Vibrational Effects on the Acoustic Performance of Multi-Layered Micro-Perforated Metamaterials

Broadband noise reduction over the low–mid frequency range in the building and transportation sectors requires compact lightweight sound absorbers of a typical subwavelength size. The use of multi-layered, closely spaced (micro-)perforated membranes or panels, if suitably optimized, contributes to these objectives. However, their elasticity or modal behaviors often impede the final acoustical performance of the partition. The objective of this study is to obtain insights into the vibrational effects induced by elastic limp membranes or panel volumetric modes on the optimized sound absorption properties of acoustic fishnets and functionally graded partitions (FGP). The cost-efficient global optimization of the partitions’ frequency-averaged dissipation is achieved using the simulated annealing optimization method, while vibrational effects are included through an impedance translation method. A critical coupling analysis reveals how the membranes or panel vibrations redistribute the locations of the Hole-Cavity resonances, as well as their cross-coupling with the panels’ first volumetric mode. It is found that elastic limp micro-perforated membranes broaden the pass-band of acoustic fishnets, while smoothing out the dissipation ripples over the FGP optimization bandwidth. Moreover, the resonance frequency of the first panels mode sets an upper limit to the broadband optimization of FGPs, up to which a high dissipation, high absorption, and low transmission can be achieved.