Causal-based optimization of micro-perforated treatments

Abstract

Enhancing the low-frequency performance of compact acoustical micro-perforated treatments is a challenging task that requires global optimization studies performed on numerical or theoretical models. However, for a given geometry, there always exists a lower frequency bound below which the treatment will exhibit poor dissipation performance. In this study, it is shown how this lower frequency bound is related to the total integrated dissipated power through a causal-based criterion. Examples are shown for the cases of a rigidly-backed micro-perforate under plane wave incidence and for a locally-reacting micro-perforated resonant silencer mounted in a duct. Such criterion provides the ultimate bandwidth-to-length ratio that can be achieved by the acoustical treatments for a given target dissipation value. One can also deduce the optimal values of individual parameters such as the hole diameters or the wall porosity that leads to a suitable balance between leakage and dissipation effects. The causal-based optimized treatments are validated against simulated or measured impedance tube data.