Effects of Nonlocal Shear Factor on Flexural Wave Dispersion in Double-Walled Carbon Nanotubes
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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.Abstract: The effects of nonlocal factors on the wave dispersion in the doublewalled carbon nanotube(DWCNT) were analyzed with the modified Timoshenko beam model modified based on the stress gradient theory. Coupling with Van der Waals force, the dispersion characteristics, such as phase velocity, frequency, critical frequency and amplitude ratio of outer tube to inner tube, were studied. The results show that: for a given wave number, both the first 4 modes’phase velocities and frequencies of the DWCNT decrease with rise of the nonlocal shear factor, in which no obvious linear law is 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. Meanwhile, the nonlocal shear factor has prominent effects on the wave dispersion characteristics of the DWCNT especially at relatively higher wave numbers.
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