Frequency stop-band optimization in micro-slit resonant metamaterials

An optimized unit cell design of a micro-slit resonant metamaterial is proposed to increase the size of the frequency stop-bands and to enhance the sound absorption at normal incidence. Micro-slit resonant metamaterials offer a compact and lightweight solution for low-frequency noise reduction, in contrast to traditional methods such as absorptive foams. A combination of numerical and semi-analytical solutions based on dispersion and absorption curves is presented. A novel algorithm allows for the decoupling of wave types from raw numerical data in the dispersion curves, without using the stiffness and mass matrices. A thorough optimization process of unit cell designs with genetic algorithms is performed. Focus is given to the first frequency stop-band, located in the frequency range of application of microslit resonant metamaterials. The process shows that relatively large resonators (with respect to the unit cell total area) produce a larger first frequency stop-band, whereas slit size has a negligible effect. The optimized design increases the first frequency stop-band by 20% and the second stop-band by 25% compared to the literature standard. The absorption curves at normal incidence of acoustic waves are derived numerically for a rigid and elastic frame of the metamaterial backed by a cavity. These curves are validated by the JCAPL semi-analytical model. The optimized unit cell design shows a 9% increase in the first peak of absorption coefficient compared to the literature standard at a cavity depth of 30 mm, and an increase of 10% at a cavity of size 53 mm. Stop-band behavior does not influence sound absorption at normal incidence of acoustic waves in the frequency range of interest.(c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

An optimized unit cell design of a micro-slit resonant metamaterial is proposed, aiming to increase the size of the frequency stop-bands and improve the sound absorption at normal incidence. Through numerical and semi-analytical solutions, the unit cell design is optimized using a genetic algorithm. The study shows that larger resonators and slit sizes have different effects on the frequency stop-bands. The optimized design significantly enhances the stop-band sizes and improves the absorption performance.