(untitled) (Advances in Applied Mathematics and Mechanics, 2014)
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.