Band evolution and 2D nonreciprocal wave propagation in strongly nonlinear meta-plates

Abstract Nonlinear meta-materials/structures can enable exotic wave phenomena, leading to extraordinary functionalities, but the bandgap properties and nonreciprocal wave manipulation in high-dimensional nonlinear metamaterials, such as plates, are not fully understood. In this study, we examine the band evolution and nonreciprocal wave propagation in a two-dimensional (2D) strongly nonlinear meta-plate based on analytical methods and numerical integration on the infinite model. The 2D dispersion curves are obtained through combining harmonic balance and Shooting-Newton iteration methods. Numerical studies show that the 2D nonlinear meta-plate exhibits band degeneration and self-adaptive propagation, analogous to 1D cases. However, as confirmed analytically, both band degeneration and self-adaptivity are regulated by the spatial wave divergence in the 2D meta-plate. Furthermore, combining nonlinear and linear portions of a meta-plate entails nonreciprocal wave propagation in 2D space with elucidated physical properties and mechanisms specific to 2D wave propagation. In light of the above, this work presents new computational methods as well as the elucidation of new wave phenomena and properties which are conducive to wave manipulation in 2D strongly nonlinear meta-materials/structures.