## 7 Conclusions  
This study employed a nonlinear elastic cantilever beam as the primary structure, scrutinized its vibration modes for energy harvesting, and employed [PERSON]'s second law, [PERSON]'s angle transformation, and Taylor series expansions to derive the equation of the nonlinear beam. By incorporating the piezoelectric equation, magnet repulsion, and lever-type single-point slapping force, the coupling equation for this system was established. The Method of Multiple Scales (MOMS) was used to analyze the frequency response, and fixed-point plots were made to ascertain the occurrence of internal resonance. The output voltage of the PZT subjected to the slap force was simulated using the fourth-order Runge \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **With** & \multirow{2}{*}{\begin{tabular}{c} **No** \\ **Slapping** \\ **Theory** \\ **Voltage (V)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **No** \\ **Slapping** \\ **Volt. (V)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Overall** \\ **Slapping** \\ **Theory** \\ **Voltage (V)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **With** \\ **Slapping** \\ **Volt. (V)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **No** \\ **Slapping** \\ **Experiment** \\ **Voltage (V)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **No** \\ **Slapping** \\ **Experiment** \\ **Voltage (V)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Overall** \\ **Experiment** \\ **Voltage (V)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Slapping** \\ **Experiment** \\ **Voltage (V)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Overall** \\ **Experiment** \\ **Voltage (V)** \\ \end{tabular} } \\ \hline Mode 1 & 1.773 & 106.38 & 1.597 & 95.82 & 1.726 & 103.56 & 1.522 & 91.32 \\ Mode 2 & 2.282 & 136.92 & 2.248 & 134.88 & 2.184 & 131.04 & 2.046 & 122.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Theoretical and experimental voltage outputs with/without slapping force. Figure 28: Voltage output without slapping force when the 1 st mode was excited, (**a**) theoretical prediction, (**b**) experimental data. Figure 29: Voltage output without slapping force when the 2 nd mode was excited, (**a**) theoretical prediction, (**b**) experimental data. Kutta method. Finally, the validity of the theoretical framework was confirmed through experiments, leading to the following conclusions regarding this foundational slap-type wind-driven power generation system:  
Utilizing [PERSON]'s theorem and experimental outcomes, it is determined that with an internal resistance of 54,000 ohms and the addition of a 5-g mass to the lever's end, this power generation system attains its highest output electrical power. The experimental data and theoretical power generation voltage analysis indicate an increasing output voltage with increasing mode. Comparing the experimental data and theoretical root mean square voltage values for voltage generation, the first and second modes align closely with theoretical predictions. However, the irregular vibration of the elastic steel sheet in the third mode is attributed to a mismatch between the changing frequency of the rotating magnetic field from the attached magnet on the rotating shaft and the elastic steel sheet, preventing it from reaching the theoretical voltage. This study confirms that the slap-type VEH concept is feasible and has better voltage generation efficiency than the traditional VEH system without slapping force. In conclusion, experiments have validated the feasibility of utilizing deformation and flapping forces on a PZT to generate electricity simultaneously. The results affirm its capability for electricity generation. The prospect is promising for commercializing such power generation systems, envisioning installations on various platforms like multi-rotor aircraft, unmanned fixed-wing aircraft, motorcycles, or bicycles.