Effect of slit length on linear and non-linear acoustic transfer impedance of a micro-slit plate

The effect of the slit length on the acoustic transfer impedance of micro-slit plates (MSPs) is investigated in the linear and non-linear regime for a specific slit geometry. This geometry is inspired by slits obtained by cutting and bending the plate. MSPs are plates with arrays of slit-shaped perforations, with the width of the order of the acoustic viscous boundary layer thickness. Impedance tube measurements on two accurately manufactured plates are compared to numerical solution of the Linearized Navier-Stokes equations and to analytical limits. The impedance of the plate is obtained by the impedance of a single slit divided by the plate porosity. The resistance of a slit is independent on the slit length and on the plate porosity. In the linear regime the resistance is accurately predicted by a two-dimensional numerical model. In the non-linear regime, the resistance is strongly dependent on the amplitude of the acoustic waves. The inertance of the slit is weakly dependent on the slit length and on the plate porosity, for low and moderate amplitudes. For high amplitudes, a complicated amplitude dependency of the inertia of short slits is found. One expects that most of the conclusions obtained can be generalised to other slit geometries.