Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field

• Free vibrations of a current-carrying nanowire in a magnetic field are studied.
• Coupled equations of motion are obtained accounting for the surface effect.
• The explicit expressions of transverse displacements and frequencies are derived.
• The roles of influential factors on the instability of the nanowire are explained.
• The effects of magnetic field and electric current on elastic fields are discussed.

Free transverse vibration and instability of current-carrying nanowires immersed in a longitudinal magnetic field are of concern. On the basis of the surface elasticity theory, a model is developed to investigate the problem. The analytical expressions of dynamic transverse displacements as well as natural frequencies of the magnetically affected nanowire for carrying electric current are obtained. The influences of the surface effect, initial tensile force within the nanowire, strength of the longitudinal magnetic field, and electric current on the natural frequencies as well as dynamic displacements are examined. The obtained results reveal that the transverse stiffness of the nanostructure is enhanced by the surface effect and the initial tensile force, while electric current or longitudinal magnetic field reduces the nanowire's stiffness. The condition which leads to the dynamic instability of the nanostructure is obtained. Further, the roles of the influential parameters on its stability are inclusively discussed.