The influence of T-square fractal shape holes on the band structure of two-dimensional phononic crystals

The influences of the T-square fractal holes on the band structures of two-dimensional phononic crystals with periodic distributed void pores are studied. Through using the finite element method, the dispersion relations in the two-dimensional phonoinc crystals with different level fractal holes are illustrated. The absolute bandgap can be easily formed in the phononic crystal with high level fractal holes, but hardly for first level ones. And the frequencies of the band structure are decreased with the increase of the fractal level. By analyzing the vibration modes of the unit cell of the phononic crystal, we find the origin of the lower frequency band is due to the locally resonant mechanism. Moreover, the impacts of the size of the fractal hole on the band structure are studied.