Vibration of Single-Walled Carbon Nanotubes by Using Nonlocal Theory

Jozef Bocko^1, and Pavol Lengvarský¹

¹Department of Applied Mechanics and Mechanical Engineering, Technical University of Košice, Faculty of Mechanical Engineering, Košice, Slovakia

Cite this paper:
Jozef Bocko and Pavol Lengvarský. Vibration of Single-Walled Carbon Nanotubes by Using Nonlocal Theory. American Journal of Mechanical Engineering. 2014; 2(7):195-198. doi: 10.12691/ajme-2-7-5

Abstract

The free bending vibration of single-walled carbon nanotubes (SWCNTs) is investigated in the present paper. A continuum approach based on nonlocal theory of beam bending is used for natural frequency computation. Analytical solutions of frequency equations are given for four types boundary conditions: clamped-free (C-F), simply-simply supported (S-S), clamped-simply supported (C-S) and clamped-clamped (C-C). The graphical representations of numerical results are shown for the first case of boundary conditions clamped end - free end.

Keywords:
single-walled carbon nanotube vibration beam nonlocal theory free vibration

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