## 4 Conclusions  
Despite extensive research on the characteristics of piezoelectric micropumps, there has been relatively little work on the vibration of rectangular piezoelectric bimorphs coupled with fluids, and almost no work on dual-bimorph systems. In this paper, we present a novel piezoelectric pumping element. We conducted extensive analysis of the vibration characteristics under structure-liquid coupled conditions using full-field optical methods based on the AF-ESPI. This analysis provided clear fringes indicating the displacement and precise estimates of resonant frequencies. LDV and impedance analysis were also used to characterize the vibrations produced by the piezoelectric pumping element. Our experimental results are in good agreement with those obtained using finite element analysis in terms of mode shape and resonant frequencies.  
The use of two piezoelectric bimorphs to drive the pumping element (rather than the single bimorph used in the previous designs) makes it possible to induce anti-phase as well as in-phase vibrations. Experimental and numerical results revealed that the resonant frequency of the anti-phase motion is lower than that of the in-phase motion. Coupling of the piezoelectric element with water or glycerine was far more pronounced than coupling with air due to the effects of density, acoustic velocity, and viscosity. In a comparison of experimental results and numerical findings, it was observed that the degree of deviation was far greater under water-coupled and glycerine-coupled conditions than under air-coupled conditions. The discrepancies in resonant frequency and mode shape between anti-phase and in-phase vibrations were also much more pronounced under fluid-coupled conditions than under air-coupled conditions. The influence of the vibration motion phase on both the flow rate and the flow velocity are also measured for the purpose of realizing the influences of different bimorph motion types on the efficiencies of the pumping element. It is indicated that the gain of flow rate obtained by the anti-phase motion of the dual-bimorph pumping element was larger than  
Figure 18: The increment of velocity for the pumping element in anti-phase vibration, in-phase vibration, and single plate.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency Voltage** & **Time (s)** & **Average Velocity (cm/s)** & **Increment of Velocity (cm/s)** \\ \hline
20 Hz & 5.7 & 10.96 & 0.8 \\
170 Hz & 5.13 & 12.18 & 2.02 \\
490 Hz & 5.9 & 10.59 & 0.43 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The average flow velocity and the velocity increment of the pump with a single bimorph.  
both those obtained by in-phase motion and by the single bimorph pumping element. For anti-phase vibration, the gain of flow rate for the first three modes were larger than those of higher frequencies. This research demonstrates the feasibility of dual-bimorph pump designs and provides an in-depth analysis of the vibration characteristics of the proposed piezoelectric pumping element.  
This study was initiated and designed by [PERSON], set-up experimental platform and conducted the experiments by [PERSON]. [PERSON] were also responsible in numerical simulations. [PERSON] and [PERSON] wrote the paper and contributed in revising the paper. All authors contributed in analyzing the simulation and experimental results.  
This research was funded by Ministry of Science and Technology (Republic of China) under Grant MOST 104-2628-E-011-002-MY3.  
The authors gratefully acknowledge the financial support of this research by the Ministry of Science and Technology (Republic of China) under Grant MOST 104-2628-E-011-002-MY3.  
The authors declare no conflict of interest.