Promotion of Instability of a Sinusoidally Deformed Flexible Plate and its Transition to Oscillatory Motions

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We experimentally study the transition to large oscillatory motions of a thin elastic plate buckled into a second mode sinusoidal deformation. This deformation, intended to promote the onset of structural instabilities, is created by applying a permanent external net compressive force to the plate through a series of equispaced tension lines. These lines are attached to the two lateral edges of the plate, which are oriented parallel to the mean flow direction. We subject the deformed plate to an incompressible flow and find an early onset of the flutter instability (lower critical flow velocity, ${U}_{c}$) and increased range of periodic large oscillatory motions relative to previous studies of plates mounted in flag or inverted-flag configurations. No upstream vortex shedding or additional transversal rigidity is provided to achieve this lower ${U}_{c}$, which are methods used by previous researchers to initiate instability. The reduced ${U}_{c}$ is instead achieved by the combination of three mechanisms: a deformed plate that exhibits bistability, the destabilizing action of the net compressive force on the plate, and the pressure drag on the plate existent prior to large plate oscillations. Subjected to a mean flow, ${U}_{o}$, the deformed plate evinces three states of motion: (a) a buckled plate with small perturbations for ${U}_{o}l{U}_{c}$ (perturbations are of the order of 0.1% of the plate's length); (b) a plate with large oscillatory motions appearing as the superposition of traveling and standing waves for ${U}_{o}g{U}_{c}$, showing fundamental oscillatory frequencies ${f}_{o}$, which scale with ${U}_{o}$, along with higher harmonics; and (c) a plate with chaotic oscillatory motions for ${U}_{o}g{U}_{t}$, a transitional flow velocity where ${U}_{t}g{U}_{c}$, characterized by a broad frequency spectrum still with a characteristic ${f}_{o}$, and slightly reduced relationship between ${U}_{o}$ and ${f}_{o}$.