Vol. 13, No. 4, 2018

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Stability and nonplanar postbuckling behavior of current-carrying microwires in a longitudinal magnetic field

Yuanzhuo Hong, Lin Wang and Hu-Liang Dai

Vol. 13 (2018), No. 4, 481–503
Abstract

The stability and nonplanar buckling problem of current-carrying microwires in the presence of longitudinal magnetic field are investigated by accounting for the nonlinearities resulted from the axial elongation of the microwire’s centerline. Based on the Euler–Bernoulli beam theory, modified couple stress theory, and Hamilton’s principle, the nonlinear governing equations of the nonplanar motions of the microwire are derived. By application of Galerkin’s approach, the nonplanar dynamic responses are evaluated for both clamped-clamped and pinned-pinned boundary conditions. The effects of dimensionless material length scale parameter, compressive load, magnetic field force, and slenderness ratio on the nonplanar buckling instability and the postbuckling configuration are discussed in detail. The obtained results show that the nonplanar buckling instability of microwires occurs when the magnetic field force becomes sufficiently large and the postbuckling configuration depends on the magnitude of magnetic field force, slenderness ratio, and initial conditions. The material length scale parameter can stabilize the microwire. Moreover, the stability boundaries for the magnetic field parameter and compressive load are analyzed, showing that an expected critical value of magnetic field parameter may be achieved by choosing a suitable compressive load as a trigger of automatic devices. Interestingly, it is found that the presence of an axial compressive load has no effect on the postbuckling shape, although it can destabilize the microwire system and amplify the postbuckling amplitude.

Keywords
nonplanar postbuckling configuration, microwire carrying electric current, modified couple stress theory, longitudinal magnetic field, buckling instability
Milestones
Received: 22 February 2018
Revised: 24 July 2018
Accepted: 30 July 2018
Published: 13 December 2018
Authors
Yuanzhuo Hong
Department of Mechanics
Huazhong University of Science and Technology
Wuhan
China
Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment
Wuhan
China
Lin Wang
Department of Mechanics
Huazhong University of Science and Technology
Wuhan
China
Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment
Wuhan
China
Hu-Liang Dai
Department of Mechanics
Huazhong University of Science and Technology
Wuhan
China
Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment
Wuhan
China