Bragg band gaps tunability in an homogeneous piezoelectric rod with periodic electrical boundary conditions

An homogeneous piezoelectric rod is shown to exhibit Bragg band gaps when an electrical boundary condition is applied periodically with the help of metallic electrodes. An analytical model is developed which formulation depends on the applied electric boundary condition and reveals that Bragg band gaps occurring in this very peculiar phononic crystal are related to the electric charge located on the electrodes. Moreover, via an accurate boundary condition (electrodes connected in short circuit, in open circuit, or through an external capacitance), full tunability of the Bragg band gaps can be achieved. Measurements of ultrasonic transmission present an overall excellent agreement with the theoretical results. This phononic crystal can be easily manufactured and presents many potential applications as frequency filters especially for radio frequency telecommunications.