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(a) Schematics of 1D standard ultrasonic metamaterials. (b) Three-dimensional (left) and cross-sectional view (right) of a standard unit. (c) The equivalent acoustic transmission line unit circuit of a standard unit. The waveguide section and the HR are modeled with distributed and lumped impedances, respectively. (d), (e), and (f) show the equivalent acoustic unit circuit of parallel-coupled structures with 2–4 HRs in a unit, respectively. indicates the incident direction of sound wave.
(a) Transmission spectra for metamaterials with HRs in each unit. The periodic constant is fixed at . (b) and (c) show the frequency dependences of effective resistance and reactance, respectively.
Dispersion relation for metamaterials with values. (a) and (b) reveal the real and imaginary parts of with frequency. The dispersion curve in a waveguide without shunt HRs is also shown as thick line.
The frequency dependence of (a) real and (b) imaginary parts of for the standard and parallel-coupled metamaterials.
The TPS simulated by FEM for metamaterials with HRs in each unit. The arrows show the moving of upper and lower band edges.
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