Unidirectional acoustic transmission is acquired in a one-dimensional graded phononic crystal. The distinct feature of the present design is that waves can propagate unidirectionally at a certain frequency from the left to right, and waves at another frequency can propagate in the opposite direction from the right to left. This two-way asymmetric propagation behavior is realized at the narrow resonant frequencies in the acoustic band gap by a novel mechanism, which is totally linear and obeys the time-reversal symmetry. Simulation shows that for the graded heterogeneous structure, the resonant peaks of frequency in the acoustic band gap for opposite propagation directions become different. In the transmission spectrum, this mechanism corresponds to a pass-band splitting, and each separated peak represents a unidirectional propagation behavior. The separation of two peaks has been proved to have a close relation to the grading degree of the material property in the spatially periodic components. The unique propagation characteristic obtained at resonant frequencies in the band gaps may provide us a new way to realize a two-way unidirectional narrow-band acoustic filter.

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