Analytical Investigation of Electromechanically Coupled Hierarchical Metamaterials for Simultaneous Vibration Attenuation and Energy Harvesting

Abstract Recent work has revealed the great value of electromechanical resonators for energy harvesting and bandgap tuning in metamaterials. However, thus far there have not been any studies of hierarchically configured resonators for energy harvesting. This work presents a theoretical study of electromechanically coupled resonator-based hierarchical metamaterials, focusing on zero-order, first-order outward, and first-order inward configurations. The study investigates the impact of integrating resistor shunt circuits on the band structure under weak and strong coupling conditions. Additionally, it explores the influence of variations in local resonator mass on the vibration attenuation and energy harvesting capability of the configurations. The dispersion relations are determined for each configuration with varying system parameters. Furthermore, the transmissibility frequency response functions are presented to observe vibration reduction and energy harvesting capability. The results reveal that a hierarchical design offers enhanced flexibility in tailoring the band structure and stronger vibration attenuation and energy harvesting. As the hierarchy level increases, there is a corresponding increase in the number of passbands. However, it’s noteworthy that weak electromechanical coupling does not influence the band structure across all hierarchy levels, while strong coupling does. Compared to the zero-order configuration’s baseline performance, both the outward and inward configurations exhibit superior abilities in vibration suppression and energy harvesting when the total system mass is constant. Results given here may be used for the optimal design of hierarchically configured energy harvesters.