摘要
基于应力梯度理论修正的Timoshenko(铁木辛柯)梁模型,结合管间Van der Waals(范德华)力,研究了非局部效应对双壁碳纳米管中弹性波各阶模态的相速度、频率、临界频率、内外管振幅比等频散特性的影响.数值模拟结果表明:在应力梯度理论修正模型下,对应同一波数,4阶模态的相速度、频率均随剪力非局部因子的增大而减小,且随着剪力非局部因子的等幅增加,相速度、频率的减小并没有明显的等幅规律;值得注意的是,3、4阶模态的内外管振幅比并不是随着剪力非局部因子的增加依次减小;在波数较高阶段,剪力非局部因子对双壁碳纳米管中波的相速度、频率、渐近频率、内外管振幅比等频散特性均有显著影响.
The effects of nonlocal factors on the wave dispersion in the double-walled carbon nanotube( DWCNT) were analyzed with the modified Timoshenko beam model modified based on the stress gradient theory. C oupling with Van der W aals force,the dispersion characteristics,such as phase velocity, frequency,critical frequency and amplitude ratio of outer tube to inner tube,were studied. The results showthat: for a given wave number,both the first 4 modes' phase velocities and frequencies of the DW C N T decrease with rise of the nonlocal shear factor,in which no obvious linear lawis found. It is notable that for the 3rd and 4th modes the amplitude ratios do not decrease with the rise of the nonlocal shear factor. M eanwhile,the nonlocal shear factor has prominent effects on the wave dispersion characteristics of the DW C N T especially at relatively higher wave numbers.
出处
《应用数学和力学》
CSCD
北大核心
2014年第5期478-486,共9页
Applied Mathematics and Mechanics
基金
国家重点基础研究发展计划(973计划)(2011CB610300)
111引智计划项目(B07050)
国家自然科学基金(11372252
11172239)
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)
高校博士点基金(20126102110023)~~
关键词
双壁碳纳米管
弯曲波传播
应力梯度理论
频散关系
double-w alled carbon nanotubes
w ave propagation
stress gradient theory
dispersion rela-tion
