Stability and vibrations of doubly parallel current-carrying nanowires immersed in a longitudinal magnetic field

This paper deals with dynamic interactions of two parallel nanowires carrying electric currents in the presence of a longitudinal magnetic field. Using Biot-Savart law and a surface elasticity model, the equations of motion are obtained. Accounting for both Lorentz and gravity forces, the static and the purely dynamic parts of the total displacements of the nanosystem are explicitly expressed. Two crucial modes of vibration, synchronous and asynchronous patterns, are identified and their characteristics are inclusively explained. It is shown that the nanosystem becomes dynamically unstable under certain conditions in the asynchronous mode. The minimum initial tensile force as well as the maximum values of the electric current and the magnetic field strength corresponding to the dynamic instability are derived. The roles of the crucial factors on the lowest asynchronous frequencies are also addressed and discussed.