RETRACTED: Meshfree vibrational scrutiny of arbitrary placed straight triple-wire-nanosystems carrying direct electric currents using surface elasticity theory

Abstract

This paper displays the potential instability as well as both lateral and transverse vibrations of triple-nanowire-systems carrying electrical current by utilizing the surface elasticity theory of Gurtin and Murdoch. Through implementing Euler–Bernoulli and Timoshenko beam theories, the surface energy-based equations of motion are developed accounting for both inertial and strain energy of the surface layer. These are, respectively, six and twelve coupled equations due to existing interwire Lorentz forces. By exploiting the Galerkin approach on the basis of an efficient meshless approach, the governing equations are reduced to appropriately coupled ordinary differential equations and then the natural frequencies are evaluated. The roles of important factors, including surface energy, shear deformation, interwire distance, electric current, radius, length, and position of nanowires on the dominant frequencies are discussed and explained.