## 2 Part Type, Machine-Made Parts and Experimental Characterizations
As standard for the material during simulations, a density of 2700 kg/m\({}^{3}\) as well as an isotropic elasticity with a Young's modulus of 70 GPa and a Poisson ratio of 0.34, resulting in a shear modulus of approx. 26.12 GPa, were assumed, which is typical for an aluminum alloy. Figure 2 shows calculated eigenmodes, including associated eigenfrequencies of a virtual part, taking the example of a geometrically mean connecting rod, that is, to each geometric parameter the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Geometric** & **Mean Value** & **Scatter Value** \\
**Parameter** & **(in mm)** & **(in mm)** \\ \hline \(d_{\text{R1}}\) & 18 & 0.15 \\ \(D_{\text{R1}}\) & 30 & 0.20 \\ \(d_{\text{R2}}\) & 24 & 0.15 \\ \(D_{\text{R2}}\) & 40 & 0.20 \\ \(h_{\text{R}}\) & 12 & 0.15 \\ \(l_{\text{R}}\) & 100 & 0.40 \\ \(w_{\text{B}}\) & 18 & 0.20 \\ \(h_{\text{B}}\) & 7 & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean value and scatter value for the generation of specific geometric dimensions of a connecting rod via random numbers depending on the geometric parameter. Figure 1: Geometric model of a connecting rod including geometric parameters. associated mean value from Table 1 was assigned. It can be seen that various eigenmodes with bending, torsional or longitudinal characteristics exist. They are labeled as _Mode-1_, _Mode-2_,... according to the order of the frequencies of the geometrically mean part in ascending order. As per simulation, 18 eigenmodes up to around 30 kHz exist, which can also be observed on machine-made parts with the help of laser Doppler vibrometry. However, depending on the mode under investigation, the associated frequency varies in a specific way according to geometric changes. Thereby, positive or negative correlations can be observed as well as slightly nonlinear correlations for larger geometric changes and interactional effects. Finally, due to the individual structure being different for each random set of geometric parameters, the eigenfrequencies are individual for a part and the modes may occur in another order compared to the geometric mean part. Within this paper, eigenfrequencies sorted by identified modes (and not by ascending frequencies) are used. It may be of interest that in a population, in which geometric dimensions vary normally distributed using the scatter values as described, the observed mean frequency values are very close to the values of the mean part given in Figure 2. The coefficients of variation are in the range of less than 1% to more than 2.5%. The eigenfrequencies vary according to normal distributions too, but different frequencies are often strongly correlated rather than being independent. In case of uniformly distributed parameter variations, the obtained frequency distribution is neither uniform nor normal and the coefficients of variation are significantly larger compared to the values observed for normal distributed geometric variations. For the investigations, a total of 29 real connecting rods were considered. They were manufactured by modern high quality machines according to the model as described. For 5 parts, which are referred to as _reference parts_, the identical mean geometry was set as nominal geometry. An additional  
Figure 2: Eigenmodes and eigenfrequencies up to 30 kHz of a connecting rod assuming mean geometry and standard material obtained by finite element method (FEM) simulation using specified settings. Qualitatively identical modes are the basis for measurements with acoustic resonance testing (ART). 24 consecutively numbered parts assuming random geometry were defined. These parts are termed as _validation parts_ within the article. Their nominal dimensions were set with 8 independent random numbers as described above, assuming the scatter values from Table 1 as well as identical but random cylinder ring heights and constant edge radii of 3 mm. The parameters of the parts with numbers 1 to 12 are based on a normal distribution, which can typically be used to describe manufacturing tolerances.