## 4 Results and Discussion  
The experiment and simulation results of the root-mean-square (RMS) open circuit voltage of MBBP-REH1 at different rotation speeds are plotted in Figure 4. In order to measure the open circuit voltage of MBBP-REH1, a load resistance of 21 M\(\Omega\) was used. It is found that the simulation results are in good agreement with the experiment results. The RMS open circuit voltage of MBBP-REH1 gradually increases with the rotation speed below 240 r/min. This is owing to the more frequent occurrence of the snap-through phenomenon at higher rotation speed, resulting in a larger RMS open circuit voltage with large displacement and velocity of the buckled beam. It can be observed that the RMS open circuit voltage shows a trough around 300 r/min. This is because the buckled beam is unable to follow the input of the excitation magnets, thus the frequency of the snap-through phenomenon is reduced. As the rotation speed further increases, the buckled beam starts to snap-through more frequently and the RMS open circuit voltage increases again. Moreover, the RMS open circuit voltage gradually decreases when the rotation speed exceeds 420 r/min. The reason is that the response of the buckled beam is unable to follow up with the high frequency interaction force between the magnets, and then the buckled beam mostly vibrates around its one stable state. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Description** & **Value** \\ \hline _Substrate_ & \\ Length \(l\) & 155 mm \\ Width \(b_{s}\) & 10 mm \\ Thickness \(h_{s}\) & 0.4 mm \\ Density \(\rho_{s}\) & 8800 kg/m\({}^{3}\) \\ Young’s modulus \(E_{s}\) & 110 Gpa \\ \hline _Piezoelectric layers_ & \\ Length \(l_{p}\) & 22 mm \\ Width \(b_{p}\) & 8 mm \\ Thickness \(h_{p}\) & 0.24 mm \\ Density \(\rho_{p}\) & 7800 kg/m\({}^{3}\) \\ Young’s modulus \(E_{p}\) & 70 Gpa \\ Piezoelectric constant \(d_{31}\) & \(-285\times 10^{-12}\) C/N \\ Relative permittivity & 3200 \\ \hline _Magnet_ & \\ Dimension of tip and fixed magnets \(a\times b\times c\) & \(15\times 15\times 5\) mm\({}^{3}\) \\ Dimension of exciting and center magnets \(A\times B\times C\) & \(10\times 10\times 10\) mm\({}^{3}\) \\ Magnet’s residual flux density \(B_{r}\) & 1.2 T \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties and geometric dimensions of the prototypes. Figure 3: (**a**) The experiment setup and (**b**) the prototype. The effects of the resistance loading on the average power of the MBBP-REH1 at 180 r/min, 300 r/min, and 420 r/min are shown in Figure 5, respectively. The average power can be given as \(P=(V_{rms})^{2}/R_{L}\), where \(V_{rms}\) is the root-mean-square voltage across the loading resistance \(R_{L}\) during a large number of periods. It can be obtained that the average power of the MBBP-REH1 first increases as the loading resistance increases, and then decreases after the loading resistance exceeds a critical value. It is shown that the average powers of MBBP-REH1 reaches its peak at 230 k\(\Omega\) for 420 r/min, 280 k\(\Omega\) for 300 r/min, and 390 k\(\Omega\) for 180 r/min, respectively. The optimal matching resistance of the rotational energy harvester is inversely proportional to the rotation speed. In order to compare the performance of MBBP-REHs under the same conditions, the resistance of 230 k\(\Omega\) is used in the following simulations and experiments. The comparison of the simulation and experiment results of the output voltages of MBBP-REHs with a loading resistance of 230 k\(\Omega\) for 60 r/min is shown in Figure 6. Figure 6a,d show the simulation and experiment of the output voltages of MBBP-REH1 versus time. It can be found that the voltage frequency is twice that of the rotational frequency, because there are two excitation magnets that generate attractive forces during one exciting cycle. The simulation and experiment results of MBBP-REH2 indicate two repulsive excitations in one period of rotation, as shown in Figure 6b,e.