Vol. 7, No. 2, 2012

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Size-dependent free vibration analysis of infinite nanotubes using elasticity theory

Jafar Eskandari Jam, Yaser Mirzaei, Behnam Gheshlaghi and Reza Avazmohammadi

Vol. 7 (2012), No. 2, 137–144

Exact elasticity theory is employed to study the (two-dimensional) free vibration of nanoscale cylindrical tubes in the presence of free surface energy. Use is made of the Gurtin–Murdoch surface elasticity model to incorporate the surface stress terms into the pertinent boundary conditions. Some numerical examples are provided to depict the influence of the surface energy, and particularly the inner radius size of the nanocylinder, on the natural frequencies of the system. The results indicate a stronger influence of surface effects for both smaller values of the outer to inner radius ratio and higher modes of vibration.

free surface energy, free vibration, nanotube, elasticity solution
Received: 28 March 2011
Revised: 8 August 2011
Accepted: 19 August 2011
Published: 6 May 2012
Jafar Eskandari Jam
Composite Material and Technology Center
Yaser Mirzaei
Department of Mechanical Engineering
Damavand Branch
Islamic Azad University
Behnam Gheshlaghi
Young Researchers Club
Science and Research Branch
Islamic Azad University
Reza Avazmohammadi
Department of Mechanical Engineering and Applied Mechanics
University of Pennsylvania
220 S 33rd St.
Philadelphia, PA 19104-6315
United States