A nonlocal continuum mechanics model is developed and applied to study the vibration of both single-walled nanotubes (SWNTs) and double-walled nanotubes (DWNTs) via elastic beam theories. The small-scale effects on vibration characteristics of carbon nanotubes are explicitly derived through a complete mechanics analysis. A qualitative validation study shows that the results based on nonlocal continuum mechanics are in agreement with the published experimental reports in this field. Numerical simulations are conducted to quantitatively show the small-scale effect on vibrations of both SWNTs and DWNTs with different lengths and diameters.
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Wang et al. (2006) studied this question.
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