## 5 Experimental Results and Discussion
### Experiments of 2# Piezolectric Brick
#### 5.2.2 Average Powers from PZT4 Patches of 2#1-2#4 on PCSs (Close-Circuit)
This is because the strain energy in PCS transfers from stretching surface to pressing surface in the vibration process and there is energy dissipation in the transaction process. 2#1 and 2#3 PZT4 patches are in the stretching state in the forced vibration process, and there is a bigger energy dissipation from 2#1 and 2#3 PZT4 patches to 2#2 and 2#4 PZT4 patches compared to that from 2#2 and 2#4 PZT4 patches to 2#1 and 2#3 PZT4 patches in the free vibration process. This phenomenon indicates that 2#1-2#4 PZT4 patches basically have the same level of deformation and energy harvesting ability in the treading process, which can be explained by Equations (9)-(11) and (16)-(18). Figure 13: Average powers from unimorph PCSs of 2# piezoelectric brick versus the load resistance and force arm length (\(F=500\) N, \(f=1\) Hz). (**a**) 2#1 PZT4 patch on PCS1; (**b**) 2#3 PZT4 patchon PCS2. Finally, to explore the influence of the frequency of exerted force on the harvesting performance of 2# piezoelectric brick, the excitation parameters are set to be: \(F\) = 500 N, \(f\) = 2 Hz, and \(L\) = 33.5 mm, the generated voltages are reported for 8 s and shown in Figure 16, and the average powers are measured and displayed in Figure 17. Obviously, the generated voltages from 2#3 PZT4 patch as shown in Figure 16b are still slightly larger than the corresponding ones from 2#1 PZT4 patch as shown in Figure 16a, which is because the same reason as 5.2.1. Similarly, in the same condition, the maximum average power from 2#3 PZT4 patch is slightly larger than the one from 2#1 PZT4 patch, which can be seen from Figure 17. Some important experimental results displayed in Figures 16 and 17 are taken out and listed in Table 4; for example, the peak-to-peak voltages, the maximum average powers from 2#1 PZT4 patch and 2#3 PZT4 patch on unimorph PCSs and their optimal load resistances are (362 V, 89.74 mW, 230.77 k\(\Omega\)) and (376 V, 94.72 mW, 230.77 k\(\Omega\)) respectively. It is worth noting that the average power from the 2#3 PZT4 patch at 2 Hz is almost double times of that at 1 Hz, however, the output voltages from 2 Hz excitation and 1 Hz excitation are basically the same. It can be seen the output average power (power density) in 2 Hz excitation can reach up to 94.72 mW (37.89 \(\mu\)W/mm\({}^{3}\)). The reason is the  
Figure 14: Average powers from bimorph PCS1 of 2# piezoelectric brick versus the load resistance and force arm length (\(F\) = 500 N, \(f\) = 1 Hz). (**a**) 2#1 PZT4 patch; (**b**) 2#2 PZT4 patch. Figure 15: Average powers from bimorph PCS2 of 2# piezoelectric brick versus the load resistance and force arm length (\(F\) = 500 N, \(f\) = 1 Hz). (**a**) 2#3 PZT4 patch; (**b**) 2#4 PZT4 patch. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Force Arm** & \(L\) **= 19.5 mm** & \multicolumn{2}{c}{\(L\) **= 26.5 mm**} & \multicolumn{2}{c}{\(L\) **= 33.5 mm**} \\ \hline
2\#1 & 4.62 mW & 444.4 K\(\Omega\) & 10.68 mW & 411.8 K\(\Omega\) & 24.11 mW & 375 K\(\Omega\) \\
2\#2 & 4.16 mW & 444.4 K\(\Omega\) & 9.93 mW & 411.8 K\(\Omega\) & 22.18 mW & 375 K\(\Omega\) \\
2\#3 & 5.18 mW & 444.4 K\(\Omega\) & 12.36 mW & 411.8 K\(\Omega\) & 25.35 mW & 375 K\(\Omega\) \\
2\#4 & 4.81 mW & 444.4 K\(\Omega\) & 11.68 mW & 411.8 K\(\Omega\) & 24.51 mW & 375 K\(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The maximum average powers from 2#1-2#4 PZT4 patches on bimorph PCSs and the corresponding optimal load resistances (\(F\) = 500 N, \(f\) = 1 Hz).