Symmetry-breaking bifurcations and subharmonic lock-in of a flexible splitter plate in cylinder wake flow

This paper investigates the flow past a flexible splitter plate attached to the rear of a fixed circular cylinder at low Reynolds number 150. A systematic exploration of the plate length ( $L/D$ ), flexibility coefficient ( $S^{*}$ ) and mass ratio ( $m^{*}$ ) reveals new laws and phenomena. The large-amplitude vibration of the structure is attributed to a resonance phenomenon induced by fluid–structure interaction. The modal decomposition indicates that resonance arises from the coupling between the first and second structural modes, where the excitation of the second structural mode plays a critical role. Due to the combined effects of added mass and periodic stiffness variations, the two modes become synchronised, oscillating at the same frequency while maintaining fixed phase difference $\pi /2$ . This further results in the resonant frequency being locked at half of the second natural frequency, which is approximately three times the first natural frequency. A reduction in plate length and an increase in mass ratio are both associated with a narrower resonant locking range, while a higher mass ratio also shifts this range towards lower frequencies. A symmetry-breaking bifurcation is observed for cases with $L/D\leqslant 3.5$ , whereas for $L/D=4.0$ , the flow remains in a steady state with a stationary splitter plate prior to the onset of resonance. For cases with a short flexible plate and a high mass ratio, the shortened resonance interval causes the plate to return to the symmetry-breaking stage after resonance, gradually approaching an equilibrium position determined by the flow field characteristics at high flexibility coefficients.