## 3 Simulation and Experiments of Vibration Characteristics of Atomizer
### Experiment  
Figure 4 shows the photograph of the equipment used for measuring the vibration mode of the piezoelectric vibrator. The power amplifier was used to provide the excitation signal during measurement.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Density** & **Elastic Modulus** & **Poisson** & **Inner/Outer Ring** & **Thickness** \\  & **(kg/m3)** & **(Gpa)** & **Poisson** & **Diameter (mm)** & **(mm)** \\ \hline PZT & 7500 & \(7.65\times 10^{\circ}10\) & 0.32 & 7.69/15.96 & 0.63 \\ Stainless steel & 8000 & 200 & 0.30 & 15.96 & 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material and geometric parameters of the piezoceramic vibrating mesh atomizer.  
Figure 3: Simulation diagram of the vibration mode of a piezoelectric vibrator.  
Figure 5 shows the frequency sweep curves of the vibration velocity and amplitude magnitude. It can be seen that the change trend of the vibration velocity and amplitude is nearly consistent. The experimental results showed that the resonance frequency of the piezoceramic vibrating mesh atomizer was set as 15.9 kHz, 78.2 kHz, 106.1 kHz, 116.5 kHz, 121.1 kHz, and 148.3 kHz, respectively. Compared to the previous simulation results, it suggests that there were another two resonance points at 106.1 kHz and 116.5 kHz in the experimental results, respectively. There were still some deviations in the corresponding resonance points between the simulation and experimental curves. The reasons for these deviations in the simulation and experimental data can be explained as follows: the finite element simulation is an ideal state, whereas the experimental process is inevitably interfered by some external influencing factors such as errors in measurement.  
Figure 6 shows the vibration modes of the resonance points. As seen from Figure 6a,b, the resonance frequencies were set as 15.9 kHz and 78.2 kHz, respectively, while the atomization could only be produced under the condition of high frequency vibration. The atomization could not be generated at  
Figure 4: Photograph of the equipment for measuring the vibration mode of the piezoelectric vibrator [29].  
Figure 5: Frequency sweep curves of the vibration velocity and amplitude magnitude [29].  
other lower resonance points. As shown in Figure 6c, the resonance frequency increased to 106.1 kHz. At this resonance point, both the vibration amplitude and vibration speed increased, thus the pump effect gradually forms, and ultimately, micro atomization is produced. Figure 6d shows the evidence that the resonance frequency became higher with a value of 116.5 kHz. As the corresponding vibration amplitude and pump effect are further increased, the atomization rate will also increase. As shown in Figure 6e, at the resonance frequency point of 121.1 kHz, the vibration velocity and frequency of the piezoelectric vibrator reached the maximum. Simultaneously, the volume change of the micro-tapered aperture located in the center of the atomizing plate also reached a maximum, and the pump effect was the strongest with the maximum atomizing rate achieved. However, as the working resonance frequency reached the largest with a value of 148.3 kHz, as shown in Figure 4, it implies that the amplitude of the piezoelectric vibrator is very small at this time, leading to the decrease in the volume change of the micro-tapered aperture, thereby the resulting pump effect is relatively weak with an atomization rate lower than the state at 121.1 kHz.