A STUDY ON THE BAND GAP CHARACTERISTICS OF METAMATERIAL BEAMS WITH FORCE-MOMENT RESONATORS

Elastic wave metamaterials are a class of composite structures or materials composed of artificially designed microstructural units arranged in periodic arrays. These materials exhibit extraordinary physical properties not found in conventional materials, which are primarily determined by the microstructural resonators (local resonance units). For flexural wave metamaterial beams, the local resonance units can be classified into three types based on their interaction forces with the host beam: force-type resonators, moment-type resonators, and force-moment coupled resonators. Currently, most research focuses on force-type resonators, while the bandgap characteristics and underlying mechanisms of metamaterial beams with force-moment coupled resonators remain insufficiently understood. To address this gap, this study employs cantilever beams to construct force-moment coupled resonators and investigates their band structures and bandgap properties. When the beam-type resonators are symmetrically arranged, they can be equivalently treated as decoupled force-moment resonators. The specific parameter relationships between them are established, and the band gap formation mechanism of metamaterial beams with decoupled force-moment resonators is elucidated through their band-edge frequency equations and natural frequency analysis of the corresponding unit cell. An approximate prediction formula for the local resonance band gap generated by metamaterial beams with decoupled force-moment resonators is also derived. In contrast, asymmetrically arranged beam-type resonators exhibit coupled force-moment interactions. By introducing an asymmetry factor, this work systematically examines the influence of coupling effects on the band structure and bandgap properties, revealing phenomena such as bandgap transition and bandgap coupling. The above conclusions were validated through experimental verification. This research enhances the understanding of metamaterial beams with force-moment coupled resonators and provides theoretical guidance for the optimized design and engineering applications of metamaterial beams. The findings contribute to a deeper insight into the interplay between force and moment interactions in metamaterial beams, paving the way for advanced vibration and wave control in structural systems.