Aero/Hydrodynamic Stability of Elastically Supported Plates in Narrow Channels With Upstream Barriers Preventing Flow Redistribution

Abstract

The dynamic stability of an elastically supported finite rigid plate centered in a straight narrow channel with incompressible flow on both sides of the plate and an upstream barrier preventing flow redistribution is analyzed. An integral equation for the pressure in a narrow channel having arbitrary small time-dependent boundary displacements is formulated and solved for the pressure distribution in terms of the boundary motion. The resulting expression for the time-dependent pressure distribution is combined with the plate differential equations of motion to yield the homogeneous equations of motion of the plate–fluid autonomous system. The Liénard–Chipart stability criterion is applied to the coefficients of the plate–fluid system equations to yield necessary and sufficient conditions for the dynamic stability of the plate–fluid system. The resulting stability requirements are expressed as algebraic inequalities involving dimensionless plate–fluid system parameters.