Low frequency coupled bandgap regulation of staggered piezoelectric supercell beam

The study proposes a staggered piezoelectric supercell beam to enhance the traditional passive periodic metamaterial bandgap. This beam features varying inductance in each cell and different degrees of interlacing in the piezoelectric plate. By adjusting the degree of staggering, the attenuation constant of the locally resonant bandgap is improved, and a low-frequency broadband bandgap is created. The dynamic model of the staggered supercell beam is established using the transfer matrix method to calculate the attenuation constant and transmissibility. Theoretical analysis indicates that the locally resonant bandgap attenuation constant of the staggered beam can be increased by 0.24 compared to the symmetrical beam, thereby mitigating the negative effect of the cascade of inductance gradients. Results indicate that a gradient setting of staggering can introduce new Bragg bandgaps at lower frequencies. Comparison of vibration attenuation results between the symmetrical and staggered beams reveals that the staggered beam generates a coupling bandgap with increased bandwidth at low frequencies due to the newly created Bragg bandgap. Experimental findings show that the staggered beam can create a coupling bandgap with a bandwidth of 170 Hz and exhibited a 7.77 dB decrease in transmission rate compared to the symmetrical beam. Numerical simulations of unit cell parameters, structural parameters, and electrical parameters elucidate the mechanism behind each bandgap. This design enhances the attenuation effect of the locally resonant bandgap and offers the ability to generate coupling broadband with customizable frequency band positions, presenting promising research prospects and ideas for low-frequency vibration isolation.