This research is organized to carry out the Natural Frequency Factors (NFFs) coupled with the most functional structure employed in the various fields of engineering and one of the essential structures in industries made by assembling Spherical (S), Cylindrical (Cy), and Conical (Co) shells named Assembled Spherical-Cylindrical-Conical Shell (ASCCS). In addition, four new sandwich nanocomposite models, including agglomerated Functionally Graded Carbon Nano-Tubes (FG-CNTs) for Top Face Sheet (TFS) and Bottom Face Sheet (BFS) and Core Layer (CL) with porosity feature, are employed to enhance applications of the ACCCS structure here. The Eshelby-Mori-Tanaka Hypothesis (EMTH) is applied to discover the TFS and BFS mechanical features for this object. The Equivalent Single Layer Technique (ESLT) is also implemented to obtain the mechanical characteristics of the new sandwich nanocomposite. In addition, to discover the effects of Elastic Boundary Conditions (EBCs), the Artificial Spring Scheme (ASS) is engaged in this work. Moreover, The First Share Deformation Theory (FSDT) and Donnell’s Simplifications (DSs) are applied to determine the fundamental relationships of the ASCCS (for each part). Also, Hamilton\\\'s method is used for each element to seek the Governing Motion Equations (GMEs) affiliated with the ASCCS. Next, the GMEs of the structure are discretized by employing the well-structured scheme titled the Generalized Differential Quadrature (GDQ) strategy. Afterward, the NFFs of the ASCCS are found by determining the eigenvalues. Then, the NFFs obtained from the presented method are compared with the NFFs determined by FE-based commercial software. Ultimately, various novel examples are planned and solved to illustrate the effects of the geometrical, material, and the EBCs changes on the NFFs of the ASCCS structure.

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