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Abstract
In this work, on the basis of a nonlocal elastic plate model, the free vibration of monolayer graphene sheets is studied. An explicit formula for estimating the fundamental frequencies of a monolayer graphene sheet from its static deflection under a uniformly distributed load is obtained. The main advantage of this formula is in its simplicity and accuracy, enabling quick calibration of the nonlocal parameter using molecular dynamics results. The influences of the nonlocality and boundary conditions on the free vibration of monolayer graphene sheets are also investigated.