Int. J. of Nanomanufacturing   »   2014 Vol.10, No.5/6

 

 

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

 

Int. J. of Nanomanufacturing, 2014 Vol.10, No.5/6, pp.415 - 423

 

Available online: 11 Dec 2014

 

 

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