Forced motion and acoustic radiation of an elastic cylinder in axial flow

We study the forced motion and far-field acoustic radiation of an elastic cylinder subject to uniform axial flow and actuated at its upstream end by small-amplitude periodic displacement and rotation. The linearized problem is analysed under subcritical conditions of low nondimensional stream-flow velocity, u < u cr , where the unforced cylinder is aligned with the external flow. It is found that the forced motion at subcritical conditions is affected by the properties of the in vacuo system. A resonance is excited when the cylinder is actuated at one of its in vacuo eigenfrequencies, ω res , manifested by relatively large deflections. Fluid flow acts to regularize this behavior by transferring energy from the upstream driver to the fluid. The dynamical description is used as a source term in the formulation of the vibroacoustic problem. Assuming the cylinder is well-streamlined and neglecting the effect of vortex shedding, the far field sound is attributed directly to cylinder vibration. Acoustic radiation of a dipole type is found in the limit where the cylinder is acoustically compact. Following the dynamical description, it is shown that fluid flow reduces the sound level compared to that in the absence of mean flow, when actuation is applied close to ω = ω res . In addition, we demonstrate that far-field sound can be controlled by varying the actuation parameters. Analytical description of the dynamical and acoustic fields is obtained in the limit u ⪡ 1 , and found in close agreement with the exact numerical solution up to u ∼ O ( 1 ) . Discrepancies between the approximate and exact solutions are observed close to the resonance frequencies, and rationalized in terms of the strong fluid–structure coupling occurring when ω → ω res . At ω = ω res , a qualitative description of the effect of fluid stream flow on the system behavior is supplied.