Power flow analysis in a hybrid phononic crystal structure

To reveal the energy transmission through a hybrid phononic crystal structure, power flow analysis is carried out in this paper. Hysteretic damping having significant relationship with power flow is added and corresponding theoretical formulas of the dispersion relation are derived. Besides, the power flow in the hybrid structure is calculated by using the finite element method. The results show that as the damping increases, the boundaries of the band gaps become smoother and dimmer, i.e., broader width. With the increase of damping, the power flow is lowered at the resonance frequencies,while slightly increases near the resonance frequencies. The power flow maps manifest energy distribution in the hybrid structure within and out of the band gaps, which can be exploited in the optimization of the structure design.