Acoustic absorption modeling of single and multiple coiled-up resonators

This work proposes an improved design procedure of sound absorption metamaterials consisting of acoustic coiled-up quarter-wave resonators that fit into a limited space, in order to broad the range of possible applications even in the low-frequency regime. Different types of models were used to understand the propagation of sound in long, narrow, and square-section tubes, including the visco-thermal loss within the structures for accurate modeling. An analytical model, which includes the definition of the different loss contributions with equivalent fluid models, has been developed: the Johnson-Champoux-Allard model for inlet losses and the “Narrow Region” model for visco-thermal loss along the tubes. A geometric parameterization procedure, for maximizing acoustic absorption at certain target frequencies, was carried out. To validate the theoretical acoustic absorption predictions, the 3D printing technique was used to fabricate samples in a plastic material (PLA) for normal incidence sound absorption coefficient measurements. Moreover, systems containing several quarter-wave resonators of different dimensions coupled in parallel or in series were designed, with the aim of broadening the absorption band; in this case, for practical reasons, only the medium-high frequency regimes were experimentally investigated.