A finite-element model is presented based on the four-variable shear deformation refined theory for active vibration control of a functionally graded carbon nanotube-reinforced composite spherical panel with integrated piezoelectric layers, acting as an actuator and a sensor. The linear distribution of the electric potential across the thickness of the piezoelectric layer and different distribution types of carbon nanotubes through the thickness of the layers are considered. The weak form of the governing equation is derived using Hamilton's principle, and a four-node nonconforming rectangular element with eight mechanical and two electrical degrees of freedom per node is introduced for discretising the domain. A constant velocity feedback approach is utilised for the active control of the panel by closed-loop control with a piezoelectric sensor and actuator. The convergence and accuracy of the model are validated by comparing numerical results with data available in literature. Some new parametric studies are also discussed in detail.

提出了基于四变量剪切变形细化理论的有限元模型，用于主动梯度控制功能梯度的碳纳米管增强复合球形板，该复合球形板具有集成的压电层，分别用作致动器和传感器。考虑跨压电层的厚度的电势的线性分布以及贯穿碳纳米管层的厚度的碳纳米管的不同分布类型。利用汉密尔顿原理推导了控制方程的弱形式，并引入了每个节点具有八个机械自由度和两个电气自由度的四节点非协调矩形单元，以离散化该域。通过使用压电传感器和执行器进行闭环控制，恒定速度反馈方法可用于面板的主动控制。通过将数值结果与文献中提供的数据进行比较，可以验证模型的收敛性和准确性。还详细讨论了一些新的参数研究。