Re-examination of nonlinear vibration, nonlinear bending and thermal postbuckling of porous sandwich beams reinforced by graphene platelets

Abstract

This paper re-examines the nonlinear free vibration, nonlinear bending and thermal postbuckling behaviors of porous sandwich beams with graphene platelets (GPL) reinforcements rested on elastic foundations. We remove the equivalent isotropic model (EIM) and introduce an inhomogeneous model. The shear modulus together with the Young’s moduli for porous GPLRC core is determined by a generic Halpin–Tsai model with porosity. Mechanical properties of both porous GPLRC core and metal face sheets are temperature dependent. Based on the framework of higher order shear deformation beam theory, the motion equations of porous sandwich beams with GPL reinforcements are established. In the modeling, the von Kármán kinematic nonlinearity, beam-foundation interaction and thermal effect are considered. By employing the two-step perturbation method, the analytical solutions are obtained for the nonlinear vibration and nonlinear bending as well as thermal postbuckling problems. Numerical investigations are performed for comparing the results obtained from the EIM and the present model. The outcomes reveal that the EIM is invalid for linear free vibration, thermal buckling and postbuckling analyses of porous sandwich beams with GPL reinforcements, but the EIM is valid in some cases for nonlinear bending and nonlinear vibration analyses of the same beam.