## 6 Conclusions  
An omnidirectional cantilever-type ECTMD is introduced herein for vibration control of lattice towers under wind loading. A wind tunnel study of a lattice tower with an ECTMD was conducted to gain insight into the performance of the ECTMD used in suppressing vibration of lattice towers. Conclusions can be drawn as follows.  
1. The wind tunnel study on the lattice tower shows that there exists a significant across-wind vibration, and it deserves efforts made to design and manufacture an omnidirectional ECTMD to suppress the bidirectional vibration. The parameter adjustability of the newly designed ECTMD in a wide range is verified experimentally. Thus, the vibration of the tower can be suppressed by tuning the frequency of the ECTMD to a value close to the first natural frequency of the tower. The parametric study of ECTMD in wind tunnel test shows that with a frequency ratio of 0.97 and an ECTMD damping ratio of 0.14, the vibration of the tower can be effectively mitigated.
2. The wind tunnel study on the vibration of a lattice tower with an ECTMD mounted indicates that the newly designed ECTMD is capable of effectively reducing the bidirectional response under various wind speed and wind directions. This may be attributed to the fact that the first two natural frequencies of the tower are very close. The ECTMD technique presented in this paper can be applied to tall structures and long-span bridges that undergo significant vibration induced by wind/earthquake loadings.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Wind Speed** **(m/s)**} & \multicolumn{4}{c}{**RMS Acceleration**} & \multicolumn{2}{c}{**Reduction Ratio (\%)**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Without ECTMD**} & \multicolumn{2}{c}{**With ECTMD**} & \multicolumn{2}{c}{**Reduction Ratio (\%)**} \\ \cline{2-7}  & **Theoretical** & **Experimental** & **Theoretical** & **Experimental** & **Theoretical** & **Experimental** \\ \hline
18.5 & 0.400 & 0.447 & 0.304 & 0.363 & 24.1 & 18.8 \\
22.6 & 0.658 & 0.672 & 0.497 & 0.513 & 24.5 & 23.7 \\
24.7 & 0.818 & 0.801 & 0.615 & 0.616 & 24.8 & 23.1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Dynamic responses in case of wind speed of 24.7m/s and wind direction angle of 0\({}^{\circ}\).  
Figure 24: Reduction ratios in along-wind direction under wind speed of 24.7 m/s and wind direction angle of 0\({}^{\circ}\). (**a**) Variation of reduction ratio with frequency ratio; (**b**) Variation of reduction ratio with damping ratio of ECTMD.  
* It is found that the effectiveness of the ECTMD model is least favorable when the wind direction is consistent with the principal axis directions of the lattice tower. Therefore, these cases should be considered in the preliminary design of ECTMDs. That is to say, if the vibration of the tower in these cases can be well mitigated, the vibration under other wind conditions can be also suppressed very well.
* A governing equation is established for the motion of the simplified model, and the equation is transformed in modal space to obtain the frequency response function of each mode. A frequency domain approach is presented to achieve variance of dynamic response. The comparison of numerical and experimental results indicates that the theoretical approach introduced herein is capable of capturing the optimal settings of the ECTMD, and producing a good prediction of the dynamic responses of the tower with or without the ECTMD.  
Conceptualization, W.L.; Investigation, Z.W. and M.H.; Methodology, W.L. and Y.C.; Software, M.H.; Supervision, W.L.; Writing--original draft, Z.W.; Writing--review & editing, Y.C.  
This research was funded by National Natural Science Foundation of China (Grant No.: 51878607, 51838012 and 51678525).  
The authors declare no conflict of interest.