Designing an electromechanical metamaterial beam with arbitrary decoupled defect modes for multi-band wave localization

Abstract Defective phononic crystals (PnCs) and metamaterials have gained considerable attention for applications in waveguiding, energy harvesting, and sensing. Despite the increasing interest, traditional defective PnCs/metamaterials are typically restricted to single or dual defect bands, with narrow tunable ranges constrained by the bandgap width. Instead of structural defects, this study introduces an approach to achieve arbitrary decoupled defect modes in defective piezoelectric metamaterial via electrically controlled defects, enabling flexible wave localization across multiple frequency bands. Specifically, we design multiple bandgaps in piezoelectric metamaterials by paralleling unit cells with higher-order resonant circuits that include ‘current-flowing’ branches and consequently propose a multi-bandgap decoupling tuning method. Based on this, a conjecture that adjusting the inductance of a single cell can produce defect bands in all bandgaps is proposed. To accurately predict defect bands, harmonic responses, and wave modes, the spectral element method, incorporating the Timoshenko beam unit, is used to describe the dynamic properties of the metamaterial, which are further validated by finite element analysis. The influence of electrical open-circuit and short-circuit conditions on defect-mode frequencies, alongside the frequency-dependent properties of the energy localization effect are investigated. Results confirm that an arbitrary number of defect bands at specific frequencies can be achieved by tuning the defective cell’s electrical impedance, with each band’s tunability and corresponding energy-localized behavior functioning independently. The proposed approach uniquely enables multi-band wave localization with a single-point defect, offering a significant advantage over conventional methods requiring multiple structural defects, and opening new avenues for programmable wave localization in complex vibration scenarios.