Harnessing rotational geometry to design reconfigurable dispersion and refractive index in nonlinear acoustic metamaterials

Abstract

We investigate 1D and 2D monatomic lattice structures composed of in-plane rotators coupled by angled elastic linkages and explore their reconfigurable dispersion, negative refraction, amplitude-dependent dynamics, and acoustoelastic effect. At small amplitude, the linear band structure can be configured to be either acoustic or optical in nature by changing the connecting locations on the rotators, which corresponds to positive and negative refractive index. An interface problem between two rotator lattices with opposite dispersion type is modeled, and illustrates negative refraction in numerical simulations—experimental measurements are in progress. Its frequency–transmission relation matches the linear theory. At higher amplitude, the hardening nonlinearity shifts the dispersion and induces amplitude-dependent transmission. A novel nonlinear phenomenon–amplitude saturation (a constant far-field transmission independent of input amplitude) is observed when the transmitted wave falls in the nonlinear stopband and simultaneously the linear passband of the receiving lattice. We analyze the nonlinear effects via perturbation methods and propose a framework for evanescent-specific nonlinear waves to explain the saturation phenomenon. Additionally, we observe a strong acoustoelastic effect in chiral-patterned rotator lattices, where a static stretch can shift the equilibrium positions of the rotators and morph the band structure from acoustic to optical.