Resonance modes and gap formation in a two-dimensional solid phononic crystal

The resonance modes near the edges of the first absolute band gap of a two-dimensional solid phononic crystal with an epoxy host are investigated in this paper. A rotary resonance mode, induced by the joint effect of the Bragg and Mie scattering, is observed near the bottom of the gap. The gap, resulting from the interaction between the rigid-body resonance and the effective homogeneous medium, coalesces with the Bragg gap, which leads to the formation of a wide gap. Then a simple analytical model is introduced to give a physically intuitive account of the rotary resonance. Finally, the effects of the array and the filling fraction on the band gap are explained by the conditions for occurrence of the resonance.