A Numerical Approach to Investigate the Influence of Resonator Setting and Volume Fraction on Stop Bands in an Acoustic Metamaterial

Abstract

A quest for physics-based understanding of engineered metamaterials inspired numerous researchers to extract intricate features such as guiding and filtering elastic waves, wave focusing, topological insulation, cloaking etc. A traditional metamaterial is composed of a heavy core along with some other materials of dissimilar mechanical properties (e.g. stiffness, density). It is well-established that the frequency band gap can be formed by introducing the desired inconsistency of material properties between stiffer resonators and adjacent embedding matrices. Frequency band gaps are fundamental requirements of many engineering applications such as vibration control, noise mitigation, and energy concentrations. Hence, advanced researches are being carried out continuously to understand the control parameters (e.g. bandwidth, starting and ending frequencies) of the frequency band gap. In this article, a mass-in-mass metamaterial using elliptical anisotropic resonators are considered to investigate the influence of resonators’ geometric factors and volume fraction on band gap parameters. While the elliptical resonator is splitted diagonally in one or both opposite ends to analyze the influence of volume fraction of the resonators on stop bands, a second set of half-circular resonators are also investigated to analyze the impact of resonator parameters on frequency bands.