Vol. 5, No. 3, 2010

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ISSN: 1559-3959
Wave propagation in carbon nanotubes: nonlocal elasticity-induced stiffness and velocity enhancement effects

C. W. Lim and Y. Yang

Vol. 5 (2010), No. 3, 459–476
Abstract

We establish the physics and understanding of nonlocal nanoscale wave propagation in carbon nanotubes (CNTs) based on nonlocal elastic stress field theory. This is done by developing an analytical nonlocal nanotube model based on the variational principle for wave propagation in CNTs. Specifically, we successfully derive benchmark governing equations of motion for analyzing wave propagation based on an analytical nonlocal shear deformable model. The physical insights of the analytical nonlocal stress model are presented through examples. Analytical solutions with significant observation of wave propagation have been predicted and the prediction compares favorably with molecular dynamic simulations. Qualitative comparisons with other non-nonlocal approaches, including the strain gradients model, the couple stress model and experiments, justify the stiffness enhancement conclusion as predicted by the new nonlocal stress model. New dispersion and spectrum relations derived using this analytical nonlocal model bring an important focus onto the critical wavenumber: stiffness of CNTs and wave propagation are enhanced below the critical wavenumber, while beyond that a sharp decrease in wave propagation is observed. The physics of nanoscale wave propagation in nanotubes are further illustrated by relating the nanoscale and the phase velocity ratio.

Keywords
critical wavenumber, nanotube, nonlocal elasticity, wave propagation
Milestones
Received: 17 July 2009
Revised: 24 November 2009
Accepted: 24 November 2009
Published: 15 October 2010
Authors
C. W. Lim
Department of Building and Construction
City University of Hong Kong
Tat Chee Avenue
Kowloon
Hong Kong
Y. Yang
Department of Building and Construction
City University of Hong Kong
Tat Chee Avenue
Kowloon
Hong Kong