In the current research, a comprehensive frequency analysis is performed for the circular sandwich plates in the pre-and post-buckling ranges occurred because of an in-plane thermal field. A sandwich system is fabricated with an open-cell foam (OCF) core and laminated composite face sheets reinforced with graphene platelets based on the functionally graded models (FG-GPLRC). The displacement field is counted using Reddy’s third-order shear deformation theory because the thick layers form the desired circular structure. Due to large deformations in the post-buckling situation, the geometrically nonlinear strain–displacement relations based on the von Kármán model are employed. The Chebyshev collocation solution is implemented to attain the discrete form of equilibrium and dynamic equations. A displacement control iterative procedure is also adopted to address the nonlinear equilibrium state of the system. Moreover, the adjacent-equilibrium criterion is considered to recognize the static paths from small-amplitude vibrations. After performing validation studies with available articles, novel results are displayed to verify the influence of geometrical and physical characteristics on the post-buckling path and fundamental natural frequency of circular sandwich plates. •A comprehensive frequency analysis is performed for the circular sandwich plates.•The pre-and post-buckling ranges induced by in-plane thermal field are assumed.•The structure is fabricated with open-cell foam core and nanocomposite face sheets.•Due to large deformations in post-buckling, the nonlinear strain-relations are considered.•The Chebyshev collocation solution is implemented to solution.