## 5 Conclusions  
In this study, six strip-like test pieces with different stacking methods were manufactured, based on FDM. Their material constants were inversely calculated. We observe a pairwise relationship because the Young's modulus is related to the printing direction, and the shear modulus is related to the plane. A total of nine material constants were input \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer Height** & \(E\) **(GPa)** & \(G\) **(GPa)** & **Extrusion Amount (mm/1 mm-Feed Material)** \\ \hline
0.1 mm & 3.27 & 1.16 & 0.0166 \\
0.15 mm & 3.34 & 1.19 & 0.0249 \\
0.2 mm & 3.19 & 1.12 & 0.0333 \\
0.3 mm & 3.06 & 1.03 & 0.0499 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Material constants with different layer heights. Figure 11: Material constants of test pieces with different layer heights. into ABAQUS to simulate the natural resonance frequency of the orthotropic material. Test pieces with different stacking methods were simulated by setting diverse directions of the test pieces. The simulation results are highly consistent with theoretical and experimental values, proving the accuracy of the inversely calculated material constants based on test results. This establishes a complete set of methods for measuring and simulating orthotropic material constants. Only the oscilloscope and sensor, e.g., strain gauge or piezoelectric film, are needed to measure the dynamic signal. Then, the mechanical property is measured by inversely calculating the frequency domain transformation. Subsequently, the influence of changing printing parameters, such as the raster angle and layer height, on the material properties was studied. It is found that when \(\theta\) increases, the measured value of \(E\) decreases, because the stiffness of the test piece becomes more dependent on the binding force between the wire materials, rather than the strength of these materials themselves; this reduces the stiffness. The maximum value of \(G\) is achieved when \(\theta=45^{\circ}\), which shows a symmetrical distribution. This is because when subjected to torsional force, materials generally experience the maximum shear stress in the direction of \(45^{\circ}\). In other words, the test piece printed along the \(45^{\circ}\) direction can withstand the maximum torsional force. In addition, Mohr's circle indicates that the torsional forces at \(\theta=30^{\circ}\) and \(\theta=60^{\circ}\) are the same, thus, leading to symmetrical distribution. Finally, the influence of the layer height was discussed. It is found that for layer heights between 0.3 mm and 0.15 mm, both \(E\) and \(G\) increase as the layer height decreases. However, when the layer height is further reduced to 0.1 mm, both \(E\) and \(G\) decrease. A smaller layer height indicates a higher degree of compactness of the stacked layers in the z-direction, thus, resulting in higher strength. However, when the set layer height is smaller, the extrusion amount per unit length of wire is also reduced, leading to the optimal value of the layer height at approximately 0.15 mm. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12136812/s1](https://www.mdpi.com/article/10.3390/app12136812/s1)]([https://www.mdpi.com/article/10.3390/app12136812/s1](https://www.mdpi.com/article/10.3390/app12136812/s1)). This study was initiated and designed by [PERSON], while [PERSON] set-up the experimental platform and conducted the experiments. [PERSON] was also responsible for the numerical simulations. [PERSON] wrote the paper. All authors contributed to analyzing the simulation and experimental results. All authors have read and agreed to the published version of the manuscript. This research was funded by Ministry of Science and Technology (Republic of China) under grant MOST 107-2221-E-002-193-MY3. Not applicable. A part of Figure 3 presented in this study are openly available in ScienceDirect at DOI: 10.1016/j.compstruct.2021.113970, reference number [30].