The Effect Of Translation Group Symmetry On Acoustic Band Gaps In Two-dimensional Phononic Crystal

Materials, energy, information are the three pillars of civilization in the current world. The history of phononic crystal (PC) is less than 20 years . Phononic crystal is a new materials which is made artificially. We could control the transmission of the classical wave by designing the structure of phononic crystals. Phononic crystal is a kind of periodic-structure material, through which there exist acoustic or elastic wave band-gaps (BG's). It belongs to a composite material. During the BG's sound and vibration are forbidden. One remarkable character of PC is that we can design these materials with BG's of different sizes and bounds by choosing different lattices, scatters, filling factors and materials with various parameters, the artificial design and optimization of the phononic band structure is meaningful for applications of phononic crystals.First we introduced the theory of band-gaps and the application of group in crystal structure.Then the basic theory and method for calculating the band structure of PC are presented, especially the plane wave expansion method (PWE). The plane-wave-expansion formulas are deduced from the elastic wave equations. And then the application of PWE to the PC models considered is illustrated. Then the regulation of translational symmetry to the phonon energy band structure of phononic crystal, as well as how to change phonon translational symmetry of the crystal artificially were analyzed. Finally liquid - liquid two-dimensional phononic crystals were calculated and analyzed as an example, and some regulars of translational symmetry and phononic crystals bandgap optimization and yield of multi-band gap were found.Previous studies basically focused on the affection between point group symmetry and phononic crystals band gaps by altering the shape of scatterer, or rotating the hole scatterer, thus alter the point group symmetry. In this paper, we changed the phononic crystal translational symmetry through rooming or rotating scatterer partly, in theory, This was another different way to adjust phononic crystals bandgap from others to change the point group symmetry. And some positive effects were found through this method on transmission control of classical wave in phononic crystals.