Abstract
A mathematical procedure is developed to calculate the parameters of a single-layer perforated plate acoustic liner in order to achieve a specified acoustic resistance θ and reactance χ for single-frequency excitation. The procedure includes the standard impedance terms (due to viscous, radiation, and backing effects), and emphasis is on terms due to high sound-amplitude and steady airflow (“nonlinear” effects). Specification of θ and χ (at one frequency) means that two quantities are used to determine the four liner parameters σ (fraction open area of plate), t (thickness of plate), d (diameter of holes), and b (depth of backing cells). The developed method has the following sequence of steps: (1) convenient values are assumed for t and d; (2) the resistance equation is solved for σ (is a cubic algebraic equation in general); and (3) the reactance equation is solved for b (involves inverse cotangent in general). Various special cases give simplifications in the solution procedure. Higher values of sound amplitude and/or steady airflow velocity necessitate higher values of σ. While the procedure applies strictly for single-frequency excitation, it is probably also valid for a highly periodic excitation. The possibility of solving for values of σ, t, d, and b to achieve specified values of θ and χ under two separate environmental conditions is also discussed.
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