Parametric analysis of bandgaps in a general metachiral lattice using discrete dynamical analysis

Abstract

To exploit low-frequency bandgaps in a chiral auxetic lattice, local resonators (LR) are usually incorporated. In that case, the tailorable bandgaps are the sub-Bragg bandgaps, whose width depend on the mass of the resonator and the effective stiffness of the elastic coupling used to attach the resonator. However, this does not allow direct control over the bandgaps above the sub-Bragg frequencies. To achieve that, in this study, we introduce the diatomic structure and include a secondary species in the lattice, resulting in highly tailorable bandgaps in the absence of the LRs. The proposed class of metachiral lattices introduces seven design parameters that can be varied to engineer the band structure over a wide frequency range. A detailed analytical study of the lattice has been conducted using a discrete Lagrangian model, and the dispersion characteristics have been studied by invoking Floquet-Bloch periodicity conditions. Appropriate finite element analysis has been conducted to compare the analytical results and corroborate the detailed parametric study thereof.