Elastic Wave Attenuation of Metamaterial Box Beam with Hybrid Resonators

Wave attenuation in a metamaterial box beam is investigated with hybrid resonators. To create the metamaterial characteristics, the box beam is designed with periodic hybrid resonators attached within it. This periodic structure results in an impedance mismatch, leading to the formation of Bragg’s bandgap (BG). The hybrid resonator is a combination of a spring-mass system (called a mechanical resonator) and a piezoelectric patch with a resistance-inductance (RL) shunt circuit. Together, they create local resonant (LR) bandgaps at a specific disturbance frequency. It will generate the hybrid BG by the merging of BG due to the RL shunted piezopatches resonator (termed RL BG) and BG due to the spring-mass resonator (termed SM BG). A mathematical model is developed using the transfer matrix method. The unit cell of the metamaterial box beam is analyzed using Bloch’s periodic theory to predict the attenuation behavior of flexural and coupled flexural and torsional waves in the whole structure. The results related to the hybrid resonator are compared with the mechanical resonator. Initially, the attenuation behavior of flexural waves in the metamaterial box beams is investigated with mechanical and hybrid resonators. The bandgap of the box beam with mechanical resonators is obtained in the frequency range of 358–408 Hz frequency range. With hybrid resonators, the frequency range of BG is 200–600 Hz. The bandwidth of a hybrid resonator is approximately eight times greater than a mechanical resonator. The resonator mass for hybrid BG requires 40% less mass compared to mechanical resonators for obtaining broader bandwidth. In the case of coupled wave analysis, the bandgap due to hybrid resonators is 221–399 Hz, and its bandwidth is three times greater than the mechanical resonators. The influence of metamaterial parameters, such as unit cell length, resistance, and inductance, on the Bragg, RL, and SM bandgap is also investigated. This study demonstrates that hybrid resonators are effective in attenuating flexural and coupled waves over a wider frequency range, all while maintaining a lower resonator mass compared to mechanical resonators.