One of the applicable shell structures related to underwater systems, covering riser pipes, ice-breaking equipment, underwear noise migrations, ballast water components, and gliders, can be considered Linked Hemispherical-Conical Shell (LHCS) structures. Accordingly, the ensuing investigation is provided to compute the Natural Frequency Values (NFVs) of the LHCS, with the opening angle at starting part of the hemispherical structure (which will be studied for the first time) enhanced by graphene-based nanocomposite materials containing Graphene Nano-Platelet (GNP) and Graphene Oxide-Powder (GOP) nanocomposites. For this reason, the Halpin-Tsai approach and the rule of the mixture are engrossed in determining the productive functionally graded mechanical criteria of the graphene-based nanocomposite materials. To obtain the main formulations of the LHCS, Donnell\\\'s assumptions and First-Order Shear Deformation Theory (FOSDT) are also engaged. Additionally, Hamilton\\\'s technique is involved in finding the kinetic equations coupled with the hemispherical and the conical parts of the LHCS. Next, the distinguished approach, Generalized Differential Quadrature (GDQ) program, is applied to discrete the kinetic equations. Subsequently, the standard eigenvalue problem determines the NFVs related to the GNP and GOP nanocomposites LHCSs. At termination, the exactness of the suggested scheme is confirmed by comparing the provided outputs with the NFVs of the submitted work (which can be used as the benchmark) with responses determined by FEM commercial software and the only benchmark study that exists in the literature. Furthermore, some novel cases are solved to estimate the effects of different geometric criteria of the LHCS, such as the opening angle of the hemispherical, the Half-Apex (HA) angle of the conical segment, the thickness related to the structure, and also the effect of GNP and GOP scattering models spread in conjunction with the thickness of the LHCS on the NFVs coupled with the GNP and GNP nanocomposites LHCS.

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