This paper is dedicated to study the vibrational behavior of Coupled Hemispherical-Conical-Conical Shells (CHCCS) structures made composite materials reinforced with nanofillers. One of the most important issue in nanocomposites is the agglomeration effect of nanofillers in hybridization procedure. In this study, two well-known nanofillers including Carbon Nano Tubes (CNTs) and Graphene Nano Platelets (GNPs) are used for reinforcement of polymer matrix. In addition, the distribution of agglomerated nanofillers throughout the thickness of the structures is assumed to be uniform and functional. Therefore, three patterns of distribution including X, O and V are employed. To study these topics, first, the authors obtain the displacement fields of CHCCS using Donnell\\\\\\\\\\\\\\\'s shell theory. In this formulation, the First Order Shear Deformation Theory (FOSDT) is utilized to consider the shear deformation effect. Second, the Hamilton\\\\\\\\\\\\\\\'s principle is used for achieving the governing equations of motion associated with the CHCCS structure. Afterwards, an efficient and robust approximation numerical solution method, namely Generalized Differential Quadrature (GDQ) method, is employed to discretize the governing system of differential equations, apply boundary and connective conditions related to the CHCCS. Since there is no applicable benchmark for this analysis, the authors prove their proposed formulation by comparing the obtained results with the outputs of FEM program for some specific problems. Furthermore, several new and complex problems are designed and solved to investigate the effect of various factors such as geometrical characteristics, weight proportions, and distribution patterns of CNTs and GNPs on the vibration parameter of CHCCS. It is worth mentioning that the effect of agglomeration parameters associated with these nanofillers on the vibrational behavior of CHCCS structures is also studied numerically.

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