# Investigation on the Acoustical Transmission Path of Additively Printed Metals
## 3 Experimental Design and Implementation  
As a base material for this approach, it was necessary to choose a material that is not only easily available for engineering and construction purposes--such as conventional steel--but also usable and processable in additive manufacturing machines. Stainless steel 316L/1.4404 was chosen to compare the damping behaviour of the drawn bar and 3D-printed samples. An oscillation test was performed to analyse the damping capability for this approach. The measurement setup is shown in Figure 4. For this purpose, a number of specimens per each measurement series were clamped into a sample holder. With an impulse hammer, a Dirac impulse was then induced to start a free oscillation. When comparing the investigated structures with the structures in Figure 4, it can easily be seen that the geometries \"Geom VH3-8\" in Figure 5 comply with particle damper (c) and the multi-unit particle damper (d). \"Geom VH1\" and \"Geom VH2\" were used as reference for the evaluation. Figure 3: Damping mechanisms in a powder-based damping structure. To compare the geometry and shape retention, the specimens were cut in the middle and the cross-section was analysed optically as shown in Figure 6.  
When comparing the inner structures of the shown geometries under consideration of the presence of sharp edges, the samples can be sequenced as: \"Geom VH6\" has no sharp edge in any direction because it is a spherical geometry, while \"Geom VH3, 4, 7 and 8\" have different edge lengths in relation to the force direction. These different lengths were considered as impedance elements affecting the dynamical behaviour. Therefore, the length of impedance elements was systematically modified. The free oscillation was plotted based on the data from the acceleration sensor. Due to the excitation with an impulse hammer, the excitation force depended on the testing personnel. One measurement series consisted of at least three samples which were exposed to forces between 35 and 70 N. The forces were recorded to analyse a possible interrelationship between excitation forces and the parameters, which described the decrease in acceleration amplitude. For comparability, the mean value of the excitation force was 43 N with a standard deviation of 6.5 N. Every sample was tested up to 20 times in order to analyse samples under comparable settings. Figure 4: Measurement setup for the free oscillation test. Figure 5: Selection of investigated samples. For the comparison of damping coefficient, in this approach the reduction of acceleration over time was investigated. Assuming that the amplitude, \(\hat{\mathrm{a}}_{\mathrm{damp}}\), of a sinusoidal wave is time-dependent, the following expression (1) can describe the acceleration over time. The widely used logarithmic decrement is not applicable because some of the measured datasets show a superimposed oscillation. With the shown equation, it is possible to calculate the \(R^{2}\) value for each point and thus exclude those data from global evaluation. For comparability, it is assumed that the oscillation could be described as a cosine function, starting (t = 0) with the maximum deflection initiated through the impulse hammer. \[\mathrm{a(t)=\hat{a}_{\mathrm{damp}}(t)\cos(\omega_{0}\;t)} \tag{1}\]  
For the amplitude function, \(\hat{\mathrm{a}}_{\mathrm{damp}}\), an initial function had to be chosen. Referring to the aim of this research approach, which is concerned with the investigation of damping, it had to be an asymptotic function converging to zero. In the context of damped oscillations, first- and second-order (2) exponential functions are widely used. \[ \begin{array}{c}\hat{\mathrm{a}}_{\mathrm{damp}}(t)=\mathrm{A}_{1}\;\mathrm{ e}^{\mathrm{d1}\;t}+\mathrm{A}_{2}\;\mathrm{e}^{\mathrm{d2}\;t}\\ \mathrm{d}_{1}=\mathrm{D}_{1}\;\omega_{0}\\ \mathrm{d}_{2}=\mathrm{D}_{2}\;\omega_{0}\end{array}