Nonlinear vibrations of circular single-layer black phosphorus resonators

Abstract

A strong nonlinear relationship between the displacement and the load in single-layer black phosphorus sheets (SLBPs) was observed under the large deflection by nanoindentation experiments. However, the nonlinear effect is rarely considered in the Nano-Electro-Mechanical-System (NEMS) resonators based on the SLBPs. In this letter, nonlinear static and dynamics behaviors of circular SLBPs (CSLBPs) are investigated using molecular dynamics (MD) simulations and a nonlinear orthotropic plate model (NOPM), respectively, where the geometrical nonlinearity is systematically considered in the NOPM. Our results show that the response-frequency curves of forced vibrations in CSLBPs meet clear hardening-type nonlinearity. The damping ratios of CSLBPs are proportional to the square of the vibration amplitude. In particular, the NOPM together with the law of energy equipartition is further utilized to study the nonlinear thermal vibrations of the CSLBPs. Checking against present MD calculations shows that the solution of the present NOPM has high accuracy. The present study should be of great help for designing NEMS resonators based on two-dimensional (2D) orthotropic materials.