The effect of flexural stiffness on the sound of a hanging filament: From a membrane to a rigid body

Abstract

We consider the acoustic field of a thin flexible filament subject to uniform mean flow and a ‘hanging chain’ tension force parallel to its unperturbed state. The filament is actuated via harmonic heaving motion at its upstream edge with prescribed frequency and small amplitude. To investigate the effect of filament flexural rigidity, we analyze the system acoustic radiation in the entire range of body structural stiffnesses. Assuming two-dimensional high Reynolds and low Mach number flow, we apply a near-field description based on potential thin airfoil theory. The near-field model is then used to formulate the source term in the Powell-Howe acoustic analogy. The far field sound is calculated applying a compact Green's function approach, yielding the leading order acoustic dipole field. In the limit of small flexural stiffness, we find that the acoustic field of a highly-elastic filament converges to the far field of a hanging membrane, dominated by the wake dipole sound. The wake sound component also dominates the system radiation in the limit of small actuation frequencies, where the filament deflects as a rigid body regardless of its structural stiffness. Sufficient increase in heaving frequency intensifies the relative contribution of filament motion dipole, resulting in significant differences between systems with different rigidities. Reflecting the impact of filament elasticity, these differences manifest the system's natural frequency response, leading to increased levels of sound for actuations at the system's eigenstates. In cases where the trailing edge wake and motion dipoles acquire similar amplitudes and opposite phases, significant sound reduction is found.