Dynamics of Two Parallel Inverted Flags in Axial Flow

Abstract

Abstract Two identical thin flexible plates, referred to as “inverted flags”, in a side-by-side arrangement are investigated theoretically. A linear model is developed to predict the onset of instability. This linear model elucidates the mechanism of instability and the sensitivity of the critical flow velocity to the gap between the two flags. The dynamics of a single flag has been studied massively, but the coupling of multiple flags is seldom reported. The Euler-Bernoulli beam theory and incompressible potential flow theory are adopted in the model. The Galerkin method and Fourier transform technique are used to solve flag displacements and fluid potentials, respectively. As the flow velocity is increased, the first mode becomes unstable via a pitchfork bifurcation. At higher flow velocities, higher modes lose stability via Hopf bifurcations. Out-of-phase and in-phase motions are predicted for the two flags. It is found that the critical velocity is independent of the flag gap-to-length ratio when it is approximately greater than 1. When the ratio is reduced, the critical velocity becomes smaller. When the ratio is extremely small, flutter occurs to the first mode before static divergence.