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

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. The proposed framework is employed to decompose the physical variables in the fluid and structural domains into frequency-ranked aeroelastic modes in a unified way. We observe the frequency synchronization between the vortex shedding and the structural vibration via mode decomposition analysis. We examine the role of flexibility in the aeroelastic mode selection and perform a systematic comparison of flow features among a rigid wing, a rigid cambered wing and a flexible membrane. 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 find that the dominant membrane vibrational 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 $25^\circ$, the aeroelastic modes corresponding to the non-integer frequency components lower than the dominant frequency are found to be associated with the bluff body vortex shedding instability. The non-periodic aeroelastic response 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.