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Active elastic metamaterials with equidistant solely-resonant bandgaps

Hasan B. Al Ba'ba'a
Nov 2023
Elastic metamaterials are man-made structures with properties that transcend naturally occurring materials. One of the most predominant features of elastic metamaterials is locally-resonant bandgaps, i.e., frequency ranges at which wave propagation is blocked. Locally-resonant bandgaps appear at relatively low frequency and arise from the existence of periodically placed mechanical local resonators. Typically, elastic metamaterials exhibit both locally-resonant and Bragg-scattering bandgaps, which can generally be different in width and frequency ranges. This paper proposes two designs of active metamaterials that only exhibit locally-resonant bandgaps, which are infinite in number, evenly spaced in the frequency spectrum, and identical in width. The mathematical model is established using the transfer matrix method (TMM) and synthesis of locally-resonant bandgaps is achieved via an active elastic element with carefully designed frequency-dependent stiffness. A single unit cell of the active metamaterial is thoroughly studied, and its dispersion relation is derived analytically, along with the bandgap limits and width. Following the dispersion analysis and bandgap parametric studies, finite arrays of the proposed active metamaterials are considered, and their frequency response is investigated and used to verify the analytical predictions from dispersion analyses. The proposed mathematical framework establishes a design methodology that could be further used to synthesize interesting dispersion behaviors in the future.
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