Abstract:
A 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.