Study on acoustic bandgaps in two-dimensional square phononic crystals with cross-like holes

The band structures of 2D vacuum/solid square phononic crystals with cross-like holes are calculated by using the finite element method, the effects of geometric parameters on bandgaps are studied and compared with those of the phononic crystals with square holes. The numerical computation is performed by Comsol Multiphysics 3.5a. The results show that no bandgap exists for phononic crystals with square holes; while that by introducing cross-like holes, the degeneracy of the bands can be separated which gives rise to bandgaps. The geometric topology of the cross-like holes has distinct influence on the bandgaps. Still the systems are shown sensitive enough to the rotation angle of holes: with the increase of the rotation angle, the width of the lowest complete bandgap will enlarge monotonously for phononic crystals with square holes, but will decrease for the cross-like holes. The results are relevant to the optimization of the acoustic bandgaps.