Flutter of a Rectangular Cantilevered Plate

We address theoretically the stability of a cantilevered rectangular plate in an uniform and incompressible axial flow. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, a flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions in the asymptotic limit of large plate span. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the plate aspect ratio. We demonstrate a new result: a plate of finite span is more stable than a plate of infinite span.