Magnetoelastic Instability of a Long Graphene Nano-Ribbon Carrying Electric Current (Advances in Applied Mathematics and Mechanics, 2014)
This paper aims at investigating the resonance frequencies and stability of a longGraphene Nano-Ribbon (GNR) carrying electric current. The governing equation ofmotion is obtained based on the Euler-Bernoulli beam model along with Hamilton'sprinciple. The transverse force distribution on the GNR due to the interaction ofthe electric current with its own magnetic field is determined by the Biot-Savartand Lorentz force laws.Using Galerkin's method, the governing equation is solved and the effect of currentstrength and dimensions of the GNR on the stability and resonance frequencies are investigated.