Waves in geometrically modulated metabeams

Abstract

Wave propagation through structures like honeycombs and re-entrant corners has gained significant attention due to their unique propagation characteristics and meta-properties like, bandgaps and negative Poisson’s ratio, having potential for vibration suppression. The inclusion of inclined members increases the effective wave path within the unit cell, lowering the group velocity. This motivates us to explore various beam-like structures with geometric modulations like diamond, hexagonal, rectangular, and re-entrant unit cells. The spectral element-based formulation is applied to construct frequency-dependent global dynamic stiffness matrices of unit cells. These matrices facilitate the examination of wave propagation and attenuation, revealing comprehensive insights into periodic structures. The analysis encompasses combined 1D wave propagation involving axial, biaxial flexure (bending and shear), and torsion. Complete attenuation bandgaps for all six wave types, with mode coupling and wave locking are found, identified from the dispersion diagrams, as key mechanisms influencing the dynamic behavior. Frequency response functions (FRFs) validate the methodology, showing minimal or no response within attenuation bandwidths. Further, numerical validation and experimental investigation of the frequency responses of the structures has been conducted. Lastly, the study explores the impact of unit cell geometry and orientation on bandgap widening and attenuation levels.