Complete sub-wavelength flexural wave band gaps in plates with periodic acoustic black holes

Acoustic Black Hole (ABH) effect shows promise for vibration control, but mainly limited to a relatively high frequency range. Though achievable in 1D periodic ABH structures, complete sub-wavelength band gaps (BGs) have not yet been realized in 2D configuration. Capitalizing on the unique wave propagation characteristics of the ABH, we propose a new type of plates containing periodically arranged double-layer ABH cells which offer complete and omnidirectional BGs. The phenomena originate from the combined effects of the ABH-specific local resonances and Bragg scattering, which are made possible through a dual process: a proper channeling of the wave propagation path and an impaired coupling between the ABH-induced local resonances and the global vibration of the unit cells. The former is warranted by a proper structural tailoring of the unit cells and the latter by the dynamics of the double-layer ABH design. It is shown that the BGs can be tuned through adjusting ABH parameters. Meanwhile, attaching the centers of the double ABH branches with a connecting cylinder can further broaden and lower the frequencies of the BGs as a result of the enhanced Bragg scattering. It is also demonstrated numerically and experimentally that remarkable vibration attenuation and energy insulation can be achieved in a plate with only a small number of ABH cells, thus pointing at the possibility of achieving sub-wavelength vibration control in structures with reasonable dimensions.