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Flow-induced vibrations of flexible surfaces driven by coherent vortical structures are ubiquitous in engineering and biological flows; from the extraction of fluidic energy via oscillating electro-active polymers to vocal fold dynamics during voiced speech production. These scenarios may involve either discrete or periodic loading conditions due to the advection of vortices past the structure. This work considers, as a function of the vortex production frequency, the fluid-structure interaction that occurs as vortices are propagated tangentially over flexible plates with variable structural properties. Velocity fields are acquired with particle image velocimetry and used to compute the vorticity and pressure fields, while the plate energy is estimated from its kinematics. Primary and secondary peaks in plate deflection amplitude and the plate energy as a function of vortex production frequency are observed at integer fractions of the fundamental plate frequency. At resonance conditions, plate energy relative to discrete vortex loading is increased by approximately three orders of magnitude, while the sub-harmonics increase the plate energy by about two orders of magnitude. Additional physical influences on the energy exchange process, including vortex-to-plate spacing and Strouhal number, are also investigated, detailing the importance of spatial and temporal interactions. The magnitude of the initial plate deflection as the vortex ring approaches the plate, due to persistent vibrations from previous interactions, is shown to retard the time at which the maximum load is applied as the increased relative vortex-to-plate spacing weakens cross-sign vorticity interactions. Finally, plate properties are scaled to model the structural properties of the vocal folds and the effect of intra-glottal vortices on vocal fold dynamics is quantified, where a negligible influence is observed.
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This content will become publicly available on June 25, 2026
On the stability of an in-line formation of hydrodynamically interacting flapping plates
The motion of several plates in an inviscid and incompressible fluid is studied numerically using a vortex sheet model. Two to four plates are initially placed in line, separated by a specified distance, and actuated in the vertical direction with a prescribed oscillatory heaving motion. The vertical motion induces the plates’ horizontal acceleration due to their self-induced thrust and fluid drag forces. In certain parameter regimes, the plates adopt equilibrium ‘schooling modes’, wherein they translate at a steady horizontal velocity while maintaining a constant separation distance between them. The separation distances are found to be quantised on the flapping wavelength. As either the number of plates increases or the flapping amplitude decreases, the schooling modes destabilise via oscillations that propagate downstream from the leader and cause collisions between the plates, an instability that is similar to that observed in recent experiments on flapping wings in a water tank (Newbolt et al., 2024,Nat. Commun., vol. 15, 3462). A simple control mechanism is implemented, wherein each plate accelerates or decelerates according to its velocity relative to the plate directly ahead by modulating its own flapping amplitude. This mechanism is shown to successfully stabilise the schooling modes, with remarkable impact on the regularity of the vortex pattern in the wake. Several phenomena observed in the simulations are obtained by a reduced model based on linear thin-aerofoil theory.
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- Award ID(s):
- 2108839
- PAR ID:
- 10642755
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1013
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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