  The absorption of sound has great significance in many scientific and
engineering applications, from room acoustics to noise mitigation. In this
context, porous materials have emerged as a viable solution towards high
absorption performance and lightweight designs. However, their performance is
somehow limited in the low frequency regime. Inspired by the concept of
recursive patterns over multiple length scales typical of many natural
materials, here, we propose a hierarchical organization of multilayered porous
media and investigate their performance in terms of sound absorption. Two types
of designs are investigated: a hierarchical periodic and a hierarchical
gradient. In both cases it is found that the introduction of multiple levels of
hierarchy allows to simultaneously (i) increase the level of absorption
compared to the corresponding bulk block of porous material, along with (ii) a
reduction of the quantity of porous material required. Both the cases of normal
and oblique incidences are examined. The methodological approach is based on
the transfer matrix method, optimization algorithms (metaheuristic Greedy
Randomized Adaptive Search Procedure), and finite element calculations. An
excellent agreement is found between the analytical and the numerical
simulations.

Applied Physics