Complete bandgaps in two-dimensional phononic crystal slabs with resonators

The bandgap properties of an open or covered phononic crystal slab with resonators are studied by using the finite element method. The results show that complete bandgap comes up for the proposed slabs with resonators due to the local resonance. The effects of the topological geometry of the resonators on the bandgaps are discussed, and optimal geometry is suggested. The mechanism of the bandgap generation is analyzed by studying the eigen modes at the bandgap edges. Equivalent spring-mass/pendulum models are developed to predict the eigen frequencies at the lower bandgap edges. The evaluated results obtained by the equivalent models are in general agreement with the numerical ones. The work in this paper is indispensable to the optimal design of the bandgaps of phononic crystal slabs.