# Impact of Aerodynamic Interactions on Aeroelastic Stability of Wing-Propeller Systems +
## 1 Introduction  
Electrification in urban air mobility is crucial for creating sustainable, quieter, and more efficient transportation systems that will revolutionize the way we navigate our cities, reducing carbon footprints and enhancing urban life. Next-generation aircraft configurations can benefit from electric propulsion in terms of aerodynamic efficiency and simplicity [1; 2], leading to the development of distributed electric propulsion systems (DEPs), where the propulsion can be placed at multiple locations. The relatively lightweight electric propulsion allows for propellers to be distributed along the wingspan, taking advantage of their high efficiency at low speeds [3]. However, these mass-optimized structures are inherently flexible. Combined with the presence of rotating propellers, the dynamic behavior becomes a critical factor, particularly for aeroelastic aspects. In the context of DEP configuration, the main aeroelastic phenomena are wing flutter and propeller whirl flutter. While wing flutter is a well-examined phenomenon, whirl flutter is receiving renewed attention due to novel configurations. Whirl flutter was discovered on the Lockheed L-188C Electra, after two fatal accidents in 1959 and 1960 [4]. The phenomenon may occur in flexible-mounted wing-propellersystems and requires one to consider the influence of rotating masses producing centrifugal, Coriolis, and gyroscopic forces/moments in addition to aerodynamic loads. The instability is driven by a whirl motion that can destabilize the pitch or yaw degree of freedom of the wing-python elastic suspension of the propeller. The foundational focus and development of suitable estimation procedures emerged in the 1960s [5; 6]. A straightforward structural model by [PERSON] and [PERSON] was developed during this period, and the associated aerodynamics were described analytically [5]. This work laid the groundwork for whirl flutter theory. The aeroelastic constraints for next-generation aircraft designs pose a critical challenge for engineers. Indeed, a thorough understanding of the aeroelastic behavior of novel aircraft configurations is essential, followed by the development of reliable aeroelastic prediction methods. Gaining a detailed understanding of the aeroelastic behavior requires examining the complex interactions between the wings and propellers, taking into account factors like propeller mounting stiffness, wing dynamics, propeller performance, and aerodynamic interactions. It is therefore not surprising that extensive research has been conducted recently on aeroelastic instabilities concerning wing flutter and propeller whirl flutter. An enhanced method for unsteady propeller aerodynamics used for whirl flutter was presented in [7] and compared to low- and mid-fidelity methods in [8]. The stabilizing effect of the propeller aerodynamic torque on whirl flutter was investigated in [9]. For coupled wing-propeller models, structural interactions between the wing and propeller were studied by [PERSON] and [PERSON] with an analytical approach validated by experimental results in [10] and recently investigated by the authors [11] using both frequency and nonlinear time-domain simulation tools, providing guidelines for the aeroelastic design of next-generation eVTOL aircraft. The influence of gyroscopic effects on aeroelastic stability of wing-propeller systems was highlighted in [12]. Concerning aerodynamic interaction, it is well known that aircraft designs with a DEP have a beneficial impact on the lift-drag ratio and overall aircraft performance [1; 2]. However, several questions remain unanswered. For instance, the effect of aerodynamic interaction between propellers and the wing on aeroelastic behavior is still under investigation. Preliminary studies indicate that both the thrust generated by propellers [13; 14] and the aerodynamic effects of propellers on the flow around the wing [15; 16] influence the aeroelastic stability. Recently, the aerodynamic interaction was discovered to be slightly destabilizing for whirl flutter cases [17].