Dynamics and instability of current-carrying microbeams in a longitudinal magnetic field

• A size-dependent model is developed for dynamic analysis of current-carrying microbeams in a longitudinal magnetic field.
• The material length scale parameter tends to enhance the stability of the microbeams.
• The mode shapes of the microbeam are generally 3-D spatial due to the presence of Lorentz forces.
• Buckling instability in higher-order modes is found to be possible.

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.

The dynamics and instability of current-carrying microbeams in a longitudinal magnetic field are remarkably affected by the material length scale (α) and magnetic field parameters (β).Figure optionsDownload as PowerPoint slide