Calculation of perforated plate liner parameters from specified acoustic resistance and reactance

A mathematical procedure is developed for calculating the parameters of a singlelayer perforated-plate acoustic liner in order to achieve a specified acoustic resistance and reactance for single-frequency excitation. The method includes the standard impedance terms, due to viscosity, radiation, and backing effects, and also the terms due to high sound amplitude and steady tangential airflow. Emphasis in the analysis is on these latter non-linear effects. Specification of acoustic resistance and reactance (at one frequency and set of environmental conditions) means that two quantities are used to determine the four liner parameters: fractional open area of plate (porosity of plate), thickness of plate, diameter of hole perforations, and depth of backing cells. The procedure has the following sequence of steps: (a) convenient values are assumed for plate thickness and hole diameter, (b) the resistance equation is solved for fractional open area, (c) the reactance equation is solved for backing depth. The solution indicates that higher values of sound amplitude and/or steady airflow necessitate larger values of fractional open area and backing depth for the fixed acoustic resistance and reactance. Various special cases give simplifications in the solution procedure and a numerical example is given.