Vibrational effects on the optimization of micro-perforated partitions based on a causality criterion

Micro-Perforated Panels constitute an alternative to classical porous materials in demanding environments due to fire-proofness, cleanability and lightweight properties. However, its performance is greatly determined by a proper selection of the constitutive physical factors. To find the optimal set of parameters, a combinatorial optimization problem has to be solved using a cost function that classically includes the absorption coefficient averaged over a frequency band. Recently, another criterion has been considered by the use of a causal integral that relates the thickness of the partition to the amount of absorption that can be achieved over a desired bandwidth. This provides a set of states that present critically-coupled resonant behavior and perfect absorption at the requested frequency while maximizing the total absorption. When considering sub-millimetric panel thickness or membranes, the effect of the panel vibrations has to be taken into account. In this study, we have extended the causality criterion to consider the effect of the panel vibration of the perforations impedance. Another model has also been examined to account for the cavities Helmholtz-type resonance and their influence on the corresponding critically-coupled states.