ENERGY CONSERVATION AND THE DAMPING OF FLEXURAL WAVES BY VORTICITY PRODUCTION

Abstract An analysis is made of the transfer of energy between structural/acoustic vibrations and fluid kinetic energy in flows at very small Mach number. A general energy balance equation is discussed for a vibrating rigid body in either incompressible or low Mach number compressible mean flows. This equation can be used to calculate the growth or decay of structural or acoustic oscillations, and to locate regions of the flow where energy exchanges are significant. A similar general treatment for vibrating elastic bodies does not seem to be possible, except in simple cases involving thin elastic plates in parallel flow. Two such problems are discussed, involving the dissipation of structural vibrations by vorticity production (i) at the trailing edge of a large elastic plate, and (ii) in the circular apertures of a perforated elastic plate in a two-sided grazing mean flow. The interaction of boundary layer turbulence with the apertures of a perforated plate can be a particularly intense source of sound, but in applications where the characteristic frequencies are small, a grazing flow perforated screen has been shown to be an efficient sink of acoustic energy. In this paper predictions are given for damping of bending waves by the same mechanism. When the fluid loading is large, such as for a steel plate in water, these predictions indicate that the damping of resonant bending waves can exceed that normally achieved by coating the plate with elastomeric damping materials, at least over a restricted range of frequencies.