft assembly were performed by exciting the structure using an instrumented hammer, a PZT patch and a transient ramp-up (see Figure 4).  
Due to the difficulty of performing hammer impacts when the disk was in water or rotating, the hammer was only used when the disk was not rotating in air. The rowing hammer technique was employed to identify the natural frequencies and mode shapes of the disk up to 300 Hz. A total of 10 impacts were performed in different positions of the disk, as presented in Figure 5a. Subsequently, the frequency response functions (FRF) between the accelerometer and the hammer signals were computed, obtaining their real and imaginary parts, as shown in Figure 5b. The FRF was calculated using a force-exponential window to minimize signal leakage. Additionally, the FRF was averaged with a RMS method and using five impacts given in each position. The natural frequencies of the structure were identified directly from the frequency peaks of the FRFs, and the mode shapes were obtained from the amplitudes and signs of the frequency peaks of the imaginary part of the FRFs.  
Figure 4: Scheme of the methodologies used to perform the experimental modal tests.  
The modal test was also performed using a PZT patch. In the current study, this alternative method to perform a modal test was first validated by comparing the results obtained with the hammer and the PZT patch when the disk was in air without rotation. Subsequently, the PZT patch was used to perform the modal analysis with the disk rotating in air and water. The disk was tested in air at 0, 50, 100, 150, 200, 250 and 300 rpm and in water at 0 and 50 rpm. Tests in water were carried out only up to 50 rpm because at higher rotating speeds the water leaked through some sensors' sealing, reaching the electrical connections and producing unreliable measurements. The PZT patch was fed a frequency-varying voltage that swept over different frequency ranges and excited the natural frequencies of the disk, which were then identified from the increase in the amplitude of the structural response at each resonance. The peaks of the signal were identified from a spectrum built using the maximum values of a waterfall spectrum for each frequency bit over the entire temporal duration of the signal (see Figure 6b). The waterfall spectra were calculated using a short-time Fourier transform (STFT) (see Figure 6a). A resolution of 0.142 Hz was obtained in the equivalent spectrum of Figure 6b using a Hanning window with an FFT block size of 30,000 points and a sliding time segment with a 10% time increment between two consecutive FFT blocks. The chirps were performed in different frequency ranges of 0-100 Hz, 100-200 Hz and 200-300 Hz for 100 s and in the range of 0-300 Hz for 300 s.  
Figure 5: (**a**) Scheme of the impact positions on the disk excited using the instrumented hammer and (**b**) the real and imaginary parts of the averaged FRF between the on-board accelerometer and the hammer signals.  
Figure 6: (**a**) Waterfall result obtained from the STFT analysis of SG3_8 when the disk was submerged in water and rotating at 50 rpm while excited with a chirp signal ranging from 0 to 100 Hz. (**b**) Maximum spectrum of the STFT, showing the different natural frequencies in water.  
Finally, a transient ramp-up test from 0 to 300 rpm with a duration of 120 s was performed to excite the natural frequencies with the mechanical imbalance. The increase in the amplitude of the structural response at certain frequencies was identified using the same methodology applied to the PZT patch tests. From these frequency peaks, the natural frequencies were directly identified.