Large enhancement of phononic gap in periodic and quasiperiodic elastic composites by using air inclusions

We find that a phononic gap in a periodic or quasiperiodic elastic composite can be significantly enhanced by inserting air inclusions into the systems. The positions of the insertion are chosen to suppress the shear potential energy of the acoustical branches and lower their frequencies. This is demonstrated in two dimensions. Gap positions and sizes as functions of the radii of the air cylinders for systems of aluminum cylinders in epoxy and steel cylinders in epoxy are presented for both triangular and 12-fold quasiperiodic lattices.