Influence of an initial incidence angle on the dynamics of inverted flags

International audienceA nonlinear fluid-elastic model is developed in order to study the dynamics of two-dimensional inverted flags subject to wind at an initial angle of attack. Theodorsen's quasi-steady aerodynamic theory is used for the inviscid fluid-dynamic modelling of the deforming flag. The Polhamus leading edge suction analogy is employed to model flow separation effects from the free end at moderate angles of attack via a nonlinear vortex-lift force. The flag dynamics is solely described by the angle of rotation within the geometrically-exact Euler-Bernoulli beam theory. The equation of motion is discretised spatially via the Galerkin method. Bifurcation diagrams are obtained using a pseudo-arclength continuation technique. The numerical results show that inverted flags undergo multiple bifurcations as the flow velocity is increased. It is shown that transition between the regimes occurs at flow velocities inversely proportional to the initial incidence angle. It is also shown that, for sufficiently large mass ratios, the existence of a strong subcritical periodic solution can lead to direct transition from the stretch-straight (undeflected) state to large-amplitude flapping motion