Journal
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
Volume 53, Issue 9, Pages 786-792Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijmecsci.2011.06.010
Keywords
Carbon nanotube; Nonlocal elasticity continuum; Free vibrations; Rayleigh-Ritz method; Molecular dynamics simulation
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In the present study, the free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. Eringen's nonlocal elasticity equations are incorporated into the classical Donnell shell theory accounting for small scale effects. The Rayleigh-Ritz technique is applied to consider different sets of boundary conditions. The displacements are represented as functions of polynomial series to implement the Rayleigh-Ritz method to the governing differential equations of nonlocal shell model and obtain the natural frequencies of DWCNTs relevant to different values of nonlocal parameter and aspect ratio. To extract the proper values of nonlocal parameter, molecular dynamics (MD) simulations are employed for various armchair and zigzag DWCNTs, the results of which are matched with those of nonlocal continuum model through a nonlinear least square fitting procedure. It is found that the present nonlocal elastic shell model with its appropriate values of nonlocal parameter has the capability to predict the free vibration behavior of DWCNTs, which is comparable with the results of MD simulations. (C) 2011 Elsevier Ltd. All rights reserved.
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