Research On Nonlinear Statics And Dynamics For Carbon Nanotubes In Hygrothermal Environment

Taking carbon nanotubes(CNTs)as the research object,this paper conducted a systematic study of the adhesion,buckling and post buckling,dynamic stability and other static and dynamic behaviors of CNTs in hygrothermal environment using Euler-Bernoulli beam model while comprehensively taking temperature,relative humidity,geometric nonlinearity,van der Waals(VDW)force and other factors into consideration.At the same time,this paper analyzed the intrinsic properties of its mechanical behaviors from the perspectives of physical mechanism and engineering.The main research content is as follows.A study of the adhesion behavior of CNTs in hygrothermal environment was performed based on continuum mechanics theory while considering the influence of relative humidity,temperature and VDW force.An accurate integration of VDW potential of the substrate during the process of CNTs' peeling was conducted while considering the influence of relative humidity,temperature,VDW force and other factors.And a model of CNTs peeling from the substrate in hygrothermal environment was established.The displacement function of CNTs in the space domain was discretized by using finite difference method,and it was solved through Path Following.Numerical calculation results showed that the greater the relative humidity,the greater the peeling force;when the relative humidity was a constant value,the peeling force was not susceptible to the changes in temperature;the peeling force gradually decreased with the increase of the peeling distance.A study of the buckling and post buckling behaviors of the CNTs under the action of axial load and the substrate VDW force was performed based on the structural stability theory while considering temperature,relative humidity and the initial distance between the CNTs and the substrate.A post buckling equilibrium equation of CNTs in hygrothermal environment was established using Euler-Bernoulli beam model,and the post buckling problem of CNTs was solved using semi-analytical method and Galerkin method.The post buckling path of CNTs in a humid and hot environment was determined.The results showed that the VDW force between the CNTs and the substrate increased with the rise of relative humidity,thus in turn influencing the stability of the CNTs;the stability of the CNTs in a high-temperature environment decreased with the rise of temperature.The stability of CNTs in a low-temperature environment increased with the rise of temperature;the lateral displacement of CNTs decreased with the increase of the fineness ratio.Under the first-order buckling mode,the fineness ratio of the CNTs would not affect the buckling critical load.Based on the theory of continuum mechanics and structural stability,the governing equation of parametric vibration generated by CNTs under the axial periodic excitation in a hygrothermal environment was established.The equilibrium equation was converted into linear equation in the form of incremental matrix by using Galerkin method and incremental harmonic balance method.Through numerical calculation,the main dynamic instability area of CNTs under humid and hot condition was obtained.The stability of CNTs decreased with the increase of relative humidity;in high-temperature environment,the stability of CNTs decreased with the increase of temperature.In low temperature environment,the stability of CNTs was improved with the rise of temperature;when the perturbation frequency was greater than the natural vibration frequency of CNTs,temperature and relative humidity had a more significant influence on the stability of CNTs.