# A Review of MEMS Scale Piezoelectric Energy Harvester
## 2 Research Progress of PEH
### Optimization of Energy Harvesters' Structure
#### 2.4.3 Broadening the Frequency Bandwidth of the PEH  
To extend the frequency bandwidth of the PEH, [PERSON] et al. [63] placed a stopper over the proof mass of the designed S-shaped cantilever beam energy harvester (as shown in Figure 10). When the cantilever engages the stopper, the responses diverge from each other and the effective stiffness of the system increases abruptly. The experimental results showed that the stopper could widen the frequency bandwidth of the PEH to a certain extent, but it also reduced the maximum output voltage of the PEH.  
In 2016, [PERSON] et al. [72] attached the spring to the cantilever to form a new type of nonlinear PEH. The size of the cantilever beam was 70 mm \(\times\) 10 mm \(\times\) 0.2 mm. With the attached spring, the energy harvester had two steady states: one is deforming upwards and another is deforming downwards in the vertical direction. The simulation results showed that the structure reduced the resonant frequency without increasing the length or decreasing the thickness compared with the conventional energy harvester, which make it possible to collect the mechanical energy generated while walking. Under the 3 m/s\({}^{2}\) external excitation, the operating frequency of the PEH was between 1 Hz and 7 Hz.  
Then, in 2016, [PERSON] et al. [73] designed a PEH incorporating a S-shaped cantilever and magnets. The S-shaped cantilever beam was connected by three cantilever beams of different lengths. Therefore, the energy harvester had three intrinsic frequencies, 41.31 Hz, 56.85 Hz and 79.78 Hz, without considering the magnetic force factor. Under the influence of the magnetic force subjected to stretching or compression, the bandwidth of the PEH's resonant frequency would be broadened.  
By combining bi-stability and internal resonance, [PERSON] et al. [74] proposed a composite nonlinear energy harvester. As shown in Figure 11, the harvester consists of a piezoelectric cantilever beam carrying a movable magnet facing a fixed magnet. The two magnets face one another with the same pole to create a bi-stable system. The bi-stable system influences the mass-spring-damping system of the cantilever beam and makes the nonlinear effect. The simulation results showed that the frequency bandwidth of the composite nonlinear energy harvester was doubled compared to the bi-stable PEH with the magnet fixed to the free end of the cantilever beam.  
Figure 10: Configuration of the PEH with an adjustable top stopper. Reprinted by permission from [PERSON] et al. Microsyst. Technol. 18, 497 (2012). Copyright 2012 Springer Nature.  
[PERSON] et al. [75] designed a parallel-plate structure for the nonlinear PEH. This structure consisted of a tunable stopper-plate, a suspended spring-plate with proof mass, the piezoelectric material and supporting frames. The vertical gap between the stopper-plate and the suspended spring-plate could be adjusted to large, small and negative gaps, respectively, by increasing the packing. The highlight of this structure is that the resonant frequency and bandwidth of the energy harvester also changed with different gaps. It showed that the output voltage of the large gap was the highest in these states. Voltage of 2.449 V could be obtained under 1.5 g external excitation. The negative gap had the largest bandwidth of up to 100 Hz at 1.5 g external excitation, while the output voltage was low (0.733 V). The resonant frequency of the small gap structure increased from 102 Hz to 173 Hz with 0.1 g external excitation because of the influence of the air elasticity effect [76].