Abstract

Longitudinal wave propagation in carbon nanotubes has been investigated by using Rayleigh-Bishop rod model and nonlocal strain gradient elasticity theory in the present study. Size dependent governing equation of motion has been obtained with variational formulation. Validation of the proposed model has been achieved with developed lattice dynamics model which considers neighborhood interaction. Least squares approach has been used in addition to the traditional calibration methodology. Number of atomic interactions, shear strain and rotary inertia effects have important effects on the calibration of scale parameters. Present results could help to continuum modeling of carbon nanotubes with accurate scale parameters.

摘要

本研究利用Rayleigh-Bishop棒模型和非局部应变梯度弹性理论研究了碳纳米管中的纵向波传播。通过变分公式获得了与尺寸相关的运动控制方程。所提出的模型的验证已经通过考虑邻域相互作用的开发晶格动力学模型来实现。除了传统的校准方法之外，还使用了最小二乘法。原子相互作用的数量、剪切应变和旋转惯性效应对尺度参数的校准有重要影响。目前的结果有助于用精确的尺度参数对碳纳米管进行连续建模。