# Impact of Aerodynamic Interactions on Aeroelastic Stability of Wing-Propeller Systems +
## 4 Results
### Stability Results with Aerodynamic Interference  
The stability results in MBDyn-DUST are presented in this section. The system is initially excited by a blended impulse force at the wing tip located before the elastic axis to excite both the out-of-plane bending and torsional dynamics. The blended impulse is applied within 2 ms and with an amplitude of 12 kN to ensure an excitation up to 30 Hz. The free response of the system, encompassing both aerodynamics and structural dynamics, was subsequently tracked. Three distinctive free stream velocities were simulated with the hybrid and the fully coupled approaches. The results for the windmilling condition are depicted in Figure 11.  
Each plot represents the dynamic response of the wing's tip node in pitch and heave. The figures on the top illustrate the response obtained with the hybrid approach, whereas the figures on the bottom display the response obtained with the fully coupled approach. At the beginning of the simulations, the transient behavior due to the blended impulse is observable. After a few milliseconds, most of the excited mo  
Figure 11: Time histories of wing tip node for hybrid and fully coupled approach in windmilling condition. Figure 10: Trim results to obtain the desired operational condition for the hybrid and fully coupled approach. aerodynamic effects. Subsequently, the poorly damped dynamic survives, which is used to identify the dynamic response characteristics. A preliminary stability assessment can be performed by visual inspection of the time histories. For both simulation approaches, an unstable behavior is observed at a free stream velocity of 133 m s\({}^{-1}\). At 125 m s\({}^{-1}\) and 130 m s\({}^{-1}\), the measured responses exhibit stable and indifferent behavior, respectively. The results of the MPE in the form of eigenfrequencies and damping ratios are summarized in Table 8.  
It should be noted that the MPE method often fails to accurately predict eigenfrequencies and damping ratios for highly damped modes. Consequently, only the poorly damped modes after the transient phase are identified. The comparison between the hybrid and the fully coupled approach reveals no significant difference, however, the fully coupled simulations return a slightly smaller flutter speed compared to the hybrid approach and SDBox. No large differences between the two analysis approaches can be observed, leading to the conclusion that the aerodynamic interaction effects in windmilling conditions are only minor in terms of stability. The time histories for the same free stream velocities, but for the thrusting propeller are presented in Figure 12. Again, stable and unstable behaviors are shown at 125 m s\({}^{-1}\) and 133 m s\({}^{-1}\). Consequently, flutter is again covered within the velocity range considered. In contrast to the windmilling condition, the comparison between the hybrid and fully coupled approaches reveals more pronounced differences in the response. Indeed, the fully coupled approach appears to be less stable across all velocities compared to the hybrid approach. These results are confirmed by the MPE method (see Table 9). Figure 12: Time histories of wing tip node for hybrid and fully coupled approach in thrusting condition. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**SDBox**} & \multicolumn{2}{c}{**Hybrid**} & \multicolumn{2}{c}{**Fully Coupled**} \\
**Vel, m s\({}^{-1}\)** & **Freq, Hz** & **Damp, \%** & **Freq, Hz** & **Damp, \%** & **Freq, Hz** & **Damp, \%** \\ \hline
125 & 10.25 & 1.70 & 10.10 & 1.30 & 10.11 & 0.57 \\
130 & 10.13 & 0.69 & 9.98 & 0.07 & 9.98 & \(-\)0.09 \\
133 & 10.07 & 0.02 & 9.92 & \(-\)0.71 & 9.91 & \(-\)0.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Frequencies and damping ratios of the flutter mode in windmilling condition. The fully coupled approach returns an unstable condition at 130 m s\({}^{-1}\). Consequently, the influence of the aerodynamic interaction on flutter is stronger in case of a thrusting operational condition.