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The paper investigates nonlinear dynamic behavior of functionally grade graphene nanoplatelets reinforced (FG-GPLRC) shell with radius as a high-order function using the classical thin shell theory (CTST) and the Von Karman-Donnell geometrical nonlinearity assumption. Different from cylindrical or conical shells, variations of radius are formulated as quadratic or/and cubic functions, generating three types of funnel shells. To verify the computation, the fundamental frequencies are compared with the previous literatures and Finite Element Analysis. The effects of various parameters including geometries, materials, temperature are considered. Obtained results of the shell promisingly make a significant contribution to various fields of engineering. [ABSTRACT FROM AUTHOR]