## 3 Comparative Analysis of FEM-Calculated and ART-Measured Eigenfrequencies
### Uncertainties and Errors of Eigenfrequencies Due To Data Acquisition Procedures  
The data acquisition procedures used, which means ART measurements and FEM calculations, lead to eigenfrequencies that may be affected by uncertainties or errors. The differences of simulated frequencies to measured values shown previously in Figure 4 are analyzed in this respect.  
The observed deviations from simulation and measurement are almost equal for all reference parts. This already indicates that random variations due to the acquisition procedures are not primarily causal. Furthermore, repeated ART measurements, as well as repeated FEM calculations (assuming physically irrelevant geometric variations to induce slightly different meshes), indicate that random effects cannot be responsible for the observed differences since the repeated acquisition procedures resulted to coefficients of variation in the magnitude of less or much less than 0.01 %. Moreover, all results mentioned in this section are based on multiple averages of both simulation and measurement data. Therefore, random effects are in any case significantly suppressed and play no role.  
Systematic influences may also affect eigenfrequencies. Measured frequencies may be influenced by various parameters regarding measurement techniques, experimental set-up, and strategies for data evaluation. These aspects are not represented by physical simulation modeling. They are therefore considered in the sense of modeling errors within the next subsection. Of course some aspects, for example the limited measurement resolution or uncertainties within temperature compensation, could influence measured eigenfrequencies slightly in a systematic way. But as such effects are considered to be minor, experimentally acquired eigenfrequencies can be seen as free of systematic errors from a practical point of view. In contrast, a convergence study showed that the FEM eigenfrequencies decrease with smaller element size. This is visualized in Figure 5, taking two modes as examples. All convergence data was extrapolated to obtain theoretical expected values at 0 mm. These were compared to the frequencies achieved when using the standard mesh size of 1.1 mm. In Figure 5, we used a linear function for Mode-1 and a quadratic function for Mode-2 for extrapolation due to the phenomenological behavior. Additionally, we only used the mesh size up to 2 mm since this range shows a relatively consistent trend. However, any dependence from the extrapolation procedure to the values expected at 0 mm is not essential for a general assessment of the convergence situation. The evaluation of the convergence data led to the result that the amount of the effect clearly depends on the mode, but the influence of the element size is ever smaller than one or two per thousand.  
In summary, we can conclude that neither uncertainties nor systematic errors within the data acquisition procedures are causal for the observed differences from simulation to measurement data. Therefore, the deviations shown in Figure 4 are due to aspects that were neglected during simulations or represented in an inaccurate way. Such model errors are addressed in the next subsection.  
Figure 5: Dependence of the eigenfrequencies from the maximum element size used for FEM regarding Mode-1 and Mode-2 of a virtual connecting rod with mean geometry (green point: standard mesh size of 1.1 mm; red dotted line and point: extrapolated behavior and expected value at 0 mm).