A Lumped-Parameter Model for Nonlinear Waves in Graphene

DOI: 10.4236/wjet.2015.32006   PDF   HTML   XML   2,723 Downloads   3,329 Views   Citations


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.

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Hazim, H. , Wei, D. , Elgindi, M. and Soukiassian, Y. (2015) A Lumped-Parameter Model for Nonlinear Waves in Graphene. World Journal of Engineering and Technology, 3, 57-69. doi: 10.4236/wjet.2015.32006.

Conflicts of Interest

The authors declare no conflicts of interest.


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