ENERGY-CONSERVATION AND THE DAMPING OF FLEXURAL WAVES BY VORTICITY PRODUCTION

An analysis is made of the transfer of energy between structural/acous tic vibrations and fluid kinetic energy in flows at very small Mach nu mber. A general energy balance equation is discussed for a vibrating r igid body in either incompressible or low Mach number compressible mea n flows. This equation can be used to calculate the growth or decay of structural or acoustic oscillations, and to locate regions of the flo w where energy exchanges are significant. A similar general treatment for vibrating elastic bodies does not seem to be possible, except in s imple cases involving thin elastic plates in parallel flow. Two such p roblems are discussed, involving the dissipation of structural vibrati ons by vorticity production (i) at the trailing edge of a large elasti c plate, and (ii) in the circular apertures of a perforated elastic pl ate in a two-sided grazing mean flow. The interaction of boundary laye r turbulence with the apertures of a perforated plate can be a particu larly intense source of sound, but in applications where the character istic frequencies are small, a grazing flow perforated screen has been shown to be an efficient sink of acoustic energy. In this paper predi ctions are given for the damping of bending waves by the same mechanis m. When the fluid loading is large, such as for a steel plate in water , these predictions indicate that the damping of resonant bending wave s can exceed that normally achieved by coating the plate with elastome ric damping materials, at least over a restricted range of frequencies . (C) 1996 Academic Press Limited