Opening Bandgap in monoatomic-diatomic convertible metamaterial with nonlinearity

Elastic metamaterials with nonlinearity have been actively studied recently due to their capability of bandgap tuning via wave amplitude. Nevertheless, previous approaches generally focused on tuning bandgap which was already formed without nonlinearities, so that they shared same limitations as in the linear bandgap cases. In this work, we propose a new nonlinear metamaterial that can open a non-existing bandgap or close the existing bandgap with nonlinear effect. The main idea is to utilize the transition between monoatomic and diatomic chains. To achieve the transition, we introduced alternating nonlinearity by using different bounding springs for even and odd masses. To theoretically describe the bandgap opening phenomena, we found that the general Lindstedt-Poincaré perturbation cannot be applied in the proposed metamaterial, so we applied Brillouin-Wigner perturbation. The proposed idea is validated with numerical simulation results. We expect our idea may extend the practical usability of nonlinear bandgap tunings and offer abundant new approaches to facilitate various advanced functionalities.