This study is dedicated to propose a numerical solution for free vibration analysis of nanocomposite conical shells. The First-order Shear Deformation Theory (FSDT) is used to achieve the governing equations. Then, an efficient numerical method, namely the Generalized Differential Quadrature Method (GDQM), is employed to solve the Donnell-type governing differential equations. The effects of the nanofillers aggregation are investigated throughout this research. It is considered that a single conical shell is composed of a variety of the constituent material. This type of material includes three phases: polymer matrix, macro-scale fibers and nano-scale Carbon Nano Tubes (CNTs). Two well-known approaches, namely Han and Chamis, are employed for the homogenization procedure to obtain the equivalent material properties. It is worth mentioning that the power pattern is employed for the functionally distribution of CNTs within the polymer matrix. Furthermore, the effects of different boundary conditions, geometric and material properties on the dimensionless frequency parameter of the multiscale nanocomposite conical shells are considered. Afterward, a parametric study is implemented to determine the deep influences of the volume fraction of the nanofillers throughout the inclusion on the vibrational behaviors of conical shells. It is found out that increasing the agglomeration parameter increases the frequency parameter of the conical structures. Moreover, increasing the power exponent of the volume fraction of FG-CNT material deals decrease of the frequency parameter of conical shells. Comparing the obtained results with the outputs of some well-known benchmarks proves the correctness, accuracy and high capability of the proposed formulation.

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