Lock-in during stall flutter under parametric excitation by harmonic longitudinal gusts

This study combines wind tunnel experiments and a minimal phenomenological model analysis to examine the effect of harmonic longitudinal (streamwise) gusts on stall flutter of a pitch-only wing in quasi-two-dimensional flow. In contrast to the more commonly known transverse-gust case, longitudinal gusting and its impact on aeroelastic dynamics remain largely underexplored. Above the onset speed of stall flutter, the gust response out of lock-in exhibits amplitude modulation (beating) in time histories and clear spectral sidebands, including a distinct beat-frequency peak, while a peak at the gust frequency itself is essentially absent. Moreover, the absence of the 1 : 1 lock-in and occurrence of the 2 : 1 lock-in indicate that longitudinal gusts act primarily through parametric, rather than externally forced, excitation. Guided by these observations, the dynamics is modelled with a minimal Mathieu-type van der Pol (M-VdP) oscillator featuring stiffness modulation. Applying the perturbation scheme, the experimentally observed spectral content is interpreted. Using the averaging method, slow-flow amplitude-phase equations are derived, which predict a 2 : 1 parametric lock-in band when the gust frequency is nearly twice the no-gust flutter frequency. Numerical solutions of the M-VdP model reproduce the principal experimental features, including the time history and sideband structure, and verify the existence and bandwidth of the 2 : 1 lock-in. The work provides new experimental and analytical insight into gust–aeroelastic coupling, and has implications for rotorcraft, UAVs and wind-turbine blades operating in unsteady inflow.