Effective elastic parameters of the two-dimensional phononic crystal

The effective acoustic velocity along two highly symmetric directions of the first Brillouin zone is studied in a two-dimensional squarely arranged solid-solid phononic crystal. The relationship between the effective elastic velocity and the wave frequency of the two lowest bands is presented, which gives the same results as those obtained directly from the band structure. Numerical calculations show that the effective acoustic velocity of the phononic crystal decreases with frequency increasing from zero to the band edge.