A Lumped-Parameter Model for Nonlinear Waves in Graphene
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Date
2015
Authors
Hazim, Hamad
Wei, Dongming
Elgindi, Mohamed B. M.
Soukiassian, Yeran
Journal Title
Journal ISSN
Volume Title
Publisher
World Journal of Engineering and Technology
Abstract
A lumped-parameter nonlinear spring-mass model which takes into account the third-order elastic
stiffness constant is considered for modeling the free and forced axial vibrations of a graphene
sheet with one fixed end and one free end with a mass attached. It is demonstrated through this
simple model that, in free vibration, within certain initial energy level and depending upon its
length and the nonlinear elastic constants, that there exist bounded periodic solutions which are
non-sinusoidal, and that for each fixed energy level, there is a bifurcation point depending upon
material constants, beyond which the periodic solutions disappear. The amplitude, frequency, and
the corresponding wave solutions for both free and forced harmonic vibrations are calculated
analytically and numerically. Energy sweep is also performed for resonance applications
Description
Keywords
Graphene, Resonance, Nonlinear Vibration, Phase Diagram, Frequency Sweep
Citation
Hamad Hazim, Dongming Wei, Mohamed Elgindi, Yeran Soukiassian; 2015; A Lumped-Parameter Model for Nonlinear Waves in Graphene; World Journal of Engineering and Technology; http://nur.nu.edu.kz/handle/123456789/1930