Study On The Effects Of Nonlocal Strain Gradient Theory On Wave Propagation Of Fluid-filled Single-walled Carbon Nanotubes

Since the application of carbon nanotubes(CNT)became a hot topic in nano science and industry,the study on mechanics behaviors of CNTs based on nonlocal stress theory and strain gradient theory are concerned by many researchers.However,the two theory play different role in analysis of mechanical properties of CNTs,and both of them have disadvantages.In this article,the dynamic behaviors of fluid filled CNTs are analyzed based on the nonlocal stress/strain gradient-couple theory contribute by Lim in 2015.The physical properties and industry application of carbon nanotubes are investigated firstly.The study methods about mechanics behaviors of carbon nanotubes are also indicated.Secondly,the dynamic model of Euler-Bernoulli beam and Timoshenko beam for fluid-filled single-walled carbon nanotube(SWCNT)are established,respectively,when the small scale effects induced by CNTs and inner fluid are simulated by the high-order nonlocal strain gradient model and slip boundary model.The governing equations of wave propagation for fluid filled SWCNT beam are derived according to Hamilton's principle.By solving the governing equations,analytical expressions of angular frequency for dynamic systems are obtained,and influence from nano-scale effects on dynamic behaviors of SWCNTs are studied.According to the simulation results on Euler-Bernoulli beam,wave propagation with low wavelength are enhanced by strain gradient and fluid slip boundary effects,when the ones with high wavelength are damped.The nonlocal stress effect only contributes decaying for the dynamic behaviors for any wavelength.These three kinds of scale effects lead to stiffness enhancement for fluid filled SWCNTs at low fluid velocity,as wave propagation are promoted.However,the wave propagation behaviors are damped at high fluid velocity,since energy transmission in this case is damped by the scale effects.According to the simulation results on Euler-Bernoulli beam,wave propagation are enhanced by strain gradient,so that strain gradient effect lead to stiffness enhancement for fluid filled SWCNTs.Fluid slip boundary effects and nonlocal stress effect contribute decaying for the dynamic behaviors,since energy transmission in this case is damped by the scale effects.