Mechanism of Band Gap Formation in Beam Networks

Abstract

Band gaps are commonly attributed to Bragg scattering or local resonance, yet it remains unclear whether these mechanisms govern band gap formation in beam networks. In this work, we explain band gap formation in beam networks in terms of a new mechanism, geometry-induced coupling between deformation modes. Specifically, band gap onset arises from axial-bending coupling at lattice nodes and scales with the axial cutoff frequency of a one-dimensional periodic beam, whereas band gap termination is primarily governed by high-frequency rotational branches associated with beam geometry. This mechanism holds for both periodic and disordered beam networks. In periodic lattices, it manifests through beam orientations at lattice nodes, whereas in disordered networks it manifests through short-beam statistics arising from variations in beam length. Together, these results establish a unified mechanism for band gap formation across both periodic and disordered beam networks, providing new insight into the physical origin of band gaps in beam-network materials.