Wei, DongmingHazim, HamadElgindi, MohamedSoukiassian, Yeran2016-02-082016-02-082015Hamad Hazim, Dongming Wei, Mohamed Elgindi, Yeran Soukiassian; 2015; A Lumped-Parameter Model for Nonlinear Waves in Graphenehttp://nur.nu.edu.kz/handle/123456789/1196A lumped-parameter nonlinear spring-mass model which takes into account the third-order elastic sti ness constant is considered for mod- eling the free and forced axial vibrations of a graphene sheet with one xed end and one free end with a mass attached. It 's demonstrated through this simple model that, in free vibration, within certain initial energy level and depending upon its length and the nonlinear elas- tic constants, there exist bounded periodic solutions which are non- sinusoidal, and that for each xed 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 cal- culated analytically and numerically. Energy sweep is also performed for resonance applications.enAttribution-NonCommercial-ShareAlike 3.0 United StatesGrapheneResearch Subject Categories::MATHEMATICSResonanceNonlinear VibrationPhase DiagramFrequency SweepArticle