Acoustic Treatment Design Scaling Methods Volume 4: Numerical Simulation of the Nonlinear Acoustic Impedance of a Perforated Plate Single-Degree- of-Freedom Resonator Using a Time-Domain Finite Difference Method

AbstractSingle-degree-of-freedom resonators consisting of honeycomb cells covered byperforated facesheets are widely used as acoustic noise suppression liners in aircraft engineducts. The acoustic resistance and mass reactance of such liners is known to vary with theintensity of the sound incident upon the panel. Since the pressure drop across a perforatedliner facesheet increases quadratically with the flow velocity through the facesheet, this isknown as the nonlinear resistance effect. In the past, two different empirical frequencydomain models have been used to predict the Sound Pressure Level effect of the incidentwave on the perforated liner impedance, one that uses the incident particle velocity inisolated narrowbands, and one that models the particle velocity as the overall velocity. Inthe absence of grazing flow, neither frequency domain model is entirely accurate inpredicting the nonlinear effect that is measured for typical perforated sheets. The timedomain model is developed in an attempt to understand and improve the model for theeffect of spectral shape and amplitude of multi-frequency incident sound pressure on theliner impedance. This is of particular concern with regard to frequency-scaling of acoustictreatment, since the possibility exists that the nonlinear resistance and mass reactanceeffects may be significant compared to the grazing flow effects at high frequencies. Acomputer code for the time-domain finite difference model is developed and predictionsusing the models are compared to current frequency-domain models.iii