Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load

In this paper, the size-dependent effects on the time-dependent bending and shearing responses of single-layer graphene sheets (SLGSs) induced by displacement of the concentrated moving load along the SLGSs are studied. Hence, the equations of motion are derived by applying two-variable refined plate theory in conjunction with the nonlocal elasticity theory via Hamilton's principle. The two independent unknowns denoting the dynamic behaviour of plates are defined by the developing state-space method for this case, and Navier-solution method is employed to obtain the bending and shearing deflections due to the variation of velocity and time. The primary results for free and forced vibrations of nanoplates are approved by existing literature to illustrate the correctness of the present formulation and solution methods. Next, a solution including both the bending and shearing dynamic deflections of SLGSs under the moving load is derived for the first time in this research. Moreover, the roles of different parameters such as load velocity, length-to-thickness ratio, and small-scale effects on the dynamic deflections of SLGSs are addressed and discussed.