Model for analytical investigation on meta-lattice truss for low-frequency spatial wave manipulation

This study proposes an analytically unprecedented model of a meta-lattice truss with local resonators to generate a broader low-frequency bandgap. By leveraging the mass–spring model, a new equivalent meta-unit cell considering the elastic shear springs is developed to accurately predict the performance of the meta-lattice truss in suppressing stress wave propagations. Theoretical analyses and numerical simulations are conducted to examine the effectiveness of the proposed model. Sensitivity analyses are also performed to investigate the influences of masses and spring parameters on the bandgap characteristics of the meta-lattice truss. Based on the theoretical prediction, the system transmission coefficient is utilized to examine the transmissibility effect among the resonators. A three-dimensional finite element model of meta-lattice truss is also built and its accuracy in predicting the stress wave propagations is verified against the analytical predictions. The structural responses in the time domain and time–frequency domain demonstrate the superiority of meta-lattice truss in suppression of wave transmission as compared to that predicted by the conventional counterparts.