Thermal vibration analysis of functionally graded graphene platelets-reinforced porous beams using the transfer function method

Functionally graded graphene platelets-reinforced (FG-GPL) porous materials are advanced, designable, lightweight, and high-strength composite materials promising in launch vehicles, space shuttles, and hypersonic vehicles as integrated heat-protection and load-bearing structures. Thermal vibration analysis ensures service safety in environments with dynamic thermal loads. A free vibration analysis model of an FG-GPL porous beam was proposed based on the micromechanical model and Timoshenko beam theory (TBT) under a nonlinear temperature profile. First, three types of functionally graded porosity distributions and graphene-platelet dispersion patterns were assumed along the thickness direction of the beam. Material properties, including elastic modulus, Poisson's ratio, and density, were calculated using the Gaussian random field scheme and Halpin-Tsai model. Second, a nonlinear temperature profile was established considering the influence of porosity and graphene platelets by solving a one-dimensional-heat-conduction equation. Third, the governing equations of thermal vibration of the beam were obtained using the TBT and Hamilton's principle. The frequencies of different porosity distributions and graphene-platelet dispersion pattern combinations were calculated by solving the governing equations using the transfer function method. Finally, the results were validated, and the parameter effects of the temperature profiles, weight fraction of graphene platelets, porosity coefficient, and thermal gradient on the fundamental frequencies were analyzed. Compared to a linear temperature profile, the frequency under a nonlinear temperature profile is hardly changed for the combined symmetrically distributed porosity and GPL beams, while it is different for the asymmetric combinations.