Vibrational and stability analysis of membrane-like current-carrying nanowires under action of longitudinal magnetic fields
Department of Civil Engineering, K.N. Toosi University of Technology, P.O. Box 15875-4416, Valiasr Ave., Tehran, Iran
Accepted: 2 June 2020
Published online: 14 July 2020
The dynamical behavior of a set of nanowires carrying electric current under action of a longitudinally applied magnetic field using the cable model is of our concern. To obtain the nanosystem’s governing equations, we use the Gurtin–Murdoch surface elasticity theory, and by applying the Lorentz formula and the Biot–Savart law, the total Lorentzian force applied on each nanowire from the existing nanosystem and longitudinal magnetic field is appropriately evaluated. Then, using the Galerkin method based on the assumed modes method, we solve the obtained equations of motion for the transverse frequencies. We also calculate the exact vibration modes using the analytical method. The concepts of synchronous and asynchronous vibrational modes are presented, and the validity of the Galerkin method based on the assumed modes is displayed by comparison with the exact approach. Finally, the influences of important parameters such as electric current intensity, magnetic field strength, interwire distance, surface effect, and population of the nanosystem on the free vibration response and the stability of the nanosystem are discussed.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020