Based on Reddy’s third-order shear deformation theory and mixed formulation, a new numerical approach in the variational framework is developed to analyze the geometrically nonlinear free vibration behavior of cylindrical panels having cutouts with various shapes (e.g., square, circular, elliptical) under arbitrary boundary conditions. It is also assumed that the panel is made of functionally graded graphene platelet-reinforced composite with various patterns for the distribution of GPLs along the thickness direction whose effective properties are estimated using the modified Halpin–Tsai model in conjunction with the rule of mixture. The proposed approach can be named VDQFEM as it utilizes the VDQ and FE methods. Efficient matrix formulation, being free from the locking problem, computational efficiency and being able to solve problems with concave and polygon domains are the main features of VDQFEM. Selected numerical results are given to investigate the influences of geometrical parameters and weight fraction/distribution pattern of GPLs on the large-amplitude vibration response of panels with various cutouts and boundary conditions.

基于Reddy的三阶剪切变形理论和混合公式，在变分框架中开发了一种新的数值方法来分析具有各种形状（如方形、圆形、椭圆形）切口的圆柱板在任意条件下的几何非线性自由振动行为。边界条件。还假设该面板由功能梯度石墨烯片状增强复合材料制成，具有沿厚度方向分布的 GPL 的各种模式，其有效性能是使用改进的 Halpin-Tsai 模型结合混合规则估计的。所提出的方法可以命名为 VDQFEM，因为它利用了 VDQ 和 FE 方法。高效的矩阵公式，没有锁定问题，计算效率和能够解决凹面和多边形域的问题是 VDQFEM 的主要特点。给出了选定的数值结果，以研究几何参数和 GPL 的重量分数/分布模式对具有各种切口和边界条件的面板的大振幅振动响应的影响。