Active elastic metamaterials with equidistant solely resonant bandgaps

Abstract

Elastic metamaterials are man-made structures with properties that transcend naturally occurring materials. One predominant feature 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 elastic 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 and synthesis of locally resonant bandgaps is achieved via an active elastic support with carefully designed frequency-dependent stiffness. A single unit cell of each proposed metamaterials is thoroughly studied, and its dispersion relation is derived analytically, along with the periodically repeating bandgap limits and widths. Following the dispersion analysis and bandgap parametric studies, finite arrays of the proposed metamaterials are considered, and their frequency response is calculated to verify the analytical predictions from dispersion analyses.