Wave Characteristic Analysis Of Viscoelastic Single-Walled Carbon Nanotubes Based On Nonlocal Strain-Gradient Theory

In recent years,carbon nanotubes(CNTs)have become a hot topic in the academic field,and continuum theory has been widely used to study the mechanical properties of nanostructures.Because of the micro size effect,the classical continuum theory has gradually developed into the nonlocal continuum theory.The structure of SWCNT can be approximated as one-dimensional structure model.Based on nonlocal elastic theory and strain gradient theory,according to three different types of beam models,namely Euler-Bernoulli beam,Rayleigh beam and Timoshenko beam models,the wave equation of CNT is derived through its free vibration equation,and the wave characteristics of SWCNT with viscoelasticity are studied.Kelvin-Voigt model is used to simulate the viscoelasticity of CNT.Taking wave number,nonlocal parameters,strain gradient scale coefficient and viscoelasticity degree as the influencing factors,the dependences of natural frequency and attenuation coefficient upon SWCNT diameter are explored,and the wave characteristics of carbon nanotube obtained by the use of these three models are compared.According to the chirality difference of graphene materials,the effects of temperature,magnetic field and Winkler modulus on frequency and phase velocity are investigated with wave number as independent variable,and the effects of these factors on cutoff frequency and critical wave number are compared.Based on Navier-Stokes theory,the wave equation of viscoelastic SWCNT for viscous fluid transport is established,and the effects of velocity,nonlocal effect,strain gradient size effect,dynamic viscosity of viscous fluid and surface effect on wave propagation of SWCNT are explored under the condition of small wave number.