Fig. 2


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(a) Dispersion relation for a periodic array of resonators placed symmetrically with respect to the wave propagation direction (x). A local resonance bandgap opens at the frequency Ω0 due to the coupling between the propagating wave on the waveguide and the resonant mode of the resonators. The bandgap opens at the edge of the Brillouin Zone, with a relatively large zero-group velocity region. (b) Dispersion relation for aperiodic array with asymmetric resonators with respect to the wave propagation direction (x). In such a case, a zero-group velocity mode arise within the Brillouin Zone due to the coupling between flexural (z-polarized) and torsional (ϕz-polarized) waves with opposite group velocity. (c,d) Arrangement of resonators corresponding to the dispersion relations in (a) and (b) respectively.

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