Causal-based acoustic optimization of micro-perforated structures with rigid backing

The acoustical design of compact micro-perforated absorbers (MPA) that exhibit high performance over a broad bandwidth is a difficult challenge, often faced in building, ventilation and transportation industries. A causal-based optimization criterion of the MPA constitutive parameters is considered as an alternative to the maximization of the frequency-weighted overall absorption. It maximizes the directional gradient norm of the total intensity reflection coefficient (in logarithmic scale) integrated over all positive wavelengths. The causal and standard optimization strategies are assessed for single- and double-layer MPAs as well as for MPA arrays, the former (resp. the latter) designs being supported by Kundt tube measurements (resp. finite element simulations). The causal criterion ensures perfect absorption and the broadest possible bandwidth at one or several Helmholtz resonances of the MPA, with efficient grouping and merging of these resonances for the optimized MPA array. The resulting performance are comparable to direct maximization of the total inverse-frequency weighted absorption.