This study focuses on the vibration behavior of a flexible membrane wing encountering an accelerating free stream, aiming to unravel its transient response. Wind-tunnel experiments are carried out to synchronously measure the time-resolved membrane deformations and surrounding flow fields. Based on the time-frequency spectrum obtained by continuous wavelet transform of the vibration signal, the time interval from the non-vibration state to the establishment of the dominant second mode state is defined as the vibration onset stage. During this stage, a chordwise first vibration mode (approximately 20 Hz) initially emerges and subsequently transitions to a second mode (approximately 40 Hz). The vibration frequency of each mode increases over time due to the increasing camber and membrane tension. The nondimensional frequencies of membrane vibration generally match the Strouhal number range reported in the literature. Time-frequency analysis reveals a coupling between the membrane vibration and the velocity fluctuations within the leading-edge shear layer. As the accelerating flow impacts, the membrane gradually approaches the shear layer, perceives the disturbances therein, and destabilizes to vibrate. Notably, the generation and transition of vibration modes stem from the coupling of Kelvin–Helmholtz instability and membrane's natural frequencies, which is due to an internal resonance within the coupled fluid–structure system. The wake retains its inherent bluff-body flow features at the beginning of the vibration onset stage, after which it becomes coupled with the membrane vibration.
He et al. (Sun,) studied this question.