Dynamics and instability of current-carrying microbeams in a longitudinal magnetic field |
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| Affiliation: | 1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China;2. Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China;1. School of Materials Science and Engineering, Shandong Jianzhu University, Jinan 250101, PR China;2. Beijing Aeronautical Manufacturing Technology Research Institute, Beijing 100024, PR China;1. Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA;2. School of Basic Sciences, Indian Institute of Technology, Bhubaneswar 751007, India;1. Department of Nanomaterial Engineering, Tarbiat Modares University, Tehran, Iran;2. Department of Electrical Engineering, Tarbiat Modares University, Tehran, Iran |
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| Abstract: | 
The dynamics and instability of current-carrying slender microbeams immersed in a longitudinal magnetic field is investigated by considering the material length scale effect of the microbeam. On the basis of modified couple stress theory, a theoretical model considering the effect of Lorentz forces is developed to analyze the free vibration and possible instability of the microbeam. Using the differential quadrature method, the governing equations of motion are solved and the lowest three natural frequencies are determined. The obtained results reveal that the electric current and the longitudinal magnetic field tend to reduce the microbeam's flexural stiffness. It is therefore shown that the lowest natural frequencies would decrease with increasing magnetic field parameter. The mode shapes of the microbeam are found to be generally three-dimensional spatial in the presence of the longitudinal magnetic field. It is interesting that buckling instability would concurrently occur in the first mode or in the higher-order modes when the magnetic field parameter becomes sufficiently large. |
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| Keywords: | Current-carrying microbeam Vibration Instability Magnetic field Modified couple stress theory Size effect |
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