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The longitudinal wave propagating in one-dimensional periodic piezoelectric composite rod with inter-coupling between different piezoelectric segments is investigated.The analytical formulae for such a structure are shown and the dispersion relation is calculated.The results show that,by introducing the inter-coupling between the different piezoelectric segments,which is accomplished by serially connecting every n piezoelectric segment into supercclls,some tunable Bragg band gaps can accordingly be opened in the low frequency region.The investigation could provide a new guideline for the tunable phononic crystal under passive control.