## 6 Results and Discussion
Note that the measured mechanical damping ratios of piezoelectric and magnetic oscillators without magnetic interaction are 0.025 and 0.02, respectively. That is to say, magnetic interaction can add extra damping to the magnetic oscillator and cut down the damping of the piezoelectric oscillator. The simulation results for the LEMEH shows good agreement with the experimental results. Accordingly, the model of the electromagnetic coupling coefficient \(\theta_{\mathrm{em}}\) is reasonable and valid. Figure 11: Frequency responses for the HEH, MEMEH, and MPEH: (**a**) experimental results; (**b**) numerical results. Figure 13 provides the investigation on the effects of the initial separation distance \(d_{0}\) between two magnets on output power. The measurement was performed at three arbitrary different separation distances 42.5, 47.0, and 52.5 mm. For the sake of contrastive analysis, the excitation acceleration was controlled at 2 m/s\({}^{2}\). It shows that the resonant frequencies shift to the right with the decreasing of the initial separation distance, which is consistent with the simulation result. It can be attributed to the increasing repulsive magnetic force and the magnetic stiffness. Consequently, the resonant frequencies can be tuned by adjusting the separation distance according to the ambient excitation frequency. Furthermore, the amplitude of the first peak output power is another issue which deserves concern. Contrary to the resonant frequency, the peak output power for the first resonance goes up continuously with the decreasing of the separation distance. In the future designing, we need to make a trade-off between the resonance and peak output power. With the decrease of \(d_{0}\), the error between experimental and numerical results of the first peak power increases, because the mechanical damping ratios were kept constant in the theoretical model, while the actual values are variable. Moreover, the damping ratio of magnetic oscillator increases more significantly than that of the piezoelectric oscillator. Figure 14 shows the output power for the HEH with different directions of magnetic force. Two magnets will attract each other with the same magnetization direction, while they will repel each other in opposite direction. Due to the attractive force, the initial distance reduces to 47 mm. As a result of the attractive force, the resonant frequencies shift to the left, while the first peak output power decreases sharply as compared to that of the HEH with repulsive force. On the contrary, the second peak output  
Figure 12: Frequency responses for the HEH, LEMEH, LPEH and LVEHs: (**a**) experimental results; (**b**) numerical results. Figure 13: Frequency responses for the HEH with different separation distances \(d_{0}\): (**a**) experimental results; (**b**) numerical results. power is obviously enhanced. That is to say, the generating efficiency of piezoelectric element is much higher than that of the electromagnetic element with the attractive force. The theoretical value of the first peak power for the HEH is lower than the measured value. The reason is that attractive force induces more deformation of the piezoelectric beam. However, the mechanical damping of magnetic oscillator is also enhanced simultaneously. In this case, the HEH is more suitable for scavenging vibration energy in the high-frequency range. However, the attractive force is still a choice for energy harvesting at the lower excitation frequency. Similarly, the direction of magnetic force needs to be selected properly depending on the excitation frequency and electric power demands.