基于非局部应变梯度欧拉梁模型的充流单壁碳纳米管波动分析

将非局部弹性理论和应变梯度理论结合,再根据流体滑移边界理论,建立了考虑流体和固体小尺度效应的充流单壁碳纳米管(SWCNT)流固耦合动力学模型,分别以非局部应力效应、应变梯度效应和流体滑移边界效应模拟微观小尺度效应对系统的影响,推导得出充流单壁碳纳米管的Euler-Bernoulli梁波动控制方程。通过对控制方程的求解,分析材料不同类型尺度效应对充流碳纳米管的振动和波动特性影响。结果显示,应变梯度效应和流体边界效应对低频波动起促进作用,对高频波动起阻尼作用,应力非局部效应则对波动始终产生阻尼作用。三种尺度效应对低流速系统的振动有促进作用,而对高流速系统产生阻尼作用。

Wave propagation of fluid-filled single-walled carbon nanotubes based on the nonlocal-strain gradient theory

Based on the high-order nonlocal strain gradient theory and slip boundary conditions of nano-scale fluid,a dynamic model of Euler-Bernoulli beams for fluid-filled single-walled carbon nanotubes (SWCNT) was established. The governing equation of wave propagation for fluid filled SWCNT beams was derived according to the Hamilton’s principle. By solving the governing equations,analytical expressions of angular frequency for dynamic systems were obtained,and the influence from nano-scale effects on dynamic behaviors of SWCNTs were studied. According to the simulation results,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 to the decay of the dynamic behaviors for any wavelength. These three scale effects lead to stiffness enhancement for fluid filled SWCNTs at low fluid velocity when 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.