In-plane magnetic field affected transverse vibration of embedded single-layer graphene sheets using equivalent nonlocal elasticity approach

The behaviour of graphene in a magnetic field has attracted considerable attention among the scientific community. In this paper, the effect of an in-plane magnetic field on the transverse vibration of a magnetically sensitive single-layer graphene sheet (SLGS) is examined using equivalent continuum nonlocal elastic plate theory. The SLGS is considered to be embedded in an elastic medium. Governing equations for nonlocal transverse vibration of the SLGS under an in-plane magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell’s relation. Numerical results from the model show that the in-plane magnetic field exerted on the SLGS increases the natural frequencies of the SLGS. This is in line with some reported results in the literature where macroscopic plates under an in-plane magnetic field are considered. Further, the nonlocal effects decrease the natural frequencies of the SLGS. The effects of the in-plane magnetic field on higher natural frequencies and different aspect ratios of SLGS are also presented.