Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses

The vibration response of a functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beam under two successive moving masses is investigated in the current study. The weight fraction of graphene nanoplatelets (GPLs) is assumed to vary continuously and smoothly in the thickness direction. The modified Halpin-Tsai micromechanics model is used to evaluate the effective Young's modulus of the FG-GPLRC beam. A new high order shear deformation theory (HSDT) is proposed for the structural behavior analysis of FG-GPLRC beams. The proposed theory assumes nonlinear distribution of transverse shear stresses and satisfies the traction-free boundary conditions at the bottom and top surfaces of the beam and hence, a shear correction factor is not required. A generalized closed-form solution methodology of the Navier-type is implemented to ensure the validity and efficiency of the present theory for the free vibration and dynamic response of the beam. The Newmark-beta method is adopted to obtain the response of the tube in time domain. Two successive moving masses are considered as the moving load acting on the beam. A parametric study is performed to investigate the effects of GPL weight fraction, distribution pattern, and distance between the two masses on the vibration responses of the beam.