Abstract:

A finite element modeling method specially for piezoelectric composite structure was proposed. Based on the classical five DOF structural shell element, using piezoelectric constitute equation and composite plate theory, a new piezoelectric shell finite element was constructed. Compared with the present commercial software, the numbers both of elements and nodes have a significant decrease. Then a smart structure was modeled using this new element. Based on the controllability Gramian matrix, an index to account for the controllability performance was presented. Then constructing a fitness function, and the placement of the piezoelectric patches was optimized using genetic algorithm. Using the optimized placement, the interesting modals of the structure can be controlled effectively with proper actuation. 

Key words: piezoelectric actuator, smart structure, placement optimization, genetic algorithm

摘要：

针对压电复合薄板结构，提出一种新的有限元建模方法。在经典五自由度壳单元基础上，结合压电本构方程，利用多层板分析理论，构建了一种新的压电shell单元。采用该单元建模与采用现有商业软件实体压电单元建模相比，网格数量和自由度都大大降低。利用该单元对压电复合结构进行建模，在系统可观性Gramian 矩阵特征值的基础上，提出一种描述系统可控性能的指标，并以该指标构建适应度函数，利用遗传算法优化压电片的分布。按照优化结果进行布置，通过适当的激励，可以对结构各阶模态进行有效控制。

关键词: 压电作动器, 智能复合结构, 位置优化, 遗传算法