Abstract
Various strategies have been proposed in recent years in the field of mechanical metamaterials to widen band gaps emerging due to either Bragg scattering or to local resonance effects. One of these is to exploit coupled Bragg and local resonance band gaps. This effect has been theoretically studied and experimentally demonstrated in the past for two- and three-phase mechanical metamaterials, which are usually complicated in structure and suffer from the drawback of difficult practical implementation. To avoid this problem, we theoretically analyze for the first time a single-phase solid metamaterial with so-called quasi-resonant Bragg band gaps. We show evidence that the latter are achieved by obtaining an overlap of the Bragg band gap with local resonance modes of the matrix material, instead of the inclusion. This strategy appears to provide wide and stable band gaps with almost unchanged width and frequencies for varying inclusion dimensions. The conditions of existence of these band gaps are characterized in detail using metamaterial models. Wave attenuation mechanisms are also studied and transmission analysis confirms efficient wave filtering performance. Mechanical metamaterials with quasi-resonant Bragg band gaps may thus be used to guide the design of practically oriented metamaterials for a wide range of applications.
Highlights
Mechanical metamaterials are engineered periodic composites with exceptional dynamic properties
This indicates that overlapping Bragg band gaps (BGs) with the local resonances in the matrix can be achieved in single-phase metamaterials
We have proposed and theoretically studied a novel BG formation mechanism in two- and single-phase phononic metamaterials
Summary
Mechanical metamaterials are engineered periodic composites with exceptional dynamic properties The possibility they provide to manipulate and attenuate elastic waves at various frequencies can be exploited for various applications, ranging from seismic shielding [1,2] or noise abatement [3] to subwavelength imaging [4] and thermal management [5]. Coupled resonant Bragg BGs have been found in co-continuous metamaterials with enhanced mechanical properties [28] All these studies involve composite metamaterial structures comprising at least two material phases, and the hybridization BG is usually associated with resonance modes of inclusions. The proposed strategy shows promise for enhanced wave attenuation mechanisms coupled with the possibility of fabricating simpler structures, promoting the exploitation of mechanical metamaterials in real applications
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