Multipolar resonance and bandgap formation mechanism of star-shaped lattice structure

Abstract

The star-shaped lattice structure is recognized as a typical auxetic metamaterial. Unlike the most research focused on the negative Poisson's ratio, in this paper the wave propagation behaviour and vibration attenuation mechanism of the periodic star-shaped lattice structure are studied based on the analytical 16 degrees of freedom (DOF) discrete mass-spring model. The dispersion relation and bandgaps of the 16 DOF mass-spring model are derived based on lattice dynamics. The dependence of the bandgap boundaries on the parameters of configuration angle, stiffness, and mass are studied accordingly. It is noteworthy that the eigenstate modes investigation reveals that the bandgaps attribute to the hybridization of the monopole, dipole, quadrupole, and rotational resonance, which is only noticed in multiphase hybrid metamaterials before. Most importantly, though examining the eigenstate modes of the degeneration points, the low-frequency bandgap between the acoustic and optical dispersion curves is opened by tuning the dominant parameters. The response of the finite periodic star-shaped lattice shows the frequency ranges with high attenuation agree well with complete bandgaps predicted by dispersion relation. The star-shaped lattice shows a very unique anisotropic solid when the slope of the dispersion curve is negative.