▎ 摘　　要

It is the first investigation regarding the vibrational responses of nanocomposite conical shells built of graphene oxide powder (GOP) and supported by Winkler and Winkler-Pasternak flexible bases. To back this up, two graded forms and a uniform distribute the GOP along the matrix. Also, the rule of mixture and Halpin-Tsai concepts discover the operative values of the nanocomposite. Addedly, the Winkler and Winkler-Pasternak flexible models simulate the interaction feature between the structure and foundations. Also, Donnell's shell and first-order shear deformation schemes are united to find the essential connections of the nanocomposite structure. By Hamilton's principle, the motion equations regarding the system can be found. Furthermore, the motion equations are discretized by applying the generalized differential quadrature scheme, a meshless method. The usual eigenvalue is used to get the natural frequencies of the structure. Moreover, some novel examples are presented to show the effect of geometrical and material properties, various boundaries, and flexible foundations on the frequencies associated with the structure.