# Nonlinear Vibrations of Low Pressure Turbine Bladed Disks: Tests and Simulations
## 6 Conclusions  
In this paper, the nonlinear vibration analysis of an LPT bladed disk was carried out by considering different configurations, namely ones which were nominally tuned, tuned with aluminum dampers, and tuned with steel dampers. The nominally tuned configuration refers to the use of an array of nominally equal blades. The effectiveness of the damping capability of each configuration was studied as well. Primarily, the experimental activity was carried out on a test rig for a redesigned 48-blade disk which served as a surrogate for the original 144-bladed disk by taking into account all the necessary scaling criteria. The BTT system was used to measure the blade response. The system response and critical frequency were obtained for each of the 48 blades which exhibited a certain range of variability due to natural mistuning. Average values were taken for further consideration. The results obtained from the experimental test bring us to the conclusion that the predominant influence on the mistuning pattern arises from natural mistuning, rather than the presence of under-platform dampers. This finding underscores the significant role of inherent manufacturing and assembly variations in the dynamic response, highlighting that UPDs contribute less to mistuning than initially anticipated. In the next section, a numerical analysis was performed with the Policontact software, which in our case required some system parameters to be taken from the experimental data. Finally, the comparison between the experimental and numerical results was carried out by evaluating the percentage difference among them. The percentage error in all the parameters and configurations did not exceed the minimum acceptable level of 10%. This, in turn, proves the reliability of our model and numerical results. The minimum percentage error was observed for peak amplitude values rather than for the critical frequency or damping efficiency, not exceeding 2% for all the configurations. The numerical model showed a good level of prediction for critical frequency and damping efficiency as well. Error differences of 6.9%, 6.16%, and 7.11% for critical frequency, as well as 8.43% and 5.82% for damping efficiency, in the cases of nominally tuned (no \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Peak Amplitude (\(\mu\)m)** & **Critical Frequency (Hz)** & **Damping Efficiency (\%)** \\ \hline Experimental & 105.1 & 512.5 & 26.27 \\ Numerical & 106.8 & 476.1 & 24.74 \\ _Difference_ & \(-\)1.61\% & 7.11\% & 5.82\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental–numerical comparison for tuned + steel configuration. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Peak Amplitude (\(\mu\)m)** & **Critical Frequency (Hz)** & **Damping Efficiency (\%)** \\ \hline Experimental & 142.5 & 509.8 & - \\ Numerical & 141.9 & 474.6 & - \\ _Difference_ & \(0.46\%\) & \(6.9\%\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental–numerical comparison for nominally tuned (no-UPD) configuration. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Peak Amplitude (\(\mu\)m)** & **Critical Frequency (Hz)** & **Damping Efficiency (\%)** \\ \hline Experimental & 128.5 & 506.2 & 9.85 \\ Numerical & 129.1 & 475 & 9.02 \\ _Difference_ & \(-\)0.45\% & \(6.16\%\) & \(8.43\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental–numerical comparison for tuned + aluminum configuration. UPDs), tuned + aluminum UPDs, and tuned + steel UPDs were obtained as a result of experimental-numerical result comparison. The best damping capability can be seen for steel dampers, the damping efficiency for which stands at the level of 26.27%, which is almost 2.7 times more than for aluminum ones. This result can be related to the higher steel density which in turn imposes a higher normal static preload, resulting in more energy dissipation due to friction. The novelty of this work lies in its innovative combination of experimental and numerical approaches to analyze the nonlinear vibrations of bladed disks.