Locally resonant band gaps achieved by equal frequency shunting circuits of piezoelectric rings in a periodic circular plate

This work presents an investigation on vibration transmission in a circular thin plate consisting of metal rings and piezoelectric rings arrayed periodically. Each piezoelectric ring is linked to an independent resistive–inductive (RL) resonant shunting circuit. For a periodic rectangular piezoelectric plate, equal inductances are commonly used in resonant shunting circuits. However, for the circular one, the locally resonant (LR) band gap (BG) cannot be formed by shunting circuits with equal inductances, because different periodic cell has a different capacitance. Instead of equivalent inductance circuits, the equal frequency shunting circuits are employed to tune the resonance frequency of each circuit into the same, thus an integrating LR BG is obtained. A transfer matrix method is used to calculate transmission factor in the low frequency range. The theoretical model is verified by finite element method (FEM). The impact of geometric and circuit parameters on the properties of the LR BG and vibration attenuation band (VAB) has also been analyzed.