# A Flutter-Based Electromagnetic Wind Energy Harvester: Theory and Experiments
## 4 Experimental Results  
To experimentally verify the predictions of the analytical model and investigate the output performance of the proposed energy harvester, a small wind tunnel with wind speeds ranging from 0 m/s to 11.2 m/s was built. Wind speed was measured using an anemometer (KIMO (Bordeaux, France) CTV100), and the waveform of voltage and the corresponding frequency were recorded by an oscilloscope (KESIGHT (Santa Rosa, CA, USA) InfiniVision DSO-X 2012A) with a 10 M\(\Omega\) probe. Energy harvesters with four positions of magnets were tested in the wind tunnel. Figure 4 shows the relationship between the root-mean square (RMS) open-circuit voltage and the wind speed of energy harvesters with four positions of magnets. The voltage increased sharply at wind speeds of 6.5 m/s, 7.5 m/s, and 9.5 m/s, when \(l_{1}\) was 55 mm, 40 mm, and 25 mm, respectively. These wind speeds can be seen as the critical wind speeds of the wind belts. As shown in Table 5, the results agreed well with analytical predictions. Therefore, the proposed analytical model can be used for the prediction of the critical wind speed of the wind belt type energy harvester. Besides, the experimental results also show that an energy harvester with magnets near the middle of the PET membrane can achieve a higher output. In a word, placing magnets near the center of the membrane can further reduce the critical wind speed and subsequently improve output performance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Magnets Locations** & \(I_{1}\) **= 55 mm** & \(I_{1}\) **= 40 mm** & \(I_{1}\) **= 25 mm** & \(I_{1}\) **= 10 mm** \\ \hline Critical wind speed (m/s) & 6.46 & 7.31 & 9.94 & 10.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Predictions of the critical wind speed of an energy harvester with different magnet positions. Since the energy harvester with central magnets has the lowest critical wind speed and considerable output performance, it was further investigated. Figure 5a shows the open-circuit voltage waveform at different wind speeds. The energy harvester can generate a steady output, indicating that it vibrated with constant amplitude. Figure 5b shows the RMS open-circuit voltage and the corresponding frequency at different wind speeds. When wind speed was below 3 m/s, there was no output, because the wind belt did not vibrate. When the wind speed reached 3 m/s, the wind belt vibrated with a small amplitude and the energy harvester was able to output small voltage. This phenomenon comes mainly from the asymmetry of the pre-stress along the y direction, so a torsional vibration with torsional axis deviating from the central axis could be observed. When the wind speed reached 6.5 m/s, violent vibration of the wind belt took place and the energy harvester was able to output an RMS voltage of 0.86 V. As the wind speed continues to increase, the voltage of the energy harvester increased approximately linearly; when the wind speed reached 11.2 m/s, the energy harvester generated an output voltage of 1.95 V. Meanwhile, the frequency of the voltage can be used to represent the flutter frequency of the wind belt. We can see that the flutter frequency increased with the wind speed, which was mainly due to enhancement of nonlinearity as the bending amplitude increased. Figure 5c shows the derived bending and torsional amplitudes at different wind speeds according to the nonlinear Equations (38) and (39). The bending and torsional amplitudes increased with the wind speed as well as the flutter frequency, which can explain why the voltage increased with wind speed. To obtain the maximum output power and the corresponding optimized load, the RMS voltage \(U_{rms}\) with different load resistance was measured. Average power can be gained according to the equation \(P_{ave}=U_{rms}^{2}/R_{l}\).