Acoustic reactance of perforated plates with bias flow and two high-amplitude harmonic excitations

It is known that the presence of a steady flow through perforations or of high-amplitude acoustics greatly impacts the acoustic impedance of perforated plates, and that perforated liners such as bias-flow liners may be subjected to sound waves at more than one tone. In this article, the effects of a steady bias flow and two uncorrelated high-amplitude harmonic acoustic excitations on the acoustic reactance of perforated plates are investigated. A semi-analytical model for the perforation’s effective length is obtained from a combination of theory and of a calibration based on experimental data. The starting point is the unsteady Bernoulli equation, with an instantaneous velocity-dependent (hence time-dependent) perforation’s effective acoustic length. By converting the time-domain unsteady Bernoulli equation into the frequency domain, for the time-domain phenomenological model chosen for the effective length, the frequency-domain effective length is a function of an effective velocity. The latter is identical to that obtained in a recent article addressing the nonlinear resistance of perforations using a double-input describing function approach. Based on this effective velocity, which is a nonlinear function of the three velocities considered in this study (bias flow velocity, and primary and secondary acoustic velocity amplitudes), a single effective Strouhal number characterises the problem. Three regimes are distinguished, which are defined by this Strouhal number value. The resulting model, which was calibrated with experimental data, can be applied — but is not limited — to the acoustic modelling of acoustic liners with or without bias flow, subjected to up to two high-amplitude oscillations. • Nonlinear semi-analytical model for the acoustic length correction. • Length correction model combining effects of bias flow and two high-amplitude tones. • An effective velocity , function of 3 velocities, governs the length correction. • Model calibrated with experimental data with bias flow and two high-amplitude tones. • Despite the numerous flow parameters, a single Strouhal number describes the problem.