Dynamic interactions between double current-carrying nanowires immersed in a longitudinal magnetic field: Novel integro-surface energy-based models

Transverse dynamic interactions between double current-carrying nanowires (CCNWs) immersed in a longitudinal magnetic field are of high interest. Using Biot-Savart and Lorentz laws, the approximate and exact magnetic forces exerted on the CCNWs are expressed. By employing Hamilton’s principle, the equations of motion of magnetically affected CCNWs are obtained in the context of the surface elasticity theory of Gurtin-Murdoch. To this end, three approximate models as well as three exact versions of governing equations based on the Rayleigh, Timoshenko, and higher-order beam theories are developed. Via reproducing kernel particle method, the frequencies of the nanosystem are evaluated. With regard to the predicted results by the exact models, the application limits of the approximate models are displayed. Subsequently, the roles of the interwire distance, slenderness ratio, CCNWs’ radius, electric current, and magnetic field strength on the fundamental frequency of the nanosystem are examined. For each of these explorations, the influences of the surface energy and shear deformation on the free dynamic response of the nanosystem are explained and discussed.