Abstract
In this paper, the mechanism for opening a locally resonant band gap in a thin elastic plate is investigated. Two previously suggested structures, which are constructed by periodically drilling holes on elastic plate and then filling them with the rubber-coated masses, or just by periodically stubbing the rubber rods with mass cap on the plate, are revisited. We find that, because of the partial band gaps for in-plane and out-of-plane plate modes cannot be appropriately overlapped, the full band gaps in both of the structures are generally narrow. The reason for this phenomenon is based on the selective coupling between the different resonant patterns of the resonant units and the in-plane and out-of-plane plate modes. Based on the understanding, a new structure with the three-layered spherical resonant units is proposed. Numerical results show that, making use of such kind of resonant units, a large sub-wavelength full band gap can be opened.
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