## 3 Experimental Setup
### Aeroelastic Model for Wind Tunnel Test  
In the wind tunnel test, similarities of some important parameters such as Strouhal number, elastic parameter and inertial parameter need to be fulfilled. The similarity of Reynolds number is not satisfactorily achieved in the wind tunnel test. However, for the angle steel tower, the Reynolds number does not significantly affect the results [38], and the similitude requirement of Reynolds number was thus relaxed. Froude number similarity mainly affects lifting aerodynamic force of the scaled model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Mode** & **Frequency (Hz)** \\ \hline
1 & 1.879 \\
2 & 1.898 \\
3 & 5.356 \\
4 & 6.668 \\
5 & 7.037 \\
6 & 7.079 \\ \hline \hline \end{tabular}
\end{table}
Table 2: First six natural frequencies of prototype structure.  
Figure 7: Mode shapes of prototype structure. (a) 1 st mode; (b) 2 nd mode; (c) 3 rd mode; (d) 4 th mode; (e) 5 th mode; (f) 6 th mode.  
It plays an important role in wind tunnel test of free-flying models, such as wings. However, for cantilever-type structures, the deflection due to the vertical gravitational loading is relatively small, compared to that caused by horizontal wind loadings. As only the horizontal vibration is considered herein, the similitude requirement of Froude number was relaxed [39].  
An aeroelastic model with a scale factor of 1:30 was designed and fabricated, having a height of 1.45 m, as shown in Figure 8. In the figure, the aeroelastic model consists of eight segments in a vertical line and connected by copper tubes. Each segment consists of angle steel members that meet the similitude requirement of windward area. To simplify the design, the members with a relatively small size are discarded, and the corresponding windward areas are incorporated into the remaining members. Generally, the natural frequencies of the steel tower model in which only geometric similarity is considered in scaling, are too high for an aeroelastic model-based wind tunnel study. Hence, copper tubes are placed between the segments as substitutes of the steel member, to reduce the overall lateral stiffness of the aeroelastic model. The details of the connection are depicted in Figure 9.  
The acceleration responses of the aeroelastic model are measured by the sensors installed at the height of 0.60 m, 0.90 m, 1.11 m, 1.34 m and 1.44 m respectively, as shown in Figure 10. The sensors are sequentially numbered, and the 'X' and 'Y' in the sensor names denote the measurements in X direction and Y direction respectively. The acceleration sensors were produced by Kistler Group, and  
Figure 8: Diagram of aeroelastic tower model.  
Figure 9: Detailed connection of copper tube and angle members.  
the mass of each sensor is about 4.0 g. The sampling frequency adopted in the data acquisition system is 2048 Hz. The experimental setup of the aeroelastic model with an ECTMD installed on its top for wind tunnel test is shown in Figure 11.  
Through free vibration tests, the primary natural frequencies of the aeroelastic model were identified and these are listed in Table 3, and the damping ratios of the aeroelastic model are 1.9% and 2.0% for the first mode in the X-direction and the first mode in the Y-direction respectively. The scale factors for the aeroelastic model are listed in Table 4. As the scale factor for frequency is determined experimentally in advance, the corresponding scale factors for dynamical similarity, e.g., scale factors for acceleration and wind speed, can then be deduced. According to similarity principles, the non-dimensional parameters of the scaled ECTMD determined in this study are the same as those for a full-scale ECTMD, which benefits the design of full-scale ECTMDs. The mass ratio, \(\mu=6.3\%\), is denoted as the ratio of the ECTMD mass to the modal mass (0.183 kg) of the first mode in Y direction.  
Figure 11: Experimental setup.  
Figure 10: Locations of acceleration sensors.