## 3 Results and Discussion
### Dependencies Between Ice Accumulation and Modal Properties  
The interdependency between ice accumulation and the shift of the natural frequencies is investigated. It has to be mentioned that the equilibrium temperature was approximately \(-17\)\({}^{\circ}\)C due to the air stream ejected by the nozzles. In order to stop the icing process, due to the system design, the hoses first had to be drained of any residual water to prevent the nozzles from freezing. This made it necessary to keep the system running with open valves, which resulted in small ice thickness deviations during the measurements. Therefore, the frequency shifts caused by the ice accumulation are evaluated with regards to the actual thickness and the maximum deviation at the time a measurement was performed. The results for five selected datasets are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Average Ice** & **EF1** & **EF2** & **EF3** & **EF4** & **EF5** \\ \cline{2-6}
**Thickness** & **87.6 Hz** & **164.9 Hz** & **278.3 Hz** & **418.0 Hz** & **486.5 Hz** \\ \hline \(\sim\)1.2 mm & \(-\)0.68\% & \(-\)0.33\% & \(-\)0.10\% & \(-\)0.09\% & 0.17\% \\ \(\sim\)2.2 mm & \(-\)1.25\% & \(-\)0.93\% & \(-\)0.43\% & \(-\)0.73\% & 0.82\% \\ \(\sim\)3.2 mm & \(-\)2.01\% & \(-\)1.26\% & \(-\)0.79\% & \(-\)0.84\% & \(-\)0.47\% \\ \(\sim\)4.0 mm & \(-\)2.39\% & \(-\)1.64\% & \(-\)1.12\% & \(-\)1.44\% & 0.13\% \\ \(\sim\)4.6 mm & \(-\)2.86\% & \(-\)2.02\% & \(-\)1.49\% & \(-\)1.71\% & \(-\)0.67\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Relative shift of the first five natural frequencies under ice accumulation at approximately \(-17\)\({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Nozzles Status** & **Temperature** & **Max. Ice** & **EF1** & **EF2** & **EF3** & **EF4** & **EF5** \\ \cline{2-6}
**(0,0,1)** & \(-\)16.8 & \(\sim\)5.7 mm & \(-\)7.89\% & \(-\)6.01\% & \(-\)4.54\% & \(-\)3.40\% & \(-\)0.70\% \\ \((0,1,0)\) & \(-\)17.3 & \(\sim\)6.9 mm & 5.82\% & 5.98\% & 5.67\% & 0.84\% & 5.65\% \\ \((1,0,0)\) & \(-\)17.8 & \(\sim\)11.7 mm & \(-\)2.00\% & \(-\)1.36\% & \(-\)0.89\% & 0.67\% & 1.88\% \\ \((1,1,1)\) & \(-\)16.9 & \(\sim\)4.6 mm & \(-\)2.86\% & \(-\)2.02\% & \(-\)1.49\% & \(-\)1.71\% & \(-\)0.67\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Relative shift of the first five natural frequencies under different ice distributions, the values are peak estimates of the averaged response spectra.  
Figure 7: Response spectra of measurements conducted with different nozzle setups.  
A noticeable decrease of natural frequencies for the majority of the first five eigenmodes can be observed. This trend corresponds to the expectations and information from the literature [20], according to which, the frequencies have to decrease as the mass increases. The fifth eigenmode shows non-monotonic behaviour, which indicates complex effects that need further investigation. The acquired spectra are presented in Figure 8, in which similar tendencies can be observed also for higher modes in the range of 550 and 1000 Hz. Modes that lie in between 450 and 550 Hz, in which the fifth eigenmode is also found, show a rather complex behaviour. The stiffness of the ice itself and the increase of mass cause opposing effects resulting in non-monotonic shifts of the natural frequencies and modal damping ratio.