Band structures of two dimensional solid/air hierarchical phononic crystals

The hierarchical phononic crystals to be considered show a two-order hierarchical feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.