Title: Energy meaning of small-scale effect on free vibration of carbon nanotubes

Authors: Li Ming; Zheng Huiming; Luo Xia; Liu Yang

Addresses: Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, China; Department of Mechanics, Wuhan University of Science and Technology, Wuhan, Hubei Province 430065, China; Department of Engineering Mechanics, College of Science, The HuangJia Lake Campus of Wuhan University of Science and Technology, Wuhan, Hubei Province 430065, China ' Department of Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei Province 430074, China ' Department of Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei Province 430074, China ' Department of Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei Province 430074, China

Abstract: The energy meaning of small-scale on free vibration of carbon nanotube is investigated in the present study by energy method. The dynamic governing equation is obtained based on non-local Euler-Bernoulli beam model. It is demonstrated that the virtual work from small-scale effect consists of two part energy, one part is rotatory kinetic energy, and the other is the work at the both ends of beam made by the small-scale effect. Furthermore, the discussions show that, though small-scale effect of inertia and van der Waals force is different, both of them contribute to the energy from rotatory angle.

Keywords: energy meaning; small-scale effect; free vibration; carbon nanotubes; CNTs; governing equation; non-local Euler-Bernoulli beam; virtual work; inertia force; van der Wals force; nanomanufacturing; nanotechnology; kinetic energy.

DOI: 10.1504/IJNM.2014.066279

International Journal of Nanomanufacturing, 2014 Vol.10 No.5/6, pp.415 - 423

Received: 14 Jan 2013
Accepted: 29 Sep 2013

Published online: 20 Dec 2014 *

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