Title: Electromechanical bandgaps in piezo-embedded mechanical metamaterials

Abstract

Elastic mechanical metamaterials are the exemplar of periodic structures. These are artificially designed structures having idiosyncratic physical properties like negative mass and negative Young’s modulus in specific frequency ranges. This unusual dynamic behavior is frequency contingent, which modulates wave propagation through these structures. Locally resonant units in the designed metamaterial facilitate bandgap formation virtually at any frequency for wavelengths much higher than the lattice length of a unit. Here, we analyze the band structure of piezo-embedded negative mass metamaterial using the generalized Bloch theorem. The addition of the piezoelectric material at the resonating unit increases the complexity of the solution. The results elucidate, the insertion of the piezoelectric material in the resonating unit provides better tunability in the band structure for simultaneous energy harvesting and vibration attenuation. Non-dimensional analysis of the system gives physical parameters that govern the formation of mechanical and electromechanical bandgaps. Thus, broader bandgap generation enhances vibration attenuation, and energy harvesting can be simultaneously available, making these structures multifunctional.