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Summary: Nonlinear Oscillations of a Double-Walled Carbon
Nanotube
Muhammad A. Hawwaa
& Hussain M. Al-Qahtanib
Department of Mechanical Engineering
King Fahd University of Petroleum & Minerals
Dhahran 31261, Saudi Arabia
Fax: (+9663) 860 2949
E-mails:
(a) drmafh@kfupm.edu.sa
(b) qahtanih@kfupm.edu.sa
corresponding author
M. A. Hawwa & H. M. Al-Qahtani
Abstract
An elastic continuum approach for modeling the nonlinear vibration of a
double-walled carbon nanotubes under harmonic excitation is presented. The carbon
nanotube is modeled as two doubly clamped beams coupled through nonlinear con-
tinuous springs representing Van der Waal bonds. Geometric nonlinearity is included
due to mid-plane stretching. A Galerkin approach is used to discretize the integro-
partial differential equation leading to two nonlinear coupled second-order ordinary
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