Nonlinear wave localization in an acoustic metamaterial

The nonlinear strain solitary waves in a metamaterial mass-in-mass lattice model are studied in the continuum limit. The main feature of the model is in the presence of the masses attached to the masses of the main chain giving rise to the coupling between the movement of the masses. An asymptotic procedure is developed to decouple the governing continuum equations and obtain the single equation for longitudinal strains. Analytical and numerical solutions of the equation reveal an influence of the nonlinearity of the metamaterial model and the attached mass on the type of strain waves localization and the number of generated localized waves. This, in turn, suggests an improvement of the model by an inclusion of a switch-on/off of the attached masses to provide a control of a nonlinear strain wave localization in the metamaterial.(c) 2023 Elsevier B.V. All rights reserved.