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Research Paper

Vibration of a Multilayered Graphene Sheet With Initial Stress

[+] Author and Article Information
Lifeng Wang

MOE Key Laboratory of Mechanics and Control for Aerospace Structures and College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China; Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kongwalfe@nuaa.edu.cn

Xiaoqiao He

Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

J. Nanotechnol. Eng. Med 1(4), 041004 (Oct 21, 2010) (5 pages) doi:10.1115/1.4002402 History: Received July 28, 2010; Revised August 07, 2010; Published October 21, 2010; Online October 21, 2010

This paper reports an investigation on the vibration of an individual multilayered graphene sheet with initial stress, based on an elastic plate model and membrane model with simply supported ends, considering the van der Waals force interaction between all layers of graphene sheets. The effect of initial stress is more obviously with an increase of half wave numbers m and n. This investigation indicates that the stiffness D, effected by thickness choose, plays a dominant role in the lowest natural frequencies, and much weaker role in high order natural frequencies. The influence of the stiffness is more significant for all natural frequencies with an increase of half wave numbers m and n. The lowest natural frequency of a multilayered graphene sheet for a given combination of m and n is independent of the van der Waals interaction but all of the other higher natural frequencies are significantly dependent on this interaction.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Natural frequencies of a double-layered square graphene with different widths when T=1 GPa, m=1, and n=1

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Figure 2

Natural frequencies of a double-layered square grapheme with different orders of mode n when T=1 GPa, a=b=10 nm, and m=1

Grahic Jump Location
Figure 3

Natural frequencies of a double-layered graphene with different initial stresses when a=10 nm, b=10 nm, m=1, and n=1: (a) fundamental natural frequencies and (b) natural frequencies

Grahic Jump Location
Figure 4

Natural frequencies of an eight-layered graphene sheet with different orders of mode fi: (a) a=10 nm, b=10 nm, m=1, and n=1 and (b) a=10 nm, b=10 nm, m=5, and n=5

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