# Impact of Aerodynamic Interactions on Aeroelastic Stability of Wing-Propeller Systems +
## 3 Dynamic Model Setup
### Coupled Multibody--Mid-Fidelity Aerodynamic Model  
The corresponding wing-propeller models used for the hybrid and fully coupled analyses in MBDyn and DUST are described below. As given in Table 1, the structural components of the system are modeled in MBDyn. An overview of the model setup is given in Figure 2. \begin{table}
\begin{tabular}{l c c} \hline  & **SDBox** & **DUST + MBDyn** \\ \hline Flutter Speed, m s\({}^{-1}\) & 93 & 95 \\ Flutter Frequency, Hz & 9.07 & 8.93 \\ \hline \end{tabular}
\end{table} 
Table 4: Flutter speed and frequency for the standalone wing. Figure 1: Twist and chord distribution of propeller blade. The wing elastic properties are modeled using three-node beam elements [29]. Structural damping for the wing is modeled with a proportional stiffness factor of 0.1%, such as for the corresponding SDBox model. The wing is clamped at its root. The mass and inertia properties of the wing are modeled using lumped masses at each structural node, accounting for the offset between the elastic axis and the center of gravity. In total, 41 nodes and 20 beam elements are used, allowing one to capture the low-frequency bending and torsional dynamics of the wing leading to the flutter. The propeller is attached at 50% of the wing semispan. The pivoting point of the propeller is rigidly connected to the nth node at a distance of 24% chord from the elastic axis (i.e., towards the leading edge). The propeller hub is connected to the pivoting point through two joints: a total joint and a deformable hinge. The deformable hinge introduces the pylon rotational stiffnesses in yaw and pitch. Damping effects are neglected on this joint. The rotor node is located at the same position as the hub node. They are both connected via an axial rotation constraint, which enforces the rotation of the propeller. Additionally, four nodes are rigidly attached to the rotor node, representing the blades. The mass of the motor is connected to the hub node (non-rotating mass). Propeller blades are assumed to be rigid. The corresponding mass/inertia is lumped at the blade center of mass. For the hybrid approach, each blade is also connected to an aerodynamic body, representing the aerodynamic model in MBDyn. As previously mentioned, this model incorporates a propeller dynamic inflow and 3D correction factors such as tip loss correction. The chord and twist distributions are specified as input parameters. For the fully coupled approach, the nodes of the propeller are selected for coupling with DUST. Propeller aerodynamics in DUST are modeled using 16 lifting line elements on each blade (see Figure 3). The aerodynamics of the wing are modeled in DUST for both the hybrid and the fully coupled approaches. Surface panels are employed to represent the wing's geometry. The wing is discretized with 30 panels in the span direction and 20 panels in chord. To accurately capture the curvature of the leading edge, the chord distribution is discretized using a half-cosine function. The number of panels defined on the wing and lifting line elements on the propeller blades has been selected to capture the wing and propeller performance in  
Figure 2: Sketch of the coupled wing-propeller model in MBDyn–DUST. steady conditions. A mesh-independent study was conducted to ensure the convergence of lift/moment coefficients for the wing and thrust/torque for the propeller. For each coupling node, displacements, velocities, and accelerations are exchanged as well as the corresponding loads using the PreCICE coupling framework [25]. The interface between structural and aerodynamic grids is obtained as a weighted average of the distance between the nodes of the two grids and used for motion interpolation and consistent force and moment reduction. The tight coupling implicit scheme guarantees the convergence of loads and kinematic quantities at each time step. The simulation process starts with the initialization of MBDyn and DUST.