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In this study, we present a global Fourier mode decomposition framework forunsteady fluid-structure interaction. We apply the framework to isolate andextract the aeroelastic modes arising from a coupled three-dimensionalfluid-membrane system. The proposed framework is employed to decompose thephysical variables in the fluid and structural domains into frequency-rankedaeroelastic modes in a unified way. We observe the frequency synchronizationbetween the vortex shedding and the structural vibration via mode decompositionanalysis. We examine the role of flexibility in the aeroelastic mode selectionand perform a systematic comparison of flow features among a rigid wing, arigid cambered wing and a flexible membrane. With the aid of our modedecomposition technique, we find that the dominant structural mode exhibits achordwise second and spanwise first mode at different angles of attack. Thestructural natural frequency corresponding to this mode is estimated using anapproximate analytical formula. By examining the dominant frequency of thecoupled system, we find that the dominant membrane vibrational mode is selectedvia the frequency lock-in between the dominant vortex shedding frequency andthe structural natural frequency. From the fluid modes and the mode energyspectra at $\alpha=20^\circ$ and $25^\circ$, the aeroelastic modescorresponding to the non-integer frequency components lower than the dominantfrequency are found to be associated with the bluff body vortex sheddinginstability. The non-periodic aeroelastic response observed at higher angles ofattack are related to the interaction between aeroelastic modes caused by thefrequency lock-in and the bluff-body-like vortex shedding.

Aeroelastic mode decomposition framework and mode selection mechanism in fluid-membrane interaction