Resonance mode analysis of finite plate strip with acoustic black holes: the gap between bandgap and attenuation band

Abstract

Acoustic Black Hole (ABH) lattice structures show promise for achieving broadband bandgap in lightweight design. Existing ABH lattice research usually assumes that the bandgaps of infinite periodic structure are roughly the same as the attenuation band with strong energy attenuation in the finite counterpart. This work is concerned with comparison of the real attenuation bandwidth of finite periodic ABH structures and the bandgap of the infinite counterpart. The plate strips consisting of different numbers of periodic ABH elements are considered. It is observed that the bandgap-predicted attenuation band is split into two narrow attenuation bands, so that the periodic ABHs fails to ensure a broadband and continuous attenuation in the finite scenarios. Results show that there are resonance modes of finite plate strips with ABHs falling into the bandgap due to the boundary reflection and would result in high transmission peaks within the bandgap-predicted attenuation band. This unexpected phenomenon suggests the gap between the attenuation bandwidth of finite periodic structure and the bandgap of the corresponding infinite one. Analysis shows that the resonance mode of finite plate strips, which reduces the bandgap-predicted attenuation bandwidth, can be tuned by geometrically disturbing the periodicity and symmetry of the finite periodic configuration.