Nonlinear vibration of thermally postbuckled FG-GRC laminated beams resting on elastic foundations

Investigated herein are the small- and large-amplitude vibrations of a thermally postbuckled graphene-reinforced composite (GRC) laminated beam supported by an elastic foundation. The piecewise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the beam. The temperature-dependent material properties of functionally graded graphene-reinforced composites (FG-GRCs) are estimated through the extended Halpin-Tsai micromechanical model. The nonlinear governing differential equations are derived from the higher-order shear deformation beam theory and the von Kármán-type strain-displacement relationships. The thermal effect, the beam-foundation interaction and the initial deflection caused by thermal postbuckling are also included. A two-step perturbation approach is applied to determine the thermal postbuckling equilibrium paths as well as the nonlinear vibration solutions for the FG-GRC laminated beams. Results are presented to demonstrate the nonlinear vibration responses of thermally postbuckled FG-GRC laminated beams under a uniform temperature field. The effects of the FG reinforcement patterns and the foundation stiffness on the nonlinear vibration responses of FG-GRC laminated beams are examined and discussed.