基于梯度理论的碳纳米管弯曲波传播规律的研究  

Modified Timoshenko Beam Models for Flexural Wave Dispersion in Carbon Nanotubes with Shear Deformation Considered

作　　者：王碧蓉[1] 邓子辰[1,2] 徐晓建[1] 

机构地区：[1]西北工业大学工程力学系,陕西西安710129 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《西北工业大学学报》2013年第5期774-778,共5页Journal of Northwestern Polytechnical University

基　　金：国家基础研究计划973项目(2011CB610300);111引智计划项目(B07050);国家自然科学基金(10972182;11172239);高校博士点基金(20106102110019);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802);西北工业大学研究生创业种子基金(Z2012060)资助

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。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.

关 键 词：碳纳米管 弯曲波 梯度理论 频散特性 非局部效应 

分 类 号：TB383[一般工业技术—材料科学与工程]