As one of the fundamental problems in fluid mechanics, the flow-induced vibration of a flexible cylinder helps shed light on various complex fluid–structure interaction phenomena, such as the coupling effect of the cross-flow and in-line motions in the relationship between external fluid forces and vortical wake patterns. This paper devised a non-uniform in-flow condition (partially uniform flow and partially still water) for flexible cylinders in experimental and numerical conditions. Consistently, a new phenomenon is observed in different scale experiments and simulations where secondary traveling wave vibration of the flexible cylinder is excited from the still water part to the uniform inflow part due to the positive external fluid energy input in the still water. Furthermore, the detailed flow visualization on the vortical wake patterns around the vibrating flexible cylinders reveals that the external fluid force sources in the still water are due to the existence of the attached vortex pair with an uneven strength, which has been observed before in the still rigid cylinder in the oscillatory flow or the rigid cylinder oscillating in the still water at Keulegan–Carpenter number from 4 to 7.
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