Vibrations and instability of double-nanowire-systems as electric current carriers

Abstract

Current-carrying nanowires are expected to be building blocks of the upcoming micro-nano-electromechanical devices, however, little is known on their dynamic interactions in a bundle. As a pivotal step towards realizing such a crucial mechanism, this work is devoted to vibrations and instability of a double-nanowire-system as an electric current carrier. Using Biot–Savart law, the Lorentz interactional forces between doubly parallel current-carrying nanowires are evaluated. Accounting for the surface elastic energy, equations of motion pertinent to the in-plane and out-of-plane vibrations are established. Using analytical techniques, the explicit expressions of both static and purely dynamic parts of the nanowires’ displacements are obtained. For each component of the transverse displacement field, two major vibration modes are observed: in-phase and out-of-phase modes. The frequencies associated with these vibration modes are analytically calculated. Further, the condition corresponds to the dynamic instability of the system is discovered, and the roles of initial tensile force, electric current, and interwire distance on frequencies and stability of the system are addressed.