Thermodynamic characteristics and bifurcation of multiwalled carbon nanotubes impacted by hydrogen atoms using Nonlocal continuum theory

In this article, the thermodynamic characteristics and bifurcation of MWCNTs impacted by hydrogen atoms were studied. The impact between MWCNTs and hydrogen atoms was regarded as white noise. Nonlinear differential items were introduced to explain the hysteretic phenomena of MWCNTs stiffness, and a nonlinear dynamic model of MWCNTs impacted by hydrogen atoms was developed where the nonlocal effect is considered. The conditions of stochastic Hopf bifurcation were identified, and the fractal boundary of the safe basin was provided. The reliability function of the system was solved, and the probability density of the first-passage time was determined. Theoretical analysis and numerical simulation show that stochastic Hopf bifurcation occurs in the variation of parameters; the boundary of safe basin has fractal characteristics, the area of safe basin decreases when the intensity of the noise increases; the hysteretic nonlinearity of MWCNTs stiffness can affect the system's stability and safe basin, which decides the actual hydrogen storage capacity of MWCNTs.