Summary
Local resonators (LRs) are commonly used in metamaterials to realize low-frequency bandgaps. Such strategies can be implemented in chiral auxetic lattices as well. The presence of thick bandgaps in the sub-Bragg frequency ranges can be demonstrated for different chiral configurations and are highly tunable based on the geometric and material properties. Additionally, geometric nonlinearities manifest owing to large amplitude oscillations of the LR and do enhance the tunability of the existing bandgaps. We investigate the effect of cubic nonlinearity on the band structure by invoking the method of multiple scales (MMS). The amplitude-dependent frequencies based on the linear dispersion curves have been obtained and significant corrections are observed. The corrections obtained for a given set of parameters are sensitive to the mode (translation or rotation dominated). Forced response of this class of materials have been considered.
