Frequency band structure and absorption predictions for multi-periodic acoustic composites

Abstract

This article introduces a computational framework for studying frequency band structure and absorption behavior in multi-periodic acoustic composite structures. Herein, multi-periodic acoustic composite structures are defined as periodically-layered acoustic media wherein each layer is composed of periodically-repeated fluid unit cells, especially those arising from the study of porous materials. Hence, at least two periodic scales (microscopic and mesoscopic, respectively) comprise the macroscopic acoustic composite media. Exploitation of the multi-periodicity allows for efficient generation of dispersion and absorption curves via the conventional multi-scale asymptotic method (for homogenizing the mesoscale) coupled to the acoustic transfer matrix methods (for the macroscale). The combined computational framework results in a single analysis procedure for evaluating complex dispersion relationships and acoustic absorption. The dispersion curves can be used to reveal frequency stop bands wherein the wave vector is highly imaginary—i.e., plane waves experience rapid attenuation. They can also be used to reinterpret classical absorption curves. The framework is applied to four multi-periodic acoustic composite structures in order to demonstrate the framework's utility and to reveal novel properties, particularly those which can be influenced by design of the mesoscopic unit cell.