## 5 Experimental Setup and Verification Analysis
### System Resistance Measurement  
To assess the electrical power of this slap-type wind-driven power generation system, we introduced a resistance into the system as a load. The optimal electrical power is achieved when the added resistance value closely matches the internal resistance of the  
Figure 16: Configuration of the slap-type VEH. Figure 17: Natural frequencies of the first three modes. system. Following [PERSON]'s theorem, the internal resistance value of this system can be determined with the following equation:  
\[V_{L}=\frac{R_{L}}{R_{T}+R_{L}}V_{T}\ \rightarrow\ R_{T}=\frac{R_{L}V_{T}}{V_{L}}R_{L} \tag{43}\]  
where \(V_{L}\) is the voltage, \(R_{L}\) denotes resistance, \(R_{T}\) represents the internal resistance, \(V_{T}\) is the open-circuit voltage. The electric power equation is written as:  
\[P=IV=I^{2}R=\frac{V^{2}}{R} \tag{44}\]  
where \(P\) is the power, \(V\) represents the voltage, I denotes the current, and \(R\) is the resistance. After combining Equations (43) and (44), the following equation can be obtained:  
\[P=\frac{{V_{L}}^{2}}{R_{L}}=\frac{{(\frac{R_{L}}{R_{T}+R_{L}}V_{T})}^{2}}{{R_{ L}}}=\frac{{R_{L}}{V_{T}}^{2}}{{(R_{T}-R_{L})}^{2}+4R_{T}R_{L}}=\frac{{V_{T} ^{2}}}{{\frac{{(R_{T}-R_{L})}^{2}}{R_{L}}+4R_{T}}} \tag{45}\]  
Equation (45) reveals that the optimal electrical power can be attained when the load resistance (\(R_{L}\)) is equal to the internal resistance (\(R_{T}\)) of the system. We conducted experiments to investigate the impact of adding mass to the end of the rigid flat plate lever responsible for slapping the PZT. Specifically, we introduced a mass of 1 g to the lever end for experimental analysis. We employed an imc(r) data processor to measure the open-circuit voltage of the system, conducting five measurements to ensure data reliability. The average voltage obtained from these experiments was 4.846 volts. Subsequently, we introduced a 30 K-ohm resistance device into the system, conducting five additional experiments to ensure data consistency. The average voltage measured with the 30 K-ohm resistance was 1.735 volts. By incorporating the average open-circuit voltage and the average voltage obtained with the 30 K-ohm resistance into Equation (43), the theoretical value of the internal resistance of the system was calculated to be approximately 53,802 ohms (rounded to 54 K ohms). In the subsequent step, we tested and added resistances of 44 K, 49 K, 54 K, 59 K, and 64 K ohms as load resistances, recording the corresponding voltage and electric power as presented in Table 1. Utilizing the data from Table 1, we generated the ohms-volts and ohms-power diagrams (refer to Figures 18 and 19). It is evident from Table 1 and Figure 19 that when the attached resistance is 54 K, the system achieves its highest output power of 0.12056 mW. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{\(\Omega\)} & \multicolumn{8}{c}{**Voltage (V)**} \\  & **1** & **2** & **3** & **4** & **5** & **Average (V)** & **mW** \\ \hline
0 & 5.015 & 4.499 & 4.936 & 4.894 & 4.888 & 4.846 & \\ \hline
30,000 & 1.785 & 1.752 & 1.695 & 1.756 & 1.685 & 1.735 & 0.1003 \\ \hline
44,000 & 2.390 & 2.323 & 2.192 & 2.323 & 2.362 & 2.318 & 0.1097 \\ \hline
4 Next, we introduced masses of 3 g, 5 g, and 7 g to the lever end for experimental analysis. Employing the imc(r) data processor, we measured the open-circuit voltage of the system with a 3-g mass added to the end of the lever. After five experiments, the average measured voltage was 6.027 volts. Subsequently, a 30 K-ohm resistance was incorporated into the system, and after five additional experiments, the average voltage with the resistance was recorded as 2.132 volts. By averaging the open-circuit voltage and the resistance-added voltage and incorporating these values into Equation (43), the theoretical internal resistance of the system was calculated to be approximately 54,801 ohms (rounded to 55 K ohms).