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Acoustic metamaterials provide unconventional and unusual approaches to control the subwavelength elastic/acoustic waves. Locally resonant acoustic metamaterials (LRAMs) attract great attention due to their potential applications as vibration isolation, low-frequency noise insulators, and wave filtering. It exhibits band gaps in a frequency range two orders of magnitude lower than ones resulting from Bragg scattering mechanism. LRAMs are of significant practical interest since the existence of band gaps is independent of the lattice symmetry. Although over past decade various attempts have been made to tailor the band gap for desired frequency range, achieving it over low-frequency band gap remains challenging. Therefore the goal of the present study is to design simplified LRAM having wide bandgap over low-frequency range. In this work, we propose a ternary LRAM by integrating a two-dimensionally periodically arranged square unit cell, consists of soft coated hard inclusion embedded in a polymer scaffold. We perform finite element simulation on the unit cell of proposed metamaterial using in-house developed computational platform. Extracting the frequencies for various wave vector over irreducible Brillioun Zone, we have generated dispersion behavior. Computational results reveal the presence of two frequency band gaps over low-frequency range. In parallel, we provide an analytical framework based on dual resonator model which clearly explains the origin of two separate low-frequency band gaps as obtained from the simulation. We perform a systematic parametric study for bandgap with various geometry, material parameters, inclusion shapes, and sizes. Thus the present study can offer a detailed design map for fabricating low-frequency acoustic metamaterial with simplified geometry towards various potential applications.
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