# Investigation on the Acoustical Transmission Path of Additively Printed Metals
## 4 Results  
The shapes shown in the Figure 5 oscillation are discussed in the following. When the three diagrams are compared, the samples have similar natural frequencies with a small offset. For the drawn bar, the frequency of the visible high-frequency oscillation is 914 Hz. For the printed bar it is 931 Hz, and for the printed with inner geometry it is 940 Hz. Through a modal analysis in COMSOL Multiphysics a similar natural frequency of 976 Hz was determined. Even though a lower natural frequency can be seen in Figure 8, the coefficient of determination is high, which can be interpreted as a small amplitude of the lower natural frequency. Following a comparison of the samples of drawn material directly with printed materials, it is apparent that the production method has an influence on the damping of the samples. This influence can also be derived from a comparison between the measurement series \"Geom VH1: Drawn bar\" and \"Geom VH2: 3D-printed bar\", which can be seen in Table 1. For these two series, the four parameters seem to stay in the same dimension, although they still indicate a clear impact of the production method. The comparison of parameters of the following Figures 8-10 are represented in a more descriptive way in Figure 11.  
Figure 8: Acceleration data and fitted curve for a drawn bar. Figure 7: Measured acceleration with marked highpoints and calculated fitting curve. Further comparison concluded that the energy decay is highly related to the shape of the inner geometry. Figures 10 and 11 indicate that the spherical shape leads to a significantly higher energy decay, thereby shortening the decay time. The natural frequency of the oscillation is almost constant for both series \"Geom VH6\" and \"Geom VH4\". For every measurement, the parameters A\({}_{1}\), A\({}_{2}\), d\({}_{1}\) and, d\({}_{2}\) were determined. For each geometry variant and each parameter, the distribution and median were calculated. The results of this calculation are shown in Table 1. It can be seen that the influence on energy decay is highly related to the shape of the inner geometry and the orientation of the shapes in relation to excitation. Figure 11 shows the possible influence of geometries, whereby the colour arrangement is chosen in such a way that the affiliation of the samples becomes apparent. The measurement series \"Geom VH7\" and \"Geom VH8\" are the same set of samples, but rotated by 180\({}^{\circ}\). The two graphs show that the orientation of the geometry is not relevant, although the shape of the geometry is decisive for the damping. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Measured Sample** & \(\mathbf{d_{1}}\) & \(\mathbf{A_{1}}\) & \(\mathbf{d_{2}}\) & \(\mathbf{A_{2}}\) \\ \hline Geom VH1: Drawn bar & \(-280.9\) & \(0.31\) & \(-48.9\) & \(0.21\) \\ \hline Geom VH2: 3D-printed bar & \(-203.2\) & \(0.62\) & \(-54.6\) & \(0.12\) \\ \hline Geom VH3: 3D-printed bar with & & & & \\ rectangular inner shape & \(-40.6\) & \(0.38\) & \(-6.3\) & \(0.07\) \\ (force\(-\)parallel) & & & & \\ \hline Geom VH4: 3D-printed bar with & & & & \\ rectangular inner shape & \(-785.4\) & \(2.62\) & \(-51.8\) & \(0.19\) \\ (force\(-\)orthogonal) & & & & \\ \hline Geom VH5: 3D-printed bar with & & & & \\ inner ellipsoidal geometry & \(-520.0\) & \(1.19\) & \(-56.1\) & \(0.04\) \\ \hline Geom VH6: 3D-printed bar with & & & & \\ inner spherical geometry & \(-617.4\) & \(1.64\) & \(-37.4\) & \(0.01\) \\ \hline Geom VH7: 3D-printed bar with & & & & \\ triangular inner shape (top-up) & \(-282.3\) & \(0.50\) & \(-0.6\) & \(0.00\) \\ \hline Geom VH8: 3D-printed bar with & & & & \\ triangular inner shape (top-down) & \(-397.5\) & \(0.95\) & \(-28.1\) & \(0.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of the parameters for function \(\hat{\mathrm{a}}_{\mathrm{damp}}\). Figure 9: Acceleration data and fitted curve for a printed bar with a rectangular inner shape (force-orthogonal).