Small Scale Effect on Boundary Conditions of Cantilever Single Carbon Nanotubes

Ming Li; Hui Ming Zheng; Luo Xia; Liu Yang

doi:10.4028/www.scientific.net/AMM.275-277.33

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 275-277Small Scale Effect on Boundary Conditions of...

Small Scale Effect on Boundary Conditions of Cantilever Single Carbon Nanotubes

Abstract:

In this paper, the boundary condition on free vibration of cantilever single-walled carbon nanotubes (SWCNTs) with Winkler elastic medium is investigated. The Euler beam theory with nonlocal elasticity is modeled as SWCNT. The analytical solution is derived and the numerical results show that the additional boundary conditions from small scale do not change natural frequencies. The reason is that the additional work made by the moment and shear force at the free end from small scale effect cancel each other, the boundary conditions due to local elasticity and nonlocal elasticity are also equivalent. Thus for simplicity, one can apply the local boundary condition to replace the small scale boundary condition.

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Periodical:

Applied Mechanics and Materials (Volumes 275-277)

Pages:

33-37

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.275-277.33

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Online since:

January 2013

Authors:

Ming Li, Hui Ming Zheng, Luo Xia, Liu Yang

Keywords:

Boundary Condition, Nanotubes, Nonlocal Euler Beams Theory, Small Scale, Vibration

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