## 4 Results and Discussions  
### Structural Validation  
In order to validate the structural model, a modal analysis simulation was done on the PVEH plate model to correlate with the displacement spectrum obtained from experiments ranging from 0 to 4000 Hz using electronic speckle pattern interferometry (ESPI). The simulated modal analysis results from FEM (Figure 9) agreed well with the experimental results obtained in Figure 10 below. The percentage difference shown in Table 2 is small between both simulated and experimental modal analysis results with values ranging from 0.042% to 4.614%. Therefore, the structural model reproduced by the computer aided modelling (CAM) is comparable to the real structure. As the desired frequency range in this research study is low (<100 Hz), only the first two modes were considered for comparisons especially the first mode or first bending mode. This model is thus verified in terms of structural perspective.  
Figure 8: Schematic diagram of electron speckle pattern interferometry (ESPI).  
The Modal Analysis simulation results shown in Figure 9 determined that the fundamental frequency of the coupled bluff splitter body and PVEH plate model is a first bending mode at 76.9 Hz having a 3.75% difference to 80 Hz obtained experimentally. The fixed boundary condition bluff splitter body was assumed to be non-contributing to the natural frequencies, thus  
\begin{table}
\begin{tabular}{c c c} \hline
**FEM Harmonic Response (Hz)** & **ESPI (Hz)** & **Difference (\%)** \\ \hline
76.9 & 80 & \(-\)3.75 \\
480.2 & 480 & 0.042 \\
1344.5 & 1340 & 0.33 \\
1707.4 & 1790 & \(-\)4.614 \\
2384.2 & 2430 & \(-\)1.884 \\
3532.5 & 3590 & \(-\)1.602 \\ \hline \end{tabular}
\end{table}
Table 2: Difference between simulated and experimental frequency.  
Figure 10: Dynamic characteristic of piezoelectric plate using ESPI and first bending mode contour observed at 80 Hz.  
Figure 9: Simulated harmonic response with model of first bending mode at 76.9 Hz.  
not affecting the displacement shape and natural frequencies. Natural frequencies only change with respect to the change of geometrical properties, material properties and boundary conditions. The discrepancy between the experimental and simulated natural frequencies happens when the three parameters mentioned above used in the simulation environment differ from the real structural model. The material properties of the PVEH in real-life may have slight difference as compared with the published material properties used in simulation. Besides, the simulation of clamping mechanism of the PVEH plate may have slight difference as compared with the real clamping device. Although these discrepancies occurred, the result with a percentage difference of lower than 5% is still considered acceptable.  
Figure 11 shows the difference in modal analysis results when considering, and without considering, the piezoelectric properties in PVEH plate. When the piezoelectric properties are being considered, the natural frequency shows a higher value, due to the piezoelectric coupling cause the plate to have stiffer properties. This modal analysis result is then act as a base reference during CSD studies in FSI simulation.