中文摘要：

文章基于三阶剪切变形理论，建立了压电复合材料层合板有限元单元模型，利用Hamilton原理推导了压电层合板结构的动力学方程，通过引入精细积分方法，利用所建立的单元对压电层合板结构进行了振动分析；基于精细积分给出了线性二次最优控制的Riccati方程的求解方法，设计了线性二次最优控制律以抑制压电层合板结构的振动。实例证明，与其它有限元模型进行比较的结果显示所建立的模型具有足够的精度，文中推导的线性二次最优控制Riccati方程的计算方法可行。对板结构的振动控制有效。

英文摘要：

A piezoelectric laminated finite element based on the three-order shear deformation theory is the bending and vibration analysis of piezoelectric laminated structures. The dynamic equations of piezoelectric laminated structure are formulated by invoking the proposed finite element and using Hamilton＇ s principle. The equations are solved via the precise integration method. The algorithm for solving the Riccati equation for the linear quadratic optimal control is presented with the precise integration method, and the hnear quadratic optimal control law is designed to eliminate the vibration. Finally, two numerical examples are given, and the results indicate that the proposed finite element is capable of analyzing the piezoelectric laminated structure with high accuracy, and the presented linear quadratic optimal control is feasible.