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.
Highlights
The graphene-based resonator and its application to mass sensing based on nonlinear waves have been poorly studied numerically [1]
Some researchers use discrete atomic or Monte Carlo approach for numerical simulation and some use local or nonlocal continuum mechanics approaches, their models are based on linear material constitutive equation for graphene ([1] [2])
Well-known that graphene behaves nonlinearly even for small strains and there is no obvious yield point or a linear portion on it’s stress-strain curve. It is proved experimentally and theoretically in [3] that the mechanical behaviour of a single layer of graphene sheet can be accuartely modeled by a continuum nonlinear constitutive equation ([4]-[6])
Summary
The graphene-based resonator and its application to mass sensing based on nonlinear waves have been poorly studied numerically [1]. Some researchers use discrete atomic or Monte Carlo approach for numerical simulation and some use local or nonlocal continuum mechanics approaches, their models are based on linear material constitutive equation for graphene ([1] [2]) It is, well-known that graphene behaves nonlinearly even for small strains and there is no obvious yield point or a linear portion on it’s stress-strain curve. Well-known that graphene behaves nonlinearly even for small strains and there is no obvious yield point or a linear portion on it’s stress-strain curve It is proved experimentally and theoretically in [3] that the mechanical behaviour of a single layer of graphene sheet can be accuartely modeled by a continuum nonlinear constitutive equation ([4]-[6]).
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