Broadening low-frequency bandgaps in piezoelectric metamaterial beams by an improved multi-modal shunt circuit

Smart metamaterials provide a promising method for active control of structural vibration, but their application is limited due to their typically narrow bandgap bandwidths. Although ordinary multi-modal shunt circuits can be used to generate multiple resonant frequencies, widening the bandgap has still been a huge challenge. By introducing negative capacitance, we improve the ordinary multi-modal shunt circuit to broaden the bandwidth produced by locally resonant piezoelectric metamaterial. This metamaterial is constructed by connecting periodically distributed piezoelectric patches with shunt circuits to the host elastic beam. The governing equations of wave motion in piezoelectric metamaterial beams are derived, and the equivalent flexural stiffness of a unit cell is obtained by the homogenization theory to predict the frequency of the bandgap. The finite element method is used to calculate the transmission spectrum and to verify the theoretical design. The effects of electrical parameters on the bandgaps are discussed in detail. Finally, an experimental study of the proposed metamaterial beam is carried out. Results show that the dual-band attenuation characteristic of the two-modal shunt circuit is effective in reducing flexural waves. This study provides an effective way to design piezoelectric metamaterial beams with multiple bandgaps for elastic wave isolation and structural vibration attenuation.