This article is dedicated to predict the vibrational behavior of composite coupled conical-conical shell structures. The structural material is composed of two phases, including polymer epoxy matrix and Carbon NanoTube (CNT) fibers. To improve the vibrational structural behavior, the distributions of CNTs throughout the thickness of shells are assumed to be Functionally Graded. In order to enhance the research, five different patterns are considered for distribution of the CNT fibers within the matrix. The governing equations of motion associated with conical shells are obtained by using Donnell\\\'s theory and Hamilton method. In addition, the five-parameter shell theory is utilized in this article. As a result, five differential equations are achieved by using variation calculation. To solve the system of differential equations, an efficient and modified Generalized Differential Quadrature Method (GDQM) is employed. All the natural frequencies of shell structures are found for different states. By considering continuity conditions, the required modification is applied to GDQM. To validate the proposed formulation, some well-known benchmarks are solved. Moreover, several numerical examples and parametric studies are implemented to show the high accuracy and capability of the authors\\\' scheme for analyzing coupled shells. To obtain accurate responses, 15 grid points are required for using in GDQM. Besides, it is observed that the minimum and maximum dimensionless frequency parameters are obtained by the patterns and , respectively.

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