Effects of magnetic field on size sensitivity of nonlinear vibration of embedded nanobeams

The influence of magnetic field on size sensitivity of nonlinear vibration of embedded nanobeams is studied based on von Karman geometric nonlinearity and nonlocal Timoshenko beam theory. Adopting Hamilton's principle, governing equations for nonlinear vibration of nanobeams are derived and then solved by using Differential Quadrature method to obtain nonlinear responses under different boundary conditions. The results reveal that high magnetic flux restrains nonlinear vibration of nanobeams. At higher magnetic flux, the nonlocal effect could be ignored. For soft foundation, nonlinear vibration of embedded nanobeams is independent on its stiffness variation, and the increase of magnetic flux broadens this range.