This paper aims at investigating the resonance frequencies and stability of a long
Graphene Nano-Ribbon (GNR) carrying electric current. The governing equation of
motion is obtained based on the Euler-Bernoulli beam model along with Hamilton's
principle. The transverse force distribution on the GNR due to the interaction of
the electric current with its own magnetic field is determined by the Biot-Savart
and Lorentz force laws.
Using Galerkin's method, the governing equation is solved and the effect of current
strength and dimensions of the GNR on the stability and resonance frequencies are investigated.
Graphene nano-ribbon resonance frequency current carrying Hamilton's principle Biot-Savart Lorenz force