Dynamic and instability analyses of FG graphene-reinforced sandwich deep curved nanobeams with viscoelastic core under magnetic field effect

Abstract

Based on the nonlocal strain gradient theory, the effect of an axial magnetic field on the free vibration and mechanical buckling responses of an FG graphene-reinforced sandwich deep curved nanobeam with viscoelastic core embedded in a viscoelastic medium is elucidated in this paper. The curved beam is also assumed to be exposed to axial external compressions. The volume fraction of the constituents of the composite face layers are presumed to be functionally graded through the thickness according to a layer-wise law. The material properties are calculated in the framework of Halpin-Tsai micromechanical scheme. Lorentz magnetic force is deduced employing electro-dynamic Maxwell's relations for a conducting body. According to a refined shear and normal deformations curved beam theory, the motion equations are introduced in the polar coordinates. Analytical solutions are obtained for the natural frequencies and critical buckling load of the viscoelastic sandwich curved nanobeams. By comparing the present results with the available data in the literature, the developed formulations are validated. Furthermore, other several numerical examples are performed to show the effects of different parameters including viscoelastic core thickness, magnetic field, structural and foundation damping factor, opening angle and graphene concentration on the frequency and buckling load of the viscoelastic sandwich curved beams.