Nonlinear static and dynamic responses of graphene platelets reinforced composite beam with dielectric permittivity

Nonlinear bending and forced vibration of graphene platelets (GPLs) reinforced composite (GPLRC) beam with dielectric permittivity are investigated. The tensile modulus and dielectric permittivity as required for structural analysis are obtained by using effective-medium theory (EMT) while Poisson's ratio and mass density are evaluated by rule of mixture. Based on Timoshenko beam theory, governing equations for nonlinear bending and forced vibration of the GPLRC beam are established and numerically solved through differential quadrature method (DQM). The dependency of the structural behaviours of the GPLRC beams on the attributes of GPL, applied external loading and electrical field are comprehensively studied. The analysis demonstrates that the performances of the GPLRC beam can be designed and actively tuned through adjusting several parameters. The bending and vibration behaviours of the beam are sensitive to smaller beam thickness, larger GPL aspect ratio and electrical voltage. Snap-through behaviour is observed for the bending and vibration of the composite beam within the involved AC frequency range. Reasons underlying the above observations are analysed and discussed to increasingly understand the structural behaviours of graphene reinforced composite structures with dielectric property.