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Directional guiding, passing or stopping of elastic waves through engineered materials have many applications to the engineering fields. Recently, such engineered composite materials received great attention by the broader research community. In elastic waves, the longitudinal and transverse motion of material particles are coupled, which exhibits richer physics and demands greater attention than electromagnetic waves and acoustic waves in fluids. Waves in periodic media exhibit the property of Bragg scattering and create frequency band gaps in which the energy propagation is prohibited. However, in addition to the Bragg scattering, it has been found that local resonance of artificially designed resonators can also play a critical role in the generation of low-frequency band gaps. It has been found that negative effective mass density and negative effective elastic modulus are created by virtue of the local resonators and are correlated with the creation of the frequency band gaps that can be artificially perturbed.

In this paper, the authors present a novel anisotropic design of metamaterial using local split-ring resonators of multiple-length scales. Unlike traditional metamaterials, multiple split rings of different dimensions are embedded in a polymer matrix. Considering the complexity of the proposed material, it is extremely difficult to find the dynamic response of the material using analytical methods. Thus, a numerical simulation was performed in order to find frequency band gaps. Simultaneously, correlation between the band gaps and negative effective mass density and negative effective elastic modulus was verified. Both unidirectional split rings and bidirectional chiral split rings were studied. The effects of discontinuity in the rings at larger scales were compared with the dynamic characteristics of full rings in the proposed metamaterial. Application of such metamaterials will be primarily for vibration isolation and impact mitigation of structures. The proposed configuration is based on unit dimension and is, thus, dimensionless. The concept can be easily commutable between macro-scale structures for low-frequency applications and micro-scale MEMS devices for high-frequency applications.