Vibration analysis of quadrilateral graphene sheets subjected to an in-plane magnetic field based on nonlocal elasticity theory

Graphene sheets have wide application, in which the integration of multiple disparate fields for the realization of expanded functionalities is of great significance. This study investigates the vibration behavior of quadrilateral single-layered graphene sheets (SLGSs) in a magnetic field using classic plate theory and incorporating nonlocal elasticity theory, concerning the small scale effect. The element-free kp-Ritz method is employed to perform the numerical simulation. The efficiency of the proposed numerical tool is verified by published results. The effect of nonlocal parameters, skew angles, magnetic parameters and boundary conditions on the vibration behavior of parallelogram SLGSs is studied. The results show that skew angles and the magnetic field help increase the fundamental frequencies of SLGSs, which indicates the potential application of SLGSs as highly sensitive mass detectors. Moreover, 14 different quadrilateral SLGSs, with different nonlocal parameters and magnetic parameters for different boundary conditions, are simulated.