Isogeometric nonlinear free vibration analysis of FG-GRC laminated Timoshenko beams with temperature-dependent material properties

This paper deals with the nonlinear vibration analysis of laminated composite beams with the graphene sheet as reinforcement in each layer. The volume fraction of graphene sheets in each lamina may be different which leads to a functionally graded (FG) structure. The elastic moduli of each layer are captured based on the modified Halpin-Tsai approach. It is assumed that the elastic moduli and thermal expansion coefficients of the reinforcement and the matrix are temperature dependent. The total potential energy of the beam is established according to the Timoshenko beam theory (TBT) and von Kármán type of geometrical nonlinearity assumptions. Then, the isogeometric approach (IGA) is constructed to represent the matrix form of the governing equations. The developed procedure is used to obtain linear and nonlinear behaviors of graphene reinforced composite (GRC) beams through several numerical examples. The effects of temperature elevation, graded distribution of graphene sheets, lay-up arrangement, aspect ratio and boundary condition on the nonlinear vibration response of functionally graded graphene reinforced composite (FG-GRC) laminated beams. It is shown that as the temperature raises, the nonlinear-to-linear fundamental frequency ratio increases.