Frequency-specific phase synchronization analysis of a stall-induced aeroelastic system undergoing 2:1 internal resonance in a low-speed wind tunnel

Wind tunnel experiments are performed on a pitch-plunge aeroelastic system possessing structural nonlinearity in the stiffness and subjected to dynamic stall conditions. With an increase in the flow speed (U), we observe a well-expected transition from decaying responses to limit cycle oscillations wherein the flutter frequencies of pitch and plunge coalesce perfectly close to the pitch natural frequency, indicating the onset of stall flutter. Interestingly, a further increase in the U yields a secondary frequency peak, emerging approximately at half of the primary frequency peak, accompanied by an intermittent period-1-period-2 (P1-P2) behaviour. Another transition is observed as the flow speed is increased further-the pitch-plunge motion starts exhibiting a beat-like response. We demonstrate that this particular behaviour is `2:1 internal resonance (IR)' and is attributed to a specific combination of structural parameters: the ratio ( omega) of natural frequencies of plunge and pitch (f(y) and f(alpha), respectively) being 0.44, and the structure possessing quadratic nonlinearity, resulting as the aerodynamic loads tune the flutter frequencies to become commensurate for a 2:1 IR. We show that a typical phase synchronization analysis is inadequate to explain the atypical transitions. To that end, we resort to a frequency-specific synchronization analysis wherein the pitch and plunge time signals are decomposed into two signals of specific frequency range. This reveals that the higher frequency signal (HFS) is always perfectly synchronized. On contrary, the lower frequency signal (LFS) is asynchronous during the intermittent regime and has strong synchrony at the onset of beats. The physical insights presented in this study can be useful for the design of increasingly slender aeroelastic structures that are often subjected to dynamic stall.