Stability and nonplanar buckling analysis of a current-carrying mircowire in three-dimensional magnetic field

Abstract

This paper investigates the stability and nonplanar buckling of a current-carrying microwire immersed in a three-dimensional (3D) magnetic field based on modified coupled stress theory and Euler–Bernoulli beam assumptions. Utilizing Hamilton’s principle, the partial differential governing equations for 3D vibrations of the current-carrying microwire are derived. These governing equations are then discretized via the Galerkin’s approach and solved by a fourth-order Runge–Kutta method. Numerical results show that the slenderness ratio and magnetic field have obvious effect on the stability of the microwire. When the applied magnetic field is along the axial direction of the undeformed microwire, the shape of the postbuckling configuration of the microwire is very sensitive to initial conditions employed. If, however, the magnetic field is deviated from the axial direction of the undeformed microwire, it is interesting that the shape of the postbuckling configuration is independent of initial conditions even if the y- and/or z-component of the 3D magnetic field strength is sufficiently small. Another attractive feature of the results is that the lateral deflection of the microwire can be adjusted by changing the magnetic field strength in each direction, which may have potential application to the microelectromechanical systems (MEMS). Finally, the influence of a 3D magnetic field on the axial displacement of the microwire is analyzed, and it is demonstrated that in practice the axial motion of the microwire may be considered negligible.