Fluid-Elastic Lock-in of a Cavity Shear Layer Instability With the Modes of a Submerged Cantilevered Beam

Abstract

Lock-in flow tones can occur for many different types of flow instabilities and structural-acoustic resonators at low Mach number. This paper examines the interaction between a shear layer instability generated by flow over a shallow cavity and the modes of an elastic cantilevered beam containing the cavity. A describing function model indicates that a cavity shear layer instability capable of producing lock-in with acoustic pipe resonances cannot achieve lock-in with equivalent structural beam resonances, particularly resonances of submerged structures. Fluid-elastic cavity lock-in is unlikely to occur due to the high level of damping that exists for a submerged structure, the high fluid-loaded modal mass, and the relatively weak source strength a cavity generates. Limited experimentation using pressure, acceleration, and particle image velocimetry (PIV) measurements has been performed which are consistent with the describing function model. A stronger source produced by a larger scale flow instability—separated flow over a bluff body—was able to lock-in with modes of the same submerged structure, further demonstrating that the concern for lock-in from a cavity shear layer instability is isolated to systems capable of stronger coupling or those dominated by fluid-acoustic resonances.