This investigation aims to determine the frequency responses associated with three-phase nanocomposite polymer-Graphene Oxide Powder (GOP)-carbon fiber spheroid and ellipsoid doubly-curved shells. In detail, the GOP nano-material is engaged to increase polymeric matrix mechanical features and form Crossbreed Matrix (CM) as well. For this reason, the rule of the mixture and the Halpin-Tsai schemes are recruited to pick up mechanical features associated with CM material. Next, carbon fibers are used to enhance mechanical criteria CM material and produce three-phase material as well. Accordingly, the Halpin-Tsai homogenization scheme is devoted to finding mechanical criteria connected to three-phase material. Afterwards, the equations of motion linked to spheroid and ellipsoid shells are mined hiring Hamilton's principle. Then, the compelling method named Generalized Differential Quadrature (GDQ) strategy is allocated to gap the basic motion equations associated with mentioned shells. At next, the standard eigenvalue computation is allocated to extract frequency responses related to the shells. To verify the offered procedure, one example is premeditated and compared with FEM commercial software. At last, various issues are arranged to excavate the trace of material mechanical and geometrical features related to the three-phase nanocomposite spheroid and ellipsoid doubly curved shells.