## 4 Results
### Effect of Wind Condition  
Using the determined favorable parameters of the ECTMD, i.e., frequency ratio of 0.97 and damping ratio 0f 0.14, the aeroelastic model is tested with and without the ECTMD, under wind speeds of 18.5, 22.6 and 24.7 m/s and wind direction angles in the range of 0\({}^{\circ}\) to 90\({}^{\circ}\).  
The RMS accelerations of the tower with and without the ECTMD are plotted against wind speed in Figure 18. Figure 18 shows that under all wind directions, the vibration responses of the tower without ECTMD increase continuously with the increasing wind speed, and the vibration responses in the X and Y directions remain relatively close to each other. It is found that the vibration responses of the tower with ECTMD are significantly lower than those of the tower without ECTMD. This proves that the ECTMD employed is capable of suppressing vibration responses at different principal axis directions of the tower under various wind conditions.  
Figure 17: Acceleration responses and reduction ratios along height under wind speed of 24.7 m/s and wind direction angle of 0\({}^{\circ}\). (**a**) Acceleration responses; (**b**) Reduction ratios.  
Figure 18: _Cont._  
Under the wind speed from 18.5 to 24.7 m/s, the RMS accelerations of the tower with and without the ECTMD are plotted against wind direction angle in Figure 19, and the corresponding reduction ratios are plotted against wind direction angle in Figure 20. Figure 19 shows that, for the tower without ECTMD, under all wind speeds, the vibration responses maintain a high level at the wind direction angles from 0\({}^{\circ}\) to 45\({}^{\circ}\), and the responses drop significantly at the angles from 45\({}^{\circ}\) to 90\({}^{\circ}\). For the tower with ECTMD, the vibration responses decrease continuously in general with the wind direction angle increasing from 0\({}^{\circ}\) to 90\({}^{\circ}\). Figure 20 shows that under all wind speeds, the reduction ratios in the X and Y directions are generally higher at the wind direction angle ranging from 30\({}^{\circ}\) to 60\({}^{\circ}\). The reduction ratios at 0\({}^{\circ}\) and 90\({}^{\circ}\) wind directions are generally lower, compared to other wind directions. The results indicate that the control effectiveness of the ECTMD becomes not favorable when the wind direction approaches the principal axis directions of the tower, similar to the results shown in the work by [PERSON] et al. (2019) in which a tall-building structure was studied. Consequently, 0\({}^{\circ}\) and 90\({}^{\circ}\) wind directions are the critical cases to be studied preferentially, for design of ECTMDs. In the case of the wind speed of 24.7 m/s, the lower bound of reduction ratio identified (the smallest reduction ratio among those in all wind directions), is higher than that found for the other wind speeds, which means that the ECTMD effectiveness is most favorable in this case. The corresponding reduction ratio ranges from 21.7% to 35.7% for the vibration in the X direction, and from 18.3% to 29.2% for the vibration in the Y direction.  
Figure 18: Variation of RMS acceleration with wind speed and wind direction. (**a**) 0\({}^{\circ}\); (**b**) 15\({}^{\circ}\); (**c**) 30\({}^{\circ}\); (**d**) 45\({}^{\circ}\); (**e**) 60\({}^{\circ}\); (**g**) 90\({}^{\circ}\).