Aeroelastic Reduced-Order Model Differential Equations in Transoni Buffeting Flow

Numerical simulation of transonic shock buffet remains a formidable challenge due to its inherently nonlinear, unsteady nature. These difficulties are further compounded for three-dimensional configurations and when aeroelastic coupling is included. Consequently, computational studies of aeroelastic shock buffet interactions have largely been confined to two-dimensional systems. This limitation motivates reduced-order models (ROMs) that can efficiently and accurately reproduce aeroelastic responses in buffeting flow. This paper presents a nonlinear unsteady aerodynamic ROM that combines self-excited nonlinear oscillator dynamics with Volterra theory to represent nonlinear memory effects. The resulting integro-differential equation ROM is identified using orthogonal matching pursuit. Application to the ONERA OAT15A airfoil demonstrates that the compact formulation reproduces key nonlinear behaviors, including aeroelastic lock-in, with high accuracy relative to the full-order model. It is shown that the “lock-in” instability occurs when buffet-induced aerodynamic damping overcomes structural damping, yielding negative net effective damping. The limitations and potential extensions of the approach are also discussed.