Flutter of a rectangular plate

Christophe Eloy (1) , Claire Souilliez (1) , Lionel Schouveiler (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

We address theoretically the linear stability of a variable aspect ratio, rectangular plate in an uniform and incompressible axial flow. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions. For different values of aspect ratio, two boundary conditions are studied: a clamped-free plate and a pinned-free plate. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, the flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. 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 aspect ratio of the plate. A new result is demonstrated: a plate of finite span is more stable than a plate of infinite span.

Mots clés: flow-induced vibration; cantilevered flexible plate; flutter instability; variable aspect-ratio

Domaines: Mécanique des fluides [physics.class-ph]

Christophe Eloy, Claire Souilliez, Lionel Schouveiler. Flutter of a rectangular plate. Journal of Fluids and Structures, 2007, 23 (6), pp.904-919. ⟨10.1016/j.jfluidstructs.2007.02.002⟩. ⟨hal-00140325⟩