In this article, the vibrational behavior of conical panels in the nonlinear regime made of functionally graded graphene platelet–reinforced composite having a hole with various shapes is investigated in the context of higher-order shear deformation theory. To achieve this aim, a numerical approach is used based on the variational differential quadrature and finite element methods. The geometrical nonlinearity is captured using the von Karman hypothesis. Also, the modified Halpin–Tsai model and rule of mixture are applied to calculate the material properties of graphene platelet–reinforced composite for various functionally graded distribution patterns of graphene platelets. The governing equations are derived by a variational approach and represented in matrix-vector form for the computational purposes. Moreover, attributable to using higher-order shear deformation theory, a mixed formulation approach is presented to consider the continuity of first-order derivatives on the common boundaries of elements. In the numerical results, the nonlinear free vibration behaviors of functionally graded graphene platelet–reinforced composite conical panels including square/circular/elliptical hole and with crack are studied. The effects of boundary conditions, graphene platelet reinforcement, and other important parameters on the vibrational response of panels are comprehensively analyzed.

在本文中，在高阶剪切变形理论的背景下，研究了由具有各种形状的孔的功能梯度石墨烯薄片增强复合材料制成的锥形面板在非线性区域的振动行为。为了实现这一目标，使用了基于变分微分正交和有限元方法的数值方法。使用 von Karman 假设捕获几何非线性。此外，应用改进的 Halpin-Tsai 模型和混合规则来计算石墨烯片层增强复合材料的材料特性，适用于石墨烯片层的各种功能梯度分布模式。控制方程通过变分方法导出并以矩阵向量形式表示以用于计算目的。而且，由于使用了高阶剪切变形理论，提出了一种混合公式方法来考虑单元公共边界上一阶导数的连续性。在数值结果中，研究了功能梯度石墨烯薄片增强复合锥形板的非线性自由振动行为，包括方形/圆形/椭圆形孔和裂纹。综合分析了边界条件、石墨烯薄片增强等重要参数对面板振动响应的影响。研究了包括方形/圆形/椭圆形孔和裂纹的功能梯度石墨烯薄片增强复合锥形面板的非线性自由振动行为。综合分析了边界条件、石墨烯薄片增强等重要参数对面板振动响应的影响。研究了包括方形/圆形/椭圆形孔和裂纹的功能梯度石墨烯薄片增强复合锥形面板的非线性自由振动行为。综合分析了边界条件、石墨烯薄片增强等重要参数对面板振动响应的影响。