The numerical investigation is performed on the vibration of the higher order shear deformable carbon nanotube reinforced composite (CNTRC) spherical panels subjected to the initial external pressure. The functionally graded nanocomposite is reinforced with the non-uniform distribution of CNTs. The problem is formulated following the higher order shear deformation shell theory (HSDT) within the variational differential quadrature numerical approach. For this purpose, the direct discretization of Hamilton’s principle is carried out with the aid of differential quadrature operators. Derivation of the variational formulation of nanocomposite spherical panels based on the HSDT and studying the effects of external pressure on the vibration behavior are the main novel aspects of this research. Several numerical examples are provided to survey the impacts of geometrical and material factors on the vibration of pressurized functionally graded CNTRC spherical panels. It is shown that the internal pressure has the most influence on the vibrational behavior of the thicker panel.

中文翻译：

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外压对高阶剪切变形 FG-CNTRC 球板振动分析的影响

对高阶剪切可变形碳纳米管增强复合材料 (CNTRC) 球形面板在初始外部压力下的振动进行了数值研究。碳纳米管的非均匀分布增强了功能梯度纳米复合材料。该问题是根据变分微分正交数值方法中的高阶剪切变形壳理论 (HSDT) 制定的。为此，哈密顿原理的直接离散化是在微分正交算子的帮助下进行的。基于 HSDT 的纳米复合材料球形面板变分公式的推导和研究外部压力对振动行为的影响是本研究的主要创新方面。提供了几个数值例子来调查几何和材料因素对加压功能梯度 CNTRC 球形面板振动的影响。结果表明，内部压力对较厚面板的振动行为影响最大。