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中文摘要：
为研究非局部效应对碳纳米管中弯曲波频散特性的影响，分别给出了应力梯度和应变梯度修正的铁木辛柯梁模型的控制方程，通过代入波函数表达式，得到频散方程。借助数值算例，得到两种修正模型在非局部因子取值变化时的频散曲线，并与分子动力学结果对比证实模型的可行性。结果表明，文中所引入的非局部因子对研究高波数阶段弯曲波频散特性十分必要。
英文摘要：
In this paper, the governing equations of modified Timoshenko beam models with stress and strain gradients are established to investigate the nonlocal shear effect on flexural wave dispersion in carbon nanotubes. The dispersion equations are analytically obtained and the dispersion curves of the two modified models are illustrated numerically with different nonlocal shear factors. The results and their analysis show preliminarily that： （ 1 ） the nonlocal factors introduced here have significant effects on analyzing the dispersion characteristic of flexural wave in carbon nanotubes, especially at the higher wave numbers; （2） the variations of nonlocal factors also influence the branches of waves depending on the different nonlocal shear factors adopted.
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