Effective parameters in beam acoustic metamaterials based on energy band structures

We present a method to calculate the effective material parameters of beam acoustic metamaterials. The effective material parameters of a periodic beam are calculated as an example. The dispersion relations and energy band structures of this beam are calculated. Subsequently, the effective material parameters of the beam are investigated by using the energy band structures. Then, the modal analysis and transmission properties of the beams with finite cells are simulated in order to confirm the correctness of effective approximation. The results show that the periodic beam can be equivalent to the homogeneous beam with dynamic effective material parameters in passband.