## 4 Results  
### Parametric Study of ECTMD  
In wind tunnel tests, by changing the length of cantilever beam and the distance between the magnet and the copper plate, the frequency and damping parameter of the ECTMD are thus adjusted to fulfil the experimental requirements. Meanwhile, the values of the frequency and damping ratio of the ECTMD can be approximated conveniently by interpolation, according to the curves shown in Figure 6. Given different frequencies and damping ratios of the ECTMD, corresponding reduction ratios are obtained and shown in Figure 14.  
It is found that, in both along-wind and across-wind directions, there exists a favorable frequency ratio with a corresponding favorable ECTMD damping ratio, using which a maximum reduction ratio can be achieved. The favorable frequency ratio is 0.97 and the favorable ECTMD damping ratio is 0.14 for both along-wind and across-wind directions. With the favorable frequency ratio and ECTMD damping ratio obtained in the first phase of the experiment, the corresponding reduction ratios are 23.1% for the vibration in the along-wind direction and 22.3% for the vibration in the across-wind direction.  
Figure 15 shows the dynamic acceleration responses of the tower top in both time domain and frequency domain, in the case of the favorable frequency ratio and damping ratio tuned for ECTMD. It is found that both the vibration amplitude in the time history and the resonant component of frequency response at the fundamental frequency are significantly suppressed by the ECTMD. In addition, only the first mode has a significant contribution to the response, and the modes with higher modal frequency are not accessible within the frequency range. Figure 16 presents a diagram of bi-directional responses of the tower top, in which the along-wind data is the data in Figure 15a within the duration of 10.9 s to 11.0 s. It is clearly observed that the ECTMD can mitigate the vibrations in the across-wind direction and the along-wind direction in the meantime.  
Figure 14: Variation of reduction ratios with ECTMD parameters under wind speed of 24.7 m/s and wind direction angle of 0\({}^{\circ}\). (**a**) Variation of reduction ratio with frequency ratio of ECTMD; (**b**) Variation of reduction ratio with damping ratio of ECTMD.  
Figure 17 illustrates the measured RMS accelerations, along with the corresponding reduction ratios obtained in the wind tunnel test. It is found that the tower vibrates in a fashion of its first mode mainly, whether the ECTMD is involved or not. Without the ECTMD, the along-wind vibration of the tower is a little smaller than the across-wind vibration, except for the top segment of the tower where the amplitudes of the vibrations in two directions are very close. This finding accounts for the motivation of using omnidirectional ECTMD which is capable of suppressing both along-wind and across-wind vibrations simultaneously. It is found that, with the presence of the ECTMD, the vibrations in the two directions are mitigated, demonstrating the effectiveness of ECTMD.  
Figure 16: Across-wind vibration versus along-wind vibration.  
Figure 15: Acceleration response under wind speed of 24.7 m/s and wind direction angle of 0\({}^{\circ}\). (**a**) Along-wind time history; (**b**) Along-wind Power-spectral density of acceleration; (**c**) Across-wind time history; (**d**) Across-wind power-spectral density of acceleration.  
It is also found that the maximum reduction ratio appears at the measuring point that is located at the tower top rather than the top point. Theoretically, if only the first mode contributes to the vibration, the reduction ratio is expected to be the same along the height. However, the contributions of the other modes, which may not be well controlled by the ECTMD, can also affect the reduction ratio. The frequency response of the point on the tower top shown in Figure 15b indicates that except for the first mode, the contributions of the other modes are negligible. This may account for the observed phenomenon.