Non-linear acoustic transfer impedance of micro-perforated plates with circular orifices

A practical description of the transitional behavior of micro-perforated plates (MPPs) is provided between the linear and strongly non-linear regimes. Micro-perforated plates are efficient sound absorbers whose application areas vary from room acoustics to duct acoustics. Although there are accurate models for the linear and strongly non-linear acoustic behavior of MPPs, the transition from one to another has not been a focus of interest so far. A series of measurements are performed with MPP samples for various excitation amplitudes. The deviation from the linear impedance is found to be a function of excitation amplitude and oscillating viscous boundary layer thickness, expressed in terms of the Strouhal number and the Shear number. Typical for MPPs is a Shear number of order unity, implying that the viscous boundary layer thickness is in the order of the perforation radius. Using the measurement data, expressions are proposed for calculating the non-linear acoustic resistance and reactance for circular perforations with sharp square edges. Some additional data is provided for the higher Shear number range. The behavior at low amplitudes for high Shear numbers deviates strongly from the typical MPP behavior. This is due to local vortex shedding at the sharp edges of the perforation.