Damping of sound and vibration by flow nonlinearity in the apertures of a perforated elastic screen

An analysis is made of the influence of flow nonlinearity in the apertures of a perforated elastic plate on the damping of sound and flexural vibrations. Fluid is forced through the perforations by the pressure differential established across the plate by the incident disturbance. The Reynolds number is assumed to be sufficiently large that separation occurs, and the reciprocating aperture hows form 'jets' on alternate sides of the plate. The growth of these jets is modelled by means of a nonlinear equation proposed by Cummings (1986). This equation is solved simultaneously with a generalized bending wave equation derived by the author (Howe, 1995a) which governs motions of a perforated elastic plate whose lengths scales are large compared to the aperture spacing. It is shown that significant attenuations of large amplitude acoustic waves can occur except when the frequency is so small that the plate is acoustically transparent. Bending waves are also damped provided the amplitude of the plate surface velocity is not too large and the frequency is small enough to ensure the formation of substantial jets in the apertures. Numerical results are given for large amplitude sound waves incident on a perforated screen in air, and for bending waves propagating over aluminium and steel screens immersed in either air or water.