## 5 Experimental Results
### Vibration Test for Resonance Tuning  
The first experiment focuses on analyzing the range of changes in the frequency response of the BWT as a result of the change in the stiffness of the MREs. The frequency response function (FRF) of the BWT, which was acquired through a modal vibration test, shows the resonant frequencies of the system. The tuning range performance of the proposed module can be analyzed using the shift in resonant frequencies when a magnetic field is applied to the MREs.  
A modal shaker was used to apply a dynamic input force to the BWT in the same direction as the oscillation of the mast rod. The shaker tip was directly connected to the mast via a force sensor. The same amplitude was applied by the shaker to the mast to generate the input force, which was recorded by the force sensor (PCB 208C01). Mast vibration was measured with an accelerometer (PCB 352C66) at a sampling rate of 1 kHz.  
The input force was applied as a sine-sweep signal with a frequency range of 0 to 20 Hz over a period of 10 s. The average vibration amplitude was about 3 mm. Only the low-frequency band from 0 to 20 Hz was chosen as the input frequency because the frequency band of interest, such as the VIV frequency and the BWT system frequency, existed within this range. Modal tests under the same conditions were repeated 10 times, and their results were averaged to obtain the frequency response function.  
The experiment was repeated on the BWT without and with the external magnetic field applied to the MREs to compare their resonant frequencies. For the case of MREs with a magnetic field (B = ON), permanent magnets were placed on the magnet bracket, and the magnetic field was measured to be 170 mT.  
The results of the frequency response function (FRF) experiment on the BWT are plotted in Figure 4. The FRF was calculated as the ratio between the mast body acceleration and the input vibration force in the frequency domain. The first resonance of the BWT without the magnetic field (B = OFF) is observed at a frequency of 2.8 Hz, which is equivalent to 2.0 m/s of wind speed.  
Figure 4: FRF results for the BWT with a frequency range of 0–20 Hz. The shift of the resonant frequency is observed by applying a magnetic field.  
When a magnetic field was applied (B = ON), this first resonance peak was shifted right to 4.6 Hz, equivalent to 3.3 m/s of vortex shedding. The resonant frequency in the first mode increased from 2.8 Hz to 4.6 Hz by 64.3% as a result of the change in MRE stiffness due to the magnetic field. These results are summarized in Table 2.  
According to the experimental results, the lock-in range for the mast increased by 64.3% with the MRE-based tuning system. The BWT with nominal MREs (0 mT) resonated when the wind speed was around 2.0 m/s with a vortex-shedding frequency of 2.8 Hz. At this wind speed or force frequency, the vibration amplitude of the BWT was comparable to that of the MREs when the MREs did not have a magnetic field applied, as shown in Figure 5. As the wind speed increased, the vibration of the BWT with the nominal MREs gradually decreased. The vibration level of the BWT eventually became lower than that of the magnetic field after the wind speed passed over 2.6 m/s. In comparison, the BWT with MREs under the magnetic field (B = ON) resonated at a higher wind speed of around 3.3 m/s, as shown in Figure 5.