Transmission of radial vibration along piezoelectric tubular phononic crystal in parallel with resonant shunting circuits

A tube phononic crystal (PC) model arrayed periodically by metal and piezoelectric segments is proposed. Each piezoelectric segment consists of two piezoelectric layers connected in parallel independently by a resonant shunting circuit. The inductor and a piezoelectric equivalent capacitor form an inductor-capacitor oscillator. Coupling vibration of extension and flexure of the thin periodic tube structure is studied by the classical shell theory and linear piezoelectric theory. Precise electric field method and transfer matrix method are applied to solve band gap structures and transmission factor curves. Two locally resonant band gaps and one Bragg band gap are distinguished. Some interesting phenomena of interaction between two locally resonant bands are found. The effects of circuit inductance, material parameters of the tube PC on these three band gaps are investigated.