A comprehensive understanding of the dynamic instability of shell structure is critical to avoid resonance damage. On the basis of that, an accurate and analytical method for investigation the dynamic instability of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) conical shell surrounded by the elastic foundations is presented in this work based on the first-order shear deformation theory. In the analysis, uniform or functionally graded distributions of reinforcements across the shell thickness are considered and the extended Voigt model is employed to estimate the CNTRC material properties. The governing equations of conical shell subjected to parametric excitation are established by the Hamilton's principle considering first order shear deformation shell theory. Then the Mathieu-Hill equations describing the parametric stability of conical shell are obtained by generalized differential quadrature (GDQ) method, and the Bolotin's method is utilized to obtain the first-order approximations of principal instability regions of shell structure. By comparing the numerical results with the existing solutions in open literature, the validity of the proposed theoretical model is verified. Finally, the influences of volume fractions and types of CNTs, lamination angle, elastic foundations stiffness and lamination angle on the dynamic stability of laminated FG-CNTRC conical shell have been investigated.

全面了解壳结构的动态不稳定性对于避免共振损坏至关重要。在此基础上，基于一阶剪切变形理论，提出了一种精确的分析方法，用于研究被弹性地基包围的功能梯度碳纳米管增强复合材料（FG-CNTRC）锥形壳的动态不稳定性。 。在分析中，考虑了整个壳厚度上钢筋的均匀分布或功能梯度分布，并采用扩展的Voigt模型来估算CNTRC材料性能。根据汉密尔顿原理，考虑一阶剪切变形壳理论，建立了受参数激励的圆锥壳控制方程。然后通过广义微分求积法（GDQ）得到描述圆锥形壳体参数稳定性的Mathieu-Hill方程，并利用Bolotin法获得壳体结构主要失稳区域的一阶近似值。通过将数值结果与公开文献中的现有解决方案进行比较，验证了所提出理论模型的有效性。最后，研究了碳纳米管的体积分数和类型，层压角，弹性基础刚度和层压角对层压FG-CNTRC圆锥壳动力稳定性的影响。s方法用于获得壳结构主要不稳定性区域的一阶近似值。通过将数值结果与公开文献中的现有解决方案进行比较，验证了所提出理论模型的有效性。最后，研究了碳纳米管的体积分数和类型，层压角，弹性基础刚度和层压角对层压FG-CNTRC圆锥壳动力稳定性的影响。s方法用于获得壳结构主要不稳定性区域的一阶近似值。通过将数值结果与公开文献中的现有解决方案进行比较，验证了所提出理论模型的有效性。最后，研究了碳纳米管的体积分数和类型，层压角，弹性基础刚度和层压角对层压FG-CNTRC圆锥壳动力稳定性的影响。