Acoustic Radiation From Bending Waves of a Plate

Abstract

In the commonly used definition of acoustic “radiation efficiency” of a plate, it is assumed that the amplitude of a traveling harmonic wave on the plate is kept constant, independent of the acoustic radiation load on the plate. As a result, this definition leads to an infinite value of the radiation efficiency when there is coincidence between the speed U of the traveling wave and the sound speed c in the surrounding fluid. The result of infinite radiation efficiency can be avoided if we consider the more realistic situation in which the plate is driven by a traveling force distribution, in which the amplitude of the force rather than the displacement is independent of the radiation load. This situation is considered here, and a modified definition of radiation efficiency is proposed. The displacement amplitude of the plate will have a maximum when the speed U of the force distribution equals the speed cb of free running bending wave on the plate. Then, if U < c, there is no power in the radiated wave and the power transferred from the plate to the fluid goes into heat as a result of viscothermal losses in the fluid. On the other hand, if U > c, the bulk of the power goes into the plane wave radiated from the plate. Finally, if U → c, the displacement and radiated power → 0 since the radiation impedance → ∞. In regard to the role of the viscothermal effects, it is interesting to find that at the coincidence frequency the contributions to the reactive part of the load impedance on the plate from the viscothermal boundary layer and the viscothermal losses in the bulk of the surrounding fluid almost cancel each other and the contributions to the resistive load are approxiamtely equal when U ∼ c.