# Piezoelectric Composite Vibrator with a Bilaminated Structure for Bending Vibration
## 4 Fabrication and Performance Test of the Bilaminated Vibrator
The parameters of the five groups of 2-2 piezoelectric composite bilaminated vibrator samples were measured via the above test method. The results are shown in Table 3. The electromechanical coupling coefficients of the 2-2 piezoelectric composite bilaminated vibrator listed in Table 3 were calculated using Equation (1). Figure 14: Preparation technology of the piezoelectric ceramic vibrator. Figure 12.0 Image of the piezoelectric ceramic bilaminated vibrator samples. \begin{table}
\begin{tabular}{c c c c c} \hline
**Number of** & **Series Resonance** & **Parallel Resonance** & **Electromechanical** & **Maximum** \\
**Vibrators** & **Frequency/\(f_{s}\) (Hz)** & **Frequency/\(f_{p}\) (Hz)** & **Coupling Coefficient/\(k_{e}\)** & **Displacement/\(S_{m}\) (10\({}^{-11}\) m)** \\ \hline
1 & 4628 & 4848 & 0.2978 & 7.81 \\
2 & 4630 & 4850 & 0.2978 & 7.79 \\
3 & 4628 & 4850 & 0.2978 & 7.82 \\
4 & 4630 & 4850 & 0.2978 & 7.79 \\
5 & 4630 & 4850 & 0.2978 & 7.81 \\ \hline \end{tabular}
\end{table} 
Table 3: Performance parameters of the 2-2 piezoelectric composite bilaminated vibrator A laser Doppler vibrometer (PSV-400 Polytec Inc., Germany) equipped with software analysis system to achieve 2D and 3D animation display and data analysis. It was used to observe the actual vibration of the five groups of 2-2 piezoelectric composite bilaminated vibrator samples under free boundary condition. The vibration dynamic diagram was shown in Figure 16, which indicated that the vibration displacement at the center of the upper and lower surfaces was the largest. The center point was selected, and the vibration displacement curve was read. The maximum vibration displacement of each group vibrator was listed in Table 3.  
In accordance with the above measurement methods, five groups of piezoelectric ceramic bilaminated vibrators were measured using an impedance analyzer and a laser Doppler vibrometer. The series resonance frequency \(f_{s}\), parallel resonance frequency \(f_{p}\), bandwidth \(B\), electromechanical coupling coefficient, and maximum vibration displacement are listed in Table 4.  
The admittance and vibration displacement curves of the 2-2 and ceramic vibrators obtained by experiments are shown in Figure 17a,b, respectively. Table 5 and Figure 17 show that the resonance frequency of the 2-2 piezoelectric composite bilaminated vibrator is lower than that of the ceramic vibrator. The maximum vibration displacement of the 2-2 piezoelectric composite bilaminated vibrator is 2.297 times that of the ceramic one. The effective \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of** & **Series Resonance** & **Parallel Resonance** & **Electromechanical** & **Maximum** \\
**Vibrators** & **Frequency/\(f_{s}\) (Hz)** & **Frequency/\(f_{p}\) (Hz)** & **Coupling Coefficient/\(k_{e}\)** & **Displacement/\(S_{m}\) (10\({}^{-11}\) m)** \\ \hline
1 & 4705 & 4925 & 0.295 & 3.389 \\
2 & 4703 & 4923 & 0.295 & 3.388 \\
3 & 4705 & 4925 & 0.295 & 3.390 \\
4 & 4703 & 4923 & 0.295 & 3.390 \\
5 & 4705 & 4925 & 0.295 & 3.389 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance parameters of the ceramic vibrators  
Figure 16: Image of the vibration dynamic diagram. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Series Resonance** & **Parallel Resonance** & **Electromechanical** & **Maximum** \\
**Frequency/\(f_{s}\) (Hz)** & **Frequency/\(f_{p}\) (Hz)** & **Coupling Coefficient/\(k_{e}\)** & **Displacement/\(S_{m}\) (10\({}^{-11}\) m)** \\ \hline
2-2 & 4628 & 4848 & 0.298 & 7.79 \\ ceramic & 4704 & 4924 & 0.295 & 3.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the average piezoelectric parameters of the 2-2 and ceramic vibratorselectromechanical coupling coefficients and bandwidth of the 2-2 piezoelectric composite bilaminated vibrator are larger than those of the ceramic one.