Investigation on the band gap adjustment of the compound phononic crystal using the insertion of elliptical cylinder

This computational study focuses on a kind of two-dimensional steel cylinder/gas square lattice phononic crystal with an elliptical cylinder inserted into the primitive cell. The crystal's energy band structure is calculated using plane wave expansion (PWE) method. The irreducible Brillouin zone (IBZ) is found to have undergone significant changes with the insertion of elliptical cylinder: the energy band extrema deviated from their original positions, and the wave vector's scanning range needs to be expanded in order to obtain reliable energy band structure. Since the elliptical cylinder is less symmetrical than the cylinder, low frequency band gap is more readily formed with the insertion. Greater filling ratio yields wider band gap. The band gap can be tuned within a wide frequency range by varying the orientation of the inserted elliptical cylinder. The band gap can form at a relatively low filling ratio by moving the inserted elliptical cylinder along y-axis.