Study on bandgaps of two-dimensional square phononic crystal slabs with cross-like holes

In this paper, the band structures of 2D vacuum/solid square phononic crystal slabs with cross-like holes are calculated by using the finite element method. The numerical computation is performed by Comsol Multiphysics 3.5a. The transmission spectra of a finite structure and the eigenmodes for the band edges of the lowest bandgap are also calculated. The results show that no bandgap exists for phononic crystal slabs with square holes; however, by introducing cross-like holes, the degeneracy of the bands are separated and wide bandgaps are generated. The band width to center frequency ratio is about eight times of that for the traditional phononic slab with circular holes by carefully designing the geometry of the cross-like holes. The eigenmodes corresponding to the band edges show that the bandgaps are governed by the flexural wave. The results are relevant to the optimization of the acoustic bandgaps.