The influence of the wake on the stability of cantilevered flexible plates in axial flow

Cantilevered flexible plates in axial flow lose stability through flutter. Using the inextensibility condition for the cantilevered nonlinear plate equation of motion and the unsteady lumped-vortex model to calculate the fluid loads, a flutter boundary has been obtained. In the time-domain analysis performed to this end, the wake behind the oscillating cantilevered plate is assumed to issue tangentially from the free trailing edge and extend downstream with an undulating form. The influence of the wake on system stability may be characterized in terms of the non-dimensional mass ratio, reduced flow velocity and flutter frequency. For large values of the mass ratio, the plate vibrates with high frequency and high-order mode content. It is shown that the wake has less influence on system stability for long plates than it does for short ones.