M.Sc Student Dunaevich Lev Flutter of a Cavity-Backed Plate with a Cutout Department of Mechanical Engineering Professor Emeritus Pinhas Bar-Yoseph Abstract

Fluid-Structure Interaction (FSI) problems arise in many practical problems, ranging from the motion of a flag in the wind to the flutter of aircraft wings. In this research a new geometry for FSI is studied. The geometry consists of an elastic plate with a cutout at its center, placed over a rigid rectangular cavity. The cavity is embedded in an infinite rigid wall. The model is reduced to two dimensions and a cross-section is solved numerically. The flow is considered laminar and incompressible.

It was found that assuming infinite plate rigidity, Rossiter modes are observed, which are a type of shear layer instability. The Rossiter modes were governed by the ratio of momentum thickness (q*) to cavity opening length (A), where for A/q*<58 the flow was stable, for 60<A/q*<95 the shear layer oscillated at the second Rossiter mode, and for  95<A/q*<180 the flow oscillated at the third Rossiter mode.

When the plate is elastic flutter is observed. For constant  A/q*, the flutter was studied as a function of flow velocity normalized by the plates’ rigidity, giving a non-dimensional velocity (V*). It was observed that for low V* the flow behaves as it does for a rigid plate. Increasing the non-dimensional velocity V* above 3.3 causes flutter, and further increase of V* causes the plate to flutter at the second (V*>4.7) and third (V*>10) modes. The flutter is also dependent on momentum thickness, which influences the critical velocity at which flutter occurs.

Mapping the flutter stability threshold as a function of A/q* and V* shows a map with four regions. For A/q*<12, the flow was undisturbed by the cavity and the plate. For 12< A/q*<58 and V*>3.3, the flow is dominated by the plate flutter. For A/q*>58 and V*<3, the flow is dominated by Rossiter modes, while for A/q*>58 and V*>3.3 a highly nonlinear mixed region exists.