# Impact of Aerodynamic Interactions on Aeroelastic Stability of Wing-Propeller Systems +
## 3 Dynamic Model Setup  
### Wing-Propeller Model  
The wing model used in this study is taken from ref. [11]. It comprises a rectangular wing with an aspect ratio of 9.12. The structural mass of the wing is approximately 205 kg. Mass and elastic distributions are considered constant with reference to the wing semispan. The baseline properties of the wing are summarized in Table 2.  
The wing model also includes structural damping through a stiffness-proportional damping factor. The eigenfrequencies and damping ratios of the isolated wing in the wind-off condition have been calculated and listed in Table 3.  
An aeroelastic investigation was conducted for the standalone wing using SDBox and DUST coupled with MBDyn. The comparison of the flutter point in terms of velocity and frequency showed excellent agreement, as reported in [11] and summarized in Table 4.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Characteristic** & **Value** \\ \hline Semispan & 5.7 m \\ Chord, \(c\) & 1.25 m \\ Elastic axis & 0.35-c \\ Center of mass axis & 0.46-c \\ Mass/unit span & 18 kg m\({}^{-1}\) \\ Inertia/unit span & 4.5 kg m \\ In-plane stiffness & \(1.16\times 10^{7}\) N m\({}^{2}\) \\ Out-of-plane stiffness & \(2.09\times 10^{6}\) N m\({}^{2}\) \\ Torsional stiffness & \(2.70\times 10^{5}\) N m\({}^{2}\) \\ Stiffness prop. damping & 0.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Baseline wing properties [11].  
\begin{table}
\begin{tabular}{c l c c} \hline \hline
**Mode** & **Description** & **Frequency, Hz** & **Damping Ratio, \%** \\ \hline
1 & First bending (out-of-plane) & 6.75 & 2.1 \\
2 & First torsion & 10.96 & 3.4 \\
3 & Second torsion & 13.79 & 4.3 \\
4 & Second bending (out-of-plane) & 30.33 & 9.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Eigenfrequencies and damping ratios for the standalone wing.  
The proposed study also employs a four-bladed propeller with a 1.8 m diameter. Mass and inertia properties are attributed to all the propeller blades and an electric motor located slightly behind of the propeller hub. The propeller properties are given in Table 5.  
Both pylon and propeller blades are assumed to be rigid, whereas the mounting stiffness at the propeller's pivoting point allows for pitch and yaw rotation modeling a flexible pylon system [9]. Consequently, a typical 2-degrees-of-freedom model for propeller whirl flutter, consistent with state-of-the-art practices, was established. The propeller blades are assumed to have a symmetrical NACA0012 airfoil. The blade geometrical parameters are presented in Figure 1 showing a linear twist and a constant chord distribution.  
To facilitate the analysis in SDBox, unsteady propeller aerodynamics were precalculated by employing lifting line elements and wake particles in DUST. Determination of the unsteady propeller derivatives for various harmonic excitation frequencies was achieved using transfer functions with the methods presented by [PERSON] et al. in refs. [7; 8]. The validation of the standalone propeller-pylon model is presented in a previous work published by the authors. Specifically, the whirl flutter stability boundaries obtained in windmilling conditions have been computed in SDBox and with the coupled MBDyn-DUST tool, showing an excellent agreement (see Figure 11 from ref. [11]).