Acoustic metamaterials have proven to be a versatile tool for the precise control and manipulation of sound waves. One of the promising designs of acoustic metamaterials employ the arrays of bubbles and find applications for soundproofing, blast mitigation, and many others. An obvious advantage of bubble-based metamaterials is their ability to be relatively thin while absorbing low-frequency sound waves. The vast majority of theories developed to predict resonant behavior of bubble-based metamaterials capitalize on Minnaert frequency. Here, we propose a novel theoretical approach to characterize bubble-based metamaterials that are based on our previous findings for a single bubble trapped in circular cavity modeled as a thin clamped plate. We obtain analytical expressions for resonant frequencies of bubble metascreens using self-consistent approximation. Two geometry factors, distance between bubble centers and distance between bubble center and interface of acoustic impedance change, are taken into account. We demonstrate the existence of multiple bandgaps and possibility of switching between them via adjustment of geometry parameters and reflector properties.
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