## 4 Results and Discussion
The result of \(S_{t}\) is in good agreement with the results given by the two cylinders arranged in a tandem pattern (\(S_{\text{t}}\) is about 1.5-1.8) described in References [44,45]. Vortex shedding from the upstream cylinder can affect the energy harvesting performance of the downstream piezoelectric beam, as shown in Section 1 (Introduction). To further investigate the wake effects on the performance of the harvester, we tested the output power of each single piezoelectric beam (the upstream and the downstream) _versus_ the velocity of water with different cylinder diameters, namely, \(D=10\) mm, 15 mm, 20 mm, 25 mm, 30 mm, 35 mm, and 40 mm. Furthermore, the resistance was also equal to 170 k\(\Omega\) here. Hence, the ratio of the spacing distance to the diameter of the cylinder (\(L/D\)) is 5.5, 4, 3.25, 2.8, 2.5, 2.28, and 2.125, respectively. Figure 6 shows the output power of both piezoelectric beams. For the upstream beam, the output power initially increases until reaching the maximum value, and then decreases with the water velocity increasing. The reason is that the vibration mode of the upstream cylinder is VIV. The output power is small when the velocity is low because both the vibration frequency and the amplitude are relatively small. With the increase of the velocity, the vibration frequency, amplitude and output power increase. When the vortex shedding frequency \(f\) is equal to the natural frequency \(\omega_{s}\) of the energy harvester, the vortex-induced resonance is obtained. Then, the dynamic response is enhanced and the maximum output power can be achieved. From  
Figure 4: Relationship between the resistance \(R\) and the output power \(P\) at velocities of 0.25 m/s, 0.31 m/s, and 0.36 m/s: (**a**) upstream beam; (**b**) downstream beam. Figure 6a, it can be found that for all diameters, the vortex-induced resonance velocities are all around 0.3 m/s in this experimental study. The reason is that the changes of the cylinder diameter (increase or decrease) synchronously change the vortex shedding frequency \(f\) and the natural frequency of the energy harvester \(\omega_{s}\) (decrease or increase), which makes it easier for the vortex shedding frequency \(f\) to reach the natural frequency \(\omega_{s}\) with little changes in velocity. Figure 6b shows that when the diameters of the cylinder are 10 mm, 15 mm, and 20 mm, the output power of the downstream beam continuously increases with the increase in velocity. The reason is that wakes from the upstream cylinder continuously enhance the vibration response of the downstream cylinder with the increase of velocity. The vibration mode of the downstream cylinder is WIV for the _L/D_ of 3.25, 4, and 5.5. However, for cylinder diameters of 25 mm, 30 mm, 35 mm, and 40 mm, the output power of the downstream beam initially increases until reaching the maximum value, and then decreases with increasing water velocity. The above results show the same trend with those of the upstream beam. This is because the vibration condition of the downstream cylinder is also VIV when the _L/D_ is small, namely 2.125, 2.28, 2.5, and 2.8. Therefore, it can be summarized that the vibration response of the upstream cylinder is VIV. Meanwhile, both the VIV and WIV modes can be obtained for the downstream cylinder. In this study, the VIV phenomenon predominated when _L/D_ was small (namely 2.125, 2.28, 2.5, and 2.8), while the WIV mode was achieved when the _L/D_ was relatively large, such as 3.25, 4, and 5.5. Figure 5: Output voltage and its Fast Fourier Transform (FFT) analysis: (**a**) output voltage of both the upstream and downstream piezoelectric beams as a function of time; (**b**) FFT analysis of the upstream beam; (**c**) FFT analysis of the downstream beam. In addition, it can be found that the output power increases until it reaches the diameter of 30 mm, and then decreases as the cylinder diameter continues to increase, as shown in Figure 6a,b. The reason is that the vibration response is weak when the cylinder diameter is small.