Study On The Strongly Nonlinear Dynamic Characteristics Of Single-Walled Carbon Nanotubes Under Stochastic Magnetic Field

Since the discovery of carbon nanotubes,carbon nanotubes have been widely applied in biochemistry,medical engineering,electronic information,aerospace and some other fields due to their excellent electrical,magnetic,thermal and mechanical properties.With the development of nanomaterials technology,people can accurately manufacture various types of nanomaterials to meet the needs of scientific research and Engineering.Nowadays,the continuum model is widely used to analyse the mechanical,electrical and thermal problems.However,at the nanoscale,the effect of small scale on the nanostructure is significant.Besides,the interference with stochastic factors can not be ignored when applied to complex environments.Based on the theory of nonlocal elasticity and stochastic dynamics,this paper focus the research on the strongly nonlinear dynamic response of carbon nanotubes under stochastic magnetic field,and the main conclusions are as follows: 1)Based on Eringen's nonlocal elasticity theory,the constitutive relationship of nonlocal elasticity theory is derived,thus we can propose the dynamic equation of single-walled carbon nanotubes,and then we considered the effect of nanotube which embedded in viscoelastic matrix.At this step,Winkler model is introduced which includes linear damping and strong nonlinear damping.Beacause of the stochastic magnetic field,the we should consider the effect of Lorentz force.Therefore,we obtained the dynamic equation of carbon nanotubes which embedded in the Viscoelastic matrix under stochastic magnetic field;2)The strongly nonlinear dynamic characteristics of carbon nanotubes under stochastic magnetic field are studied,the natural frequency of the strong nonlinear dynamic system is obtained by using the energy function method,and the drift coefficient and diffusion coefficient are solved.Besides,the stationary probability density function of the dynamic response of the system is given.The bifurcation characteristics of the system are simulated by the software of Mathematica.The results show that,with the increase of magnetic field strength,the stability of the system decreases firstly and then increases,which is called stochastic resonance phenomenon.The fractal boundary of the system's safety basin decreases gradually with the increase of magnetic permeability,leading to lower reliability.