Bandgap characteristics of the two-dimensional missing rib lattice structure

In this paper,the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem.The tuning of the width and position of the bandgap is achieved by changing the local structural parameters,i.e.,the rotation angle,the short beam length,and the beam thickness.In order to expand the regulation of the bandgap,the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed.The results show that the mass density and stiffness of the structure have significant effects on the bandgap,while Poisson’s ratio has no effect on the bandgap.By analyzing the first ten bands of the reference unit cell,it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction,and these bandgap widths are wider.The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure,and this dipole resonance originates from the coupling of the bending deformation of the beam elements.In the band structure,the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance,which is different from that with the conventional negative slope formed by the coupling of two resonance modes.This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials,as well as for the regulation of bandgaps and the suppression of elastic waves.