## 3 Results and Discussion
### Effect of Build Direction on the Dynamic Property  
Figure 9 provides the frequency response of the ME plates fabricated with different build directions, which were X, Z and Oblique directions. No filtering was implemented as no specific frequency band needed to be filtered out. Table 7 details the data. Since Sample X\({}_{0}\) had the lowest values of resonant response, its anti-vibration capability was the best compared with Sample O\({}_{0}\) and Z\({}_{0}\). Therefore, the sample's anti-vibration capability would be improved if it was built in the X direction. Table 8 details the effect of different build directions on the inherent characteristics of ME plates. It could be seen that the influencing trend of different build directions was predicted precisely. The difference between predictions and measurements in natural frequency was from 2.3% to 13.4% and the predicted mode shapes were the same as the measurements. These further confirmed that the theoretical modeling was reliable in predicting the plate's dynamic inherent characteristics. Furthermore, different build directions would change the samples' elastic modulus, shear modulus and density, and further influenced the corresponding natural frequencies. For example, the material property values of Sample Z\({}_{0}\) were the smallest among Z\({}_{0}\), X\({}_{0}\) and O\({}_{0}\), as listed in Table 2, the corresponding natural frequency was the lowest, with the first three measured natural frequencies separately being 15.2 Hz, 130.3 Hz and 323 Hz. The predicted data was 14.1 Hz, 112.8 Hz and 290.9 Hz. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multirow{2}{*}{**Samples**} & \multicolumn{3}{c}{**Order**} \\ \cline{3-5}  & & **1 st** & **2 nd** & **3 rd** \\ \hline \multirow{3}{*}{Average measured natural frequency \(A\) (Hz)} & L\({}_{0.1}\) & 16.6 & 148.9 & 375.1 \\  & L\({}_{0.15}\) & 18.0 & 154.9 & 384.8 \\  & L\({}_{0.2}\) & 20.1 & 167.1 & 392.3 \\ \hline \multirow{3}{*}{Average predicted natural frequency \(B\) (Hz)} & L\({}_{0.1}\) & 17.0 & 150.2 & 342.7 \\  & L\({}_{0.15}\) & 19.3 & 170.1 & 396.4 \\  & L\({}_{0.2}\) & 21.3 & 189.3 & 434.3 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Error (\%) \\ \(|B-A|/A\) \\ \end{tabular} } & L\({}_{0.1}\) & 2.4 & 0.9 & 8.6 \\  & L\({}_{0.15}\) & 7.2 & 9.8 & 3.0 \\ \cline{1-1}  & L\({}_{0.2}\) & 6.0 & 13.3 & 10.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The effect of different layer height on samples’ inherent characteristics. plates under cantilever boundary conditions. The ME plate's material properties will be deteriorated as the extrusion width decreases. Increasing layer height will improve the corresponding material property. When the build direction changes from X to Z, the material property of the sample will be reduced. Compared with the measurements, the theoretical model set up based on the bidirectional beam function combination method was validated, and it could give reliable predictions in the inherent characteristic of ME plates. The influencing trend of the processing parameters was predicted precisely. The natural frequency discrepancy was below 13.4%, and the predicted mode shapes were similar to the measured ones. In addition, different processing parameters, i.e., extrusion width, layer height and build direction, mainly led to the differences in samples' elastic modulus, shear modulus and density. When these values were greater, the anti-vibration capability became better and the corresponding natural frequency was higher. As the structural characteristics were not changed with varying processing parameters, there was no change in the mode shape. Besides, the material used here was polylactic acid (PLA), which is just a type of common material. The modeling and testing methods mentioned in this present work could also be applied to other materials. This paper provided a theoretical basis and technical support for further research in improving the dynamic performance of ME products. Conceptualization, S.J. ; data curation, Y.S. and Y.S.