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The bistable fluttering response of heavy inverted flags with different aspect ratios ( $AR$ ) is investigated to determine how the vortical structures affect the intermittent vibration response of the flag. A heavy inverted flag in a uniform flow may exhibit several response modes; amongst them are three major modes that occur over an extended velocity range: stationary, large-scale periodic oscillation and one-sided deflected modes. Significant hysteretic bistability is observed at the transition between these modes for all $AR$ , which is notably different from the conventional flag vibration with a fixed leading edge and free trailing edge where no hysteresis is observed at the lower $AR$ limit ( $AR<1$ ). The difference is associated with the distinct roles of vortices around the flag. Experiments with flags made of spring steel are conducted in a wind tunnel, where the flow speed is steadily increased and later decreased to obtain different oscillatory modes of the heavy inverted flags. The experimental results are used to validate the numerical model of the same problem. It is found that different critical velocities exist for increasing and decreasing flow velocities, and there is a sustained hysteresis for all $AR$ controlled by the initiation threshold and growth of the leading-edge and side-edge vortices. The effect of the vortices in the bistable oscillation regime is quantified by formulating a modal force partitioning approach. It is shown that $AR$ can significantly alter the static and dynamic vortex interaction with the flexible plate, thereby changing the flag's hysteresis behaviour and bistable response.
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This content will become publicly available on October 25, 2026
Investigating the significance of flatness defects in the origin of hysteresis in flag flutter
Flag flutter frequently features a marked difference between the onset speed of flutter and the speed below which flutter stops. The hysteresis tends to be especially large in experiments as opposed to simulations. This phenomenon has been ascribed to inherent imperfections of flatness in experimental samples, which are thought to inhibit the onset of flutter but have a lesser effect once a flag is already fluttering. In this work, we present an experimental confirmation for this explanation through motion tracking. We also visualize the wake to assess the potential contribution of discrete vortex shedding to hysteresis. We then mould our understanding of the mechanism of bistability and additional observations on flag flutter into a novel, observation-based, semiempirical model for flag flutter in the form of a single ordinary differential equation. Despite its simplicity, the model successfully reproduces key features of the physical system such as bistability, sudden transitions between non-fluttering and fluttering states, amplitude growth and frequency growth.
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- Award ID(s):
- 2145189
- PAR ID:
- 10644404
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1021
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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