Contact dynamics of a fluttering flag under gravity effect

Abstract

Thin structures with elasticity found in nature, such as flags and leaves, are under the influence of gravity in the process of interacting with uniform flow. In addition, a situation in which an elastic sheet collides with another rigid body may occur in the course of motion. In this study, the stability and post-critical behaviors of a flag, which interacts with uniform flow under gravity and is in contact with a nearby rigid wall, are experimentally investigated to elucidate the effects of gravity and contact on flutter dynamics and find design principles for the application to triboelectric energy harvesting. By varying the free-stream velocity and the distance between the clamped leading edge of the flag and the rigid wall, different modes are classified into static, flutter, partial contact, and full-contact. In terms of instability and contact process of the flag, the distance between the clamped leading edge of the flag and the rigid wall is a critical parameter. Therefore, we introduce a new dimensionless velocity considering this parameter and confirm that the transition of the mode is determined by this new dimensionless velocity. The new dimensionless velocity also characterizes the dynamic behaviors such as the dimensionless amplitude and reduced frequency of the flag.