Causally-guided acoustic optimization of single-layer rigidly-backed micro-perforated partitions: Theory

This theoretical study adapts results obtained in electromagnetism on the optimal performance of radar slab absorbers to the field of acoustics to enhance the broadband dissipation of single-layer rigidly-backed micro-perforated absorbers (MPAs) under normal incidence. Based on the causality principle, an integral identity is derived. It shows that the MPA ultimate wideband performance, that integrates contributions of the intensity reflection coefficient over all the positive wavelengths, is upper bounded by the absorber cavity depth. A sensitivity analysis led to the proposal of a causal-based optimization criterion in order to find optimal MPAs that achieve maximum wideband performance while reaching perfect absorption at their Helmholtz resonance frequency. This simple criterion maximizes the sensitivity of the total reflected intensity with respect to the micro-perforated panel constitutive parameters. It can be readily implemented using numerical quadrature and optimization solvers. It is shown to be a suitable alternative to maximization of the total absorption and inverse-frequency weighted absorption for single-layer MPA broadband optimization.