Multiple wide complete bandgaps of two-dimensional phononic crystal slabs with cross-like holes

This paper investigates the bandgap properties of two-dimensional phononic crystal slabs with cross-like holes by using the finite element method. The effects of the slab thickness and the geometry parameters of the holes on the bandgaps are discussed. No bandgap appears in the system with the square holes if the symmetry of the holes is the same as that of the lattice. However if the square holes are replaced with the cross-like holes, multiple wide bandgaps at lower frequencies are generated. The bandgaps are significantly dependent on the slab thickness and the geometry (including the size, shape and rotation) of the cross-like holes. The vibration modes at the bandgap edges are computed and analyzed to clarify the mechanism of the bandgap generation. It is found that the generation of the bandgap is due to the flexural vibration localized in the lumps or connectors. The appearances of the higher modes with the cut-off frequencies which decrease with the thickness increasing result in the decrease of the upper bandgap edge, and finally lead to vanishing of the bandgap. The study in this paper could be indispensable to practical applications of phononic crystal slabs such as bandgap tuning. (c) 2012 Elsevier Ltd. All rights reserved.