Modulation instability in nonlinear acoustic metamaterials with coupling coefficients

Abstract

In this paper, the modulation instability is analyzed in a novel model of coupled pairs of chains with coupling coefficient parameters. We derive the coupled system of the nonlinear equation by using the Lindstedt-Poincare perturbation and the multi-scale method. From the linear stability analysis, an expression for the modulation instability growth rate is established, and we assessed the effects of the coupling strength on the modulation instability spectrum in acoustic and optical modes. In acoustic metamaterials, it appears that modulation instability develops and results in the formation of wave trains. We also demonstrated that the modulation instability bandwidth can be reduced or expanded depending on the effectiveness of the coupling coefficient as well as the angular frequency. Through the numerical experiments, we showed the propagation of the modulated wave patterns, manifesting the existence of the modulation instability growth rate in the structure. It results from this investigation that conventional materials where microstructural configurations are designed to exhibit unusual properties are attractive to modulated wave structures. In future works, soliton dynamics, rogue waves, and localized modes will be investigated to give rise to several applications.