In the present manuscript, the generalized differential quadrature method (GDQM) will be employed in order to solve the free vibration problem of three-phase carbon fiber/nanotube/polymer hybrid nanocomposite conical shells, rested on a two-parameter elastic medium, regarding for the influence of the agglomeration of the carbon nanotubes (CNTs) on the dynamic responses of the shell for the first time. The equivalent material properties of the multi-scale hybrid nanocomposite will be derived according to a two-step homogenization procedure including the Eshelby-Mori-Tanaka method incorporated with the modified form of the rule of the mixture. Afterward, the strain-displacement relationships of the continuous system will be obtained using the classical shell theory for thin-walled conical shells. Extending the Hamilton’s principle for the conical shell, the motion equation of the problem will be enriched. At the end, the associated boundary condition will be used in associated with the GDQ discretization for the purpose of extracting the natural frequency of the continuous system. The verification tests reveal that the presented mathematical framework is powerful enough to estimate the dynamic response of the system. The results of this study show that existence of agglomeration phenomenon can dramatically affect the dynamic behaviors of the nanocomposite structure.

在本手稿中，将采用广义微分正交方法（GDQM）来解决三相碳纤维/纳米管/聚合物混合纳米复合圆锥壳的自由振动问题，该壳基于两参数弹性介质，对于碳纳米管（CNT）的团聚首次对壳的动态响应产生影响。多尺度杂化纳米复合材料的等效材料性能将根据两步均化程序得出，其中包括Eshelby-Mori-Tanaka方法以及改进后的混合物规则形式。然后，将使用经典的薄壳圆锥壳理论来获得连续系统的应变-位移关系。扩展圆锥壳的哈密顿原理，将丰富该问题的运动方程。最后，关联的边界条件将与GDQ离散化关联使用，以提取连续系统的固有频率。验证测试表明，所提出的数学框架功能强大，足以估算系统的动态响应。这项研究的结果表明，附聚现象的存在可以极大地影响纳米复合结构的动力学行为。验证测试表明，所提出的数学框架功能强大，足以估算系统的动态响应。这项研究的结果表明，附聚现象的存在可以极大地影响纳米复合结构的动力学行为。验证测试表明，所提出的数学框架功能强大，足以估算系统的动态响应。这项研究的结果表明，附聚现象的存在可以极大地影响纳米复合结构的动力学行为。