Effects of nonlinear temperature field on the free vibration of functionally graded graphene platelet-reinforced porous plates

Functionally graded graphene platelet-reinforced (FG-GPL) porous materials exhibit superior properties, including low density, high stiffness-to-weight ratios, and enhanced thermal conductivity properties, making them the most promising candidates for aerospace, automotive, biomedical, and electronic applications. Thermal environments have a significant influence on the vibration characteristics of FG-GPL porous structures, yet they remain insufficiently studied. This study investigated the thermo-mechanical vibration of FG-GPL porous plates in nonlinear temperature fields using a novel semi-analytical approach combining the Galerkin strip distributed method and transfer function method (GSDTFM). Firstly, an FG-GPL porous rectangular plate model incorporating three porosity distributions and GPL dispersion patterns through the thickness direction was developed based on the closed-cell Gaussian random field scheme, Halpin–Tsai micromechanics model, and rule of mixture. Secondly, the thermal vibration governing equations were derived via Kirchhoff plate theory and Hamilton’s principle. Then, the equations are solved using the GSDTFM. After validating the accuracy of the model, parameter studies of the nonlinear temperature field on thermally induced forces and natural frequencies were carried out. Further, a comparative analysis was conducted to investigate the influence of porosity coefficient and graphene weight fraction on natural frequencies under both ambient temperature conditions and nonlinear temperature fields. Key findings revealed that the spatial configuration of temperature fields is predominantly dictated by the porosity distribution; temperature elevation not only ‌amplifies porosity coefficient-dependent frequency tendencies (typically by 17.5%) but also attenuates the growth rate (typically by 17.5%) of frequency-graphene weight fraction curves.