A local-resonance piezoelectric phononic crystal consisting of a quadrangular prism piezoelectric scatterer polarized along the z-axis and wrapped by a plexiglass layer is proposed in this work. The short-circuit external electrical boundary condition is selectively added to the upper and lower surfaces of the piezoelectric scatterer to tune the distribution of polarized charges generated by the localized vibration modes. The band structures of the unit cell are calculated using the finite element method, where the upper boundary of the second complete bandgap is replaced by a passband of type of quadrupole local resonance mode. This passband lies entirely in the second bandgap under the open-circuit external electrical condition. The results of the band structures are verified by the transmission loss of the semi-infinite structure in the frequency domain. Two piezoelectric waveguides with complex paths are designed, showing that elastic waves propagate completely along the given waveguide paths at a particular frequency range. The proposed phononic crystals without additional circuit elements can be assembled into waveguides with arbitrary reconfigurable paths, transmitting elastic waves.
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