Abstract
By using a two-step homogenization approach, we derive analytical formulas of effective mass density ${\ensuremath{\rho}}_{e}$ and effective bulk modulus ${B}_{e}$ for two- and three-dimensional acoustic metamaterials of Helmholtz resonators (HRs) in fluid. A negative ${B}_{e}$ is found at certain frequencies due to the monopolar resonance, leading to a low-frequency acoustic band gap. A unified picture is presented for metamaterials of HRs and three-component metamaterials of negative ${\ensuremath{\rho}}_{e}$. Our work supports recent observations in a one-dimensional array of HRs [N. Fang et al., Nat. Mater. 5, 452 (2006)] and presents important high-dimensional extensions for exploring more fascinating phenomena.
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