Amplitude-induced bandgap: New type of bandgap for nonlinear elastic metamaterials

Abstract

In this paper, we report a new type of bandgap phenomenon called "amplitude-induced bandgap", which is induced by amplitude in nonlinear metamaterials. Generally, bandgap phenomena in elastic metamaterials or phononic crystals have been achieved by the artificial unit cells which prevent wave propagation with Bragg scattering or internal resonance. However, the amplitude-induced bandgap originates from the amplitude and nonlinearity unlike previously discovered bandgap phenomena. Accordingly, the amplitude-induced bandgap is shown to exhibit various peculiar characteristics that have not been previously observed. Here, an analytic investigation about the amplitude-induced bandgap is conducted based on the perturbation approach in a nonlinear softening monoatomic chain. Also, various peculiar characteristics of the amplitude-induced bandgap are studied in detail. Numerical simulations using finite element analysis are carried out to validate the amplitude induced bandgap. In addition, the transmission characteristics of nonlinear bandgap are also analytically studied based on the recursive method and numerically verified through the simulations. (C) 2020 Elsevier Ltd. All rights reserved.