The vibration behavior of porous nano-composite Assembled Paraboloidal-Cylindrical Shell (APCS) structures is evaluated in the present study. In detail, Graphene Oxide Powder (GOP) nanomaterials are served to improve the mechanical features correlated with porous polymer and metal matrices in order to build a Hybrid Polymer Matrix (HPM) and Hybrid Metal Matrix (HMM). For this purpose, the Halpin-Tsai and Rule of Mixture methods are employed to determine the mechanical features associated with the HMM and HPM. In addition, the First Shear Deformation Hypothesis (FSDH) is combined with Hamilton’s principle to determine the governing equations of APCSs, which are then discretized and solved according to the Generalized Differential Quadrature (GDQ) approach. Next, the eigenvalue strategy is implemented to determine the frequency responses of porous nanocomposite APCS structures, whose results are successfully compared to predictions from classical finite elements. Some novel examples are organized and solved to examine the impact of the geometrical and mechanical characteristics on the natural frequencies of porous nanocomposite APCS structures. As beneficial results: FGX and FGO distributions of GOPs throughout the thickness direction for porous HMM and HPM nanocomposite APCS yield the highest and lowest values related to the minimum frequency regarding Csingle bondC BC, while these values were determined to couple with the FGV and FGA related to the C-F and F-C BCs. An increased porosity level reduced the overall stiffness of the APCS and frequency response. Subsequently, frequencies related to a non-porous HPM nanocomposite APCS were significantly higher than those from porous nanocomposite APCS. The model of the porosity and values related to the porosity models did not cause to change in the CWN that the minimum frequency happened in.

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