A semi-analytical model for the combined aeroelastic behaviour and gust response of a flexible aerofoil

The combined aeroelastic behaviour and gust response of a flexible aerofoil is explored theoretically. The analysis comprises a structural model based on Rayleigh’s beam equation, which describes the aerofoil's chordwise dynamics. The aerodynamic load is accounted for via Peters' state-space model for the case of a morphing aerofoil undergoing arbitrary pitching and plunging motion. By assuming a suitable modal expansion for the structural displacement, Ritz's method is used to solve the coupled aeroelastic equations of motion in the fashion of a classic Mass–Damper–Spring system. The proposed model is validated against both previous work and established results appertaining to the stability analysis and gust response of a rigid Typical Section, with a vertical wind gust being taken as the aerodynamic perturbation. The influence of chordwise flexibility on both aeroelastic stability and gust response is investigated critically for different cases.