Coupling between two kinds of band gaps of a shunted tube piezoelectric phononic crystal

Abstract

A tube-type piezoelectric phononic crystal model is proposed to study interaction between locally resonant and Bragg band gaps, which is arrayed periodically by metal and piezoelectric segments. Each piezoelectric segment consists of a shell with series-connected and opposite directions polarized double layers and a resonant shunting circuit. According to the interaction between Bragg scattering and local electromagnetic oscillation, three regions corresponding to the inductance can be divided as follows: quasi-short circuits region, coupling region, and quasi-open circuits region. Some interesting phenomena are found from the coupling between Bragg scattering and locally resonant of electromagnetic oscillation. (1) In the coupling region, a pass band splits a Bragg band gap into two band gaps. But the cut-off frequency of the second band gap does not change with the inductance. (2) In the quasi-open circuits region, Bragg and locally resonant band gaps exist independently. (3) The first band gap transits from Bragg scattering to local resonance when the inductance increases from quasi-short circuits region to quasi-open circuits region. (4) The cut-off frequency of the first band gap is always less than the estimated resonant frequency of inductor-capacitor oscillators. Finally, the theoretical result is validated by two kinds of finite element models based on ANSYS.