Nonlinear primary resonance behavior of graphene platelet-reinforced metal foams conical shells under axial motion

Investigated in this paper is the nonlinear forced vibration response of axially moving graphene platelet-reinforced metal foams (GPLRMF) conical shells. According to Reddy's high-order shear deformation theory and von Karman's geometric nonlinearity, the governing equations with highly nonlinear terms for the GPLRMF conical shells are obtained and discretized by Galerkin principle. Subsequently, considering the simply supported boundary condition, the multiple scale method is employed to determine the amplitude-frequency response curves of GPLRMF conical shells. Numerical analyses are performed to verify the correctness of present method. In the end, the effects of porosity distribution form, graphene platelets (GPLs) distribution pattern, damping coefficient, porosity coefficient, coning angle, GPLs weight fraction, geometrical dimensions and the position of the external load, axially moving velocity as well as pre-stressing force on the nonlinear-forced vibration response curves of the GPLRMF conical shells are presented.