Dispersion analysis of a two-dimensional metastable metastructure considering damping and nonlinear effects

Because of its remarkable dispersion properties, wave propagation in periodical elastic metamaterials and metastructures has attracted serious attention. Metastable metastructure, whose mechanical properties can be tuned by internal reconfiguring and metastable states switching, could be a promising candidate to achieve tunable band structures. However, in previous studies, only linear dispersion analyses of multistable/metastable structure were performed, and the effect of damping was not considered. In this research, dispersion properties of a two-dimensional metastable metastructure considering the damping and nonlinear effects are investigated. By using the perturbation method, nonlinear dispersion relation of the metastable structure is derived analytically. Results show that, by switching the internal configuration of the metastable structure, band structure can be tuned significantly, and new partial and complete passbands are created. Damping will cause a downward shift to the frequency branches of the band structures, stiffness-proportional damping will mainly affect the optical modes (higher frequency branches), while mass-proportional damping will mainly affect the acoustic modes (lower frequency branches). Nonlinearity will increase the frequencies of optical modes; however, it will have a little effect on the acoustic modes. The insights and reasons of these newly observed phenomena are discussed.