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Mathematical Problems in Engineering
Volume 2013, Article ID 517695, 9 pages
Research Article

Nonlinear Analysis of Electrically Actuated Carbon Nanotube Resonator Using a Novel Discretization Technique

1Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 31261, Dhahran, Saudi Arabia
2Applied Mechanics and Systems Research Laboratory, Tunisia Polytechnic School, University of Carthage, BP 743, 2078 La Marsa, Tunisia

Received 21 April 2013; Revised 22 August 2013; Accepted 22 August 2013

Academic Editor: Sarp Adali

Copyright © 2013 Hassen M. Ouakad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Static as well as dynamic analyses have been performed on clamped-clamped carbon nanotube (CNT) resonator. The nonlinear CNT model is investigated with a novel discretization technique: a differential quadrature method (DQM) to discretize the spatial variables and a finite difference method (FDM) for limit-cycle solutions. Parametric study is performed by varying the electric load, as well as the initial curvature (due to fabrication). It is found that the pull-in voltage decreases nonlinearly with initial curvature and linearly with residual stresses. The eigenvalue problem is also solved to obtain the bending natural frequencies of the system as function of the DC voltage as well as the initial curvature of the CNT. Frequency-response curves near some selected resonant frequencies are plotted to better understand the nanotubes' dynamic behavior. Different linear and nonlinear phenomena are depicted such as dynamic pull-in, hardening, and softening behavior and veering of the odd modes. We have found that even when exciting the CNT near its first natural frequency, the vibration mode located at the veering process significantly alters the CNT's motion and hence may decrease its overall quality factor.