Summary
Nonlinear meta-materials/structures can enable exotic wave propagation phenomena which ultimately lead to extraordinary functionalities that are not accessible in nature materials. Despite the increasing attention received, the properties and underlying physical mechanisms of band structures and bandgaps in high-dimensional nonlinear metamaterials, such as plates, remain unclear. Here we propose and examine a meta-plate with embedded strongly nonlinear oscillating units to show the evolution process of typical nonlinear band structures using analytical and numerical methods. Based on the band properties of nonlinear meta-plate, we integrate linear and nonlinear meta-plate to break reciprocal wave propagation in the 2D plate. The non-reciprocity properties of the modulated elastic waves may bring about exciting engineering applications. This study provides modelling and computational methods for high-dimensional strongly nonlinear meta-materials/structures, and fills the gaps in the understanding of the mechanism and properties of nonlinear wave propagation in 2D plates.
