## 4 Results and Discussion
Figure 6c,f illustrate the simulation and experiment results of the output voltages of MBBP-REH3. There are an attractive force excitation and a repulsive excitation in one cycle for MBBP-REH3. With respect to the attractive force excitation, the repulsive force excitation can generate higher output voltages. This can be explained as follows. For the attractive magnet arrangement, the center magnet tends to follow with the excitation magnet as it rotates. From the other point of  
Figure 4: The root-mean-square (RMS) of the open circuit voltage of MBBP-REH1 at different rotation speeds. Figure 5: Effects of the resistance loading on the average powers of MBBP-REH1 at 180 r/min, 300 r/min, and 420 r/min. view, the rotational magnet seems to drag the center magnet forward. This causes the velocity of the buckled beam to remain at a relative stable stage until the rotation angle becomes too large to maintain a high enough attraction force between two magnets. Hence, a relative flat voltage output occurs during the interaction period. In contrast, for the repulsive magnet arrangement, the beam could snap-through suddenly with a high velocity as the excitation magnet approaches, and then damps out around the far-end stable position. Therefore, a fast oscillating voltage output with high amplitude can be observed. The simulation results are in good accordance with the experiment results for different excitation magnets arrangements. Figure 7 shows the comparison of the average powers of MBBP-REHs across a loading resistance of 230 k\(\Omega\) under different rotation speeds. The maximum average powers of MBBP-REH1, MBBP-REH2, and MBBP-REH3 are 682.7 \(\upmu\)W at 360 r/min, 711.7 \(\upmu\)W at 240 r/min, and 672.2 \(\upmu\)W at 300 r/min, respectively. It can be observed that there are two peaks for average powers of all MBBP-REHs when the rotation speed changes from 60 r/min to 600 r/min. The trend of the power as a function of the rotating speed is explained, as follows. Firstly, the frequency of the snap-through phenomenon increases with the rotation speed, thus the output power increases gradually. However, for higher speeds after the first peak average power point, the beam is unable to follow the input excitation, thus the snap-through frequency and average power  
Figure 6: Comparison of the time domain waveform of the output voltages of MBBP-REH1, MBBP-REH2, and MBBP-REH3 under the rotation speed of 60 r/min: simulation (a–c) and experiment (**d–f**). Figure 7: The comparison of the average power of MBBP-REHs across a loading resistance of 230 k\(\Omega\) at different rotation speeds. decrease until the trough between two peaks. By further increasing the speed, it is observed that the snap-through frequency and the generated power increase again until the second peak point. The average power of MBBP-REH1 and MBBP-REH2 are found to gradually decrease after the rotation speed exceeds the second peak points of MBBP-REH1 and MBBP-REH2. It is due to the reason that the response of the buckled beam cannot follow up with the high frequency interaction force between the magnets, and then the buckled beam mainly vibrates around its one stable state. However, the average power of MBBP-REH3 increases and experiences a relative flat rotation speed response when the rotation speed exceeds 960 r/min. This is due to the introduction of a high frequency alternating excitation by the alternative magnets arrangement. The time domain waveform of generated voltage of MBBP-REHs with a resistance of 230 k\(\Omega\) are shown in Figure 8. Each graph of generated voltage in Figure 8 corresponds to one unique point in Figure 7. From Figure  
The average power of MBBP-REH1 for the loading resistance of 230 k\(\Omega\) with different excitation distances is shown in Figure 10. It can be observed that the average power of MBBP-REH1 increases significantly as the excitation distance (\(d\)) decreases. Meanwhile, the speed gap between the first and second resonant peaks reduces when the excitation distance decreases.