Reexamination for linear and nonlinear free vibration of porous sandwich cylindrical shells reinforced by graphene platelets

This paper reexamines the linear and nonlinear free vibration responses of porous sandwich cylindrical shells with graphene platelet (GPL) reinforcements surrounded by an elastic medium under temperature conditions. The graphene platelets reinforced composite (GPLRC) core is assumed to be multilayers, and each layer may have different values of porosity coefficient to achieve a piece-wise functionally graded pattern. By introducing an inhomogeneous model instead of the equivalent isotropic model (EIM), the Young's moduli along with the shear modulus of porous GPLRC core are predicted through a generic Halpin-Tsai model in which the porosity is included. Thermo-mechanical properties of porous GPLRC core and metal face sheets are assumed to be temperature dependent. Motion equations of porous sandwich cylindrical shells reinforced by GPLs are formulated based on the Reddy's third order shear deformation theory. In the modeling, von Karman nonlinear strain-displacement relationships, shell-foundation interaction and thermal effect are also taken into account. The analytical solution for the nonlinear vibration problem is obtained by applying a two-step perturbation approach. Numerical studies are performed to compare the results obtained from the present model and the EIM. The results reveal that, in most cases, the difference of the fundamental frequency between the two models is over 10% and in that case the EIM is not suitable for the linear free vibration analysis of porous sandwich cylindrical shells reinforced by GPLs, whereas for the nonlinear-to-linear frequency ratio curves, the difference between the two models is less than 2% when the non-dimensional vibration amplitude reaches 1.0 and in that case the EIM may be valid in the analysis for the same shell.