Geometric optimization of a multiple coiled-up resonators for a broad band acoustic absorption

In order to investigate new solutions to obtain high absorption at low frequency, the concept of quarter-wave acoustic resonators coiled-up metamaterial has been applied to limit the thickness thanks to the possibility of ”rolling” their channels. This study is based on a metamaterial made of n quarter-wave coiled-up resonators in parallel: once the minimum frequency of absorption (e.g. 100 Hz) and the second harmonic (300 Hz) have been defined, this frequency range is divided into n different resonators so that the envelope of the high-harmonics is such as to obtain a high broadband absorption. Starting from the study of a single resonator, an analytical model was defined to calculate the normal incidence absorption coefficient and then it was extended to systems with n-resonators in parallel using the parallel equivalent circuit theory. This models were validated with impedance tube measurements and then used for a geometric optimization: defined a metamaterial with 16 resonators in parallel (minimum frequency of 100 Hz), the geometry was varied to maximize the absorption coefficient. The optimized geometry was than simulated using a 3D FEM model to consider the real development of the channels. The results of both analytical and FEM models will be discussed.