In this study, we present a global Fourier mode decomposition framework for unsteady fluid–structure interaction. We apply the framework to isolate and extract the aeroelastic modes arising from a coupled three-dimensional fluid–membrane system. We investigate the frequency synchronization between the vortex shedding and the structural vibration via mode decomposition analysis. We explore the role of flexibility in the aeroelastic mode selection and perform a systematic comparison of flow features among a rigid flat wing, a rigid cambered wing and a flexible membrane. The camber effect can enlarge the pressure suction area on the membrane surface and suppress the turbulent intensity, compared to the rigid flat wing counterpart. With the aid of our mode decomposition technique, we find that the dominant structural mode exhibits a chordwise second and spanwise first mode at different angles of attack. The structural natural frequency corresponding to this mode is estimated using an approximate analytical formula. By examining the dominant frequency of the coupled system, we show that the dominant membrane vibration mode is selected via the frequency lock-in between the dominant vortex shedding frequency and the structural natural frequency. From the fluid modes and the mode energy spectra at $\alpha =20^{\circ }$ and 25°, the aeroelastic modes corresponding to the non-integer frequency components lower than the dominant frequency are observed, which are associated with the bluff body vortex shedding instability. The non-periodic aeroelastic behaviors observed at higher angles of attack are related to the interaction between aeroelastic modes caused by the frequency lock-in and the bluff-body-like vortex shedding. Using the mode decomposition analysis, we suggest a feedback cycle for flexible membrane wings undergoing synchronized self-sustained vibration. This feedback cycle reveals that the dominant aeroelastic modes are selected through the mode and frequency synchronization during fluid–membrane interaction to exhibit similar modal shapes in the membrane vibration and the pressure pulsation.

在这项研究中，我们提出了非定常流固耦合的全局傅里叶模式分解框架。我们应用该框架来隔离和提取由耦合的三维流体膜系统产生的气动弹性模式。我们通过模式分解分析研究涡旋脱落和结构振动之间的频率同步。我们探索了灵活性在气动弹性模式选择中的作用，并对刚性平翼、刚性弧形翼和柔性膜之间的流动特征进行了系统比较。与刚性平翼对应物相比，弧度效应可以扩大膜表面的压力吸入面积并抑制湍流强度。借助我们的模式分解技术，我们发现主要结构模态在不同的攻角下表现出弦向第二和展向第一模态。使用近似解析公式估计对应于该模式的结构固有频率。通过检查耦合系统的主频率，我们表明主膜振动模式是通过主涡脱落频率和结构固有频率之间的频率锁定来选择的。从流体模式和模式能谱在 我们表明，主要的膜振动模式是通过主要涡旋脱落频率和结构固有频率之间的频率锁定来选择的。从流体模式和模式能谱在 我们表明，主要的膜振动模式是通过主要涡旋脱落频率和结构固有频率之间的频率锁定来选择的。从流体模式和模式能谱在$\alpha =20^{\circ }$和25°，观察到与低于主频率的非整数频率分量对应的气动弹性模态，这与钝体涡旋脱落不稳定性有关。在较高攻角下观察到的非周期性气动弹性行为与频率锁定和钝体状涡旋脱落引起的气动弹性模式之间的相互作用有关。使用模式分解分析，我们建议对经历同步自持振动的柔性膜翼进行反馈循环。该反馈循环表明，在流体 - 膜相互作用期间，通过模式和频率同步选择主要气动弹性模式，以在膜振动和压力脉动中表现出相似的模态形状。