A Lumped-Parameter Model for Nonlinear Waves in Graphene

Abstract

A lumped-parameter nonlinear spring-mass model which takes into account the third-order elastic sti ness constant is considered for modeling the free and forced axial vibrations of a graphene sheet with onexed 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 elastic constants, there exist bounded periodic solutions which are nonsinusoidal, 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 calculated analytically and numerically. Energy sweep is also performed for resonance applications.