Vibration and sound of an elastic wing actuated at its leading edge

Abstract

The motion and sound of a thin elastic plate, subject to uniform low-Mach flow and actuated at its leading edge, is studied. The linearized response to arbitrary small-amplitude translation and rotation is analyzed using Fourier decomposition of the forcing signal. Both periodic (sinusoidal) and non-periodic (“step-jump”) actuations are investigated. When the frequency spectrum of the forcing signal contains an eigenfrequency Ω res of the unforced system, a resonance motion is excited and the plate oscillates at the corresponding eigenmode. The dynamical description is applied to formulate the acoustic problem, where the sources of sound include the plate velocity and fluid vorticity. Acoustic radiation of a dipole type is calculated and discussed in the limit where the plate is acoustically compact. In the case of sinusoidal excitation, plate elasticity has two opposite effects on sound radiation, depending on the forcing frequency: at frequencies close to Ω res , the near-resonance motion results in the generation of high sound levels; however, at frequencies far from Ω res , plate elasticity reduces the amplitude of plate deflection (compared to that of a rigid plate), leading to noise reduction. In the case of non-periodic actuation, the plate-fluid system amplifies those frequencies that are closest to Ω res , which, in turn, dominate the acoustic signature. The results identify the trailing edge noise as the main source of sound, dominating the sound generated by direct plate motion. We suggest the present theory as a preliminary tool for examining the acoustic signature of flapping flight, common in insects and flapping micro-air-vehicles.